introduction to subatomic physics "revolution in the science can be done only by excellent,...

Introduction to Subatomic PhysicsRevolution in the science can be done only by excellent perfectly simple theory and on the base of very carefully performed and unambiguously interpreted experimental measurement

Vladimiacuter Wagner

Nuclear Physics Institute of ASCR Řež E_mailWAGNERUJFCASCZ WWW httphpujfcascz~wagner

9) Basic properties of nucleus and nuclear forces 10) Models of atomic nuclei11) Radioactivity 12) Basic properties of nuclear reactions

1) WSC Williams Nuclear and Particle Physics Oxford Science Publications 20012) Ashok Das Thomas Ferbel Introduction to Nuclear and Particle Physics John Wiley amp Sons 1994 3) B Povh K Rith Ch Scholz F Zetsche Particles and Nuclei An Introduction to the Physical Concepts Springer 20044) A Beiser Concepts of Modern Physics McGraw-Hill Companies Date Published 19955) Glen F Knoll Radiation Detection and Measurement John Wiley amp Sons Inc 2000

Recommended textbooks

1) Three levels of submicroscopic domain2) Tools for microscopic domain description3) Relativistic properties4) Quantum properties5) Measurement in submicroscopic domain6) Structure of matter 7) Collision kinematics 8) Cross section quantity

Three size levels of submicroscopic domain studiesVariety of our ordinary surroundings (macroscopic world) is consisted of atoms and molecules originating in chemical bonding of atoms

Description of the submicroscopic domain

Atomic physics ndash physics of an electron cloud of an atom chemical bonding of atoms to molecules only electromagnetic interaction

Nuclear physics ndash physics of atomic nuclei and interactions inside interaction of a nucleus and electron shells interaction of nucleus and elementary particles physics of nuclear matter strong weak and electromagnetic interactions

Subnuclear physics (elementary particle physics or also high energy physics) ndash physics of elementary particles and interactions - strong weak and electromagnetic

Scale Size Energy 1) Interaction Momentum 2)

[m] [MeV] [MeVc] Atomic ~10-10 ~ 000001 elmg (molecul) 0002Nuclear ~10-14 ~ 8 strong (nuclear) 20Subnuclear ~10-15 ~ 200 strong 200

1) Bonding energy of an electron in a atom or energy of molecular bonding nucleon bonding energy energy needed for elementary particles creation (comparable with their rest energies ndash masses)

2) Calculated using characteristics size and Heisenberg uncertainty principle ΔpmiddotΔx ~ ħ

Scale in Scale in

Atom

Nucleus

Proton

Quark Electron

Characteristic rest masses

matom mnucleus = 938 260 000 MeVc2

(mp = 1836 me mp = 93827 MeVc2 = 167262middot10-27kg) mparticles = 0511 MeVc2 (electron) 91 187 MeVc2 (Z0 boson)

Characteristic times 1c=33middot10-9 s m transit through nucleus ~ 4middot10-23 s interactions ndash strong ~ 10-23 s weak ~ 10-10 - 10-6 s and electromagnetic ~ 10-16 - 10-6 s

Science is searching for a objective description of our world

Uniformity of Universe description on whole time and space scale enables the possibility of extrapolation on the base of present state rarr past or future state are predicted

19th and 20th centuries - new tools for description (applied within the range of extreme values of physical quantities)

Microscopic domain - special theory of relativity - high velocities transferred energies - quantum physics ndash very small values of masses particle distances transferred action

Megaworld - special theory of relativity ndash high velocities transferred energies - general theory of relativity ndash very big intensities of the gravitation field

Tools for microscopic domain studies

Dependence of special theory of relativity manifestation on velocity

Special theory of relativity Quantum physics

Show itself during processes with action transfer in the range Differences between classical Newtonian mechanics

and Einsteinacutes special theory of relativity (Galileo and Lorentz transformations) are significant only for velocities v of the body against reference frame near to the velocity of the light c (3middot108 ms)

Comparison of de Broglie wave length λ for objects with different mass m (me ndash electron mass mj nucleus mass rj ndash nucleus radius)

Influence of measurement alone on the measured objectFundamental uncertainty of measurement

px ħ Et ħMotion of relativistic particles in the accelerator

h = 6626middot10-34 Js = 414middot10-21 MeV s

Stochastic character

Relativistic propertiesRelation between whole energy and mass E = mc2

For rest energy of system in the rest E0 = m0c2 For kinetic energy then EKIN = E-E0 = mc2 - m0c2

For relativistic systems possibility to determine of energy changes by measurement of mass change and vice versa

Nonrelativistic objects (EKIN m0c2) changes of mass are not measurable

(further p and v are magnitudes of momentum and particle velocity)

Relation between energy E and momentum p and kinetic energy EKIN=f(p)

E2 = p2c2 + (m0c2)2 EKIN = (p2c2 + (m0c2)2) - m0c2

Nonrelativistic aproximation (p m0c) ndash correspondence principle

(for square root were take first members of binomial development ndash it is valid (1x)n 1nx pro x1)

It is valid for velocity v v = pc2E pc2EKIN for p m0c or m0 = 0 v = c

Invariant quantity m0c2 = (E2 - p2c2)

EKIN = m0c2 (p2(m0c)2 +1) - m0c2 p22m0 = (m0v2)2

Ultrarelativistic approximation (p m0c) EKIN E pc

Quantum propertiesThe smaller masses and distances of particles ndash the more intensive manifestation of quantum properties

Quantitative limits for transformation of classical mechanics to the quantum one is given by Heisenberg uncertainty principle ΔpΔx geћ Correspondence principle is valid - for ΔpΔx gtgt ћ occurs transformation of quantum mechanics to the classical mechanics

Exhibition of both wave and particle properties

Discrete character of energy spectrum and other quantities for quantum objects (spectra of atoms nuclei particles their spins hellip)

Quantum physics is on principle statistic theory This is difference from the classical statistic theory which assumes principal possibility to describe trajectory of every particle (the big number of particles is problem in reality)

It is done only probability distribution of times of unstable nuclei or particles decay

Objects act as particles as well as waves

Classical theory Quantum theory

Particle state is described by six numbers x y z px py pz in given time

Particle state is fully described by complex function (xyz) given in whole space

Time development of state is described by Hamilton equations drdt = partHpartp dpdt = - partHpartrwhere H is Hamilton function

Time development of state is described by Schroumldinger equation iħpartΨpartt = ĤΨwhere Ĥ is Hamilton operator

Quantities x and p describing state are directly measurable

Function is not directly measurable quantity

Classical mechanics is dynamical theory Quantum mechanics has stochastic character Value of |(r)|2 gives probability of particle presence in the point r Physical quantities are their mean values

1) Description of state of the physical system in the given time2) The equations of motion describing changes of this state with the time3) Relations between quantities describing system state and measured physical quantities

Quantum mechanics (as well as classical) must include

Measurements in the microscopic domain

Relation between accuracy of mean value determination of stochastic quantity on number of measurement N (assumption of independent

measurement ndash Gaussian distribution)

Man is macroscopic object ndash all information about microscopic domain are mediated

The smaller studied object rarr the smaller wave length of studying radiation rarr the higher E and p of quanta (particles) of this radiation High values of E and p rarr affection even destruction of studied object ndash decay and creation of new particles

Relation between wave length and kinetic energy EKIN for different particles (rA ndash size of atom rj ndash radius of nucleus rL ndash present size limit)

Stochastic character of quantum processes in the microscopic domain rarr statistical character of measurements

Main method of study ndash bombardment of different targets by different particles and detection of produced particles at macroscopic distances from collision place by macroscopic detection systems

Important are quantities describing collision (cross sections transferred momentums angular distributions hellip)

Interaction ndash term describing possibility of energy and momentum exchange or possibility of creation and anihilation of particles The known interactions 1) Gravitation 2) Electromagnetic 3) Strong 4) Weak

Description by field ndash scalar or vector variable which is function of space-time coordinates it describes behavior and properties of particles and forces acting between them

Quantum character of interaction ndash energy and momentum transfer through v discrete quanta

Exchange character of interactions ndash caused by particle exchange

Real particle ndash particle for which it is valid 22420 cpcmE

Virtual particle ndash temporarily existed particle it is not valid relation (they exist thanks Heisenberg uncertainty principle) 2242

0 cpcmE

Interactions and their character

Structure of matter

Standard model of matter and interactions

Hadrons ndash baryons (proton neutron hellip) - mesons (π η ρ hellip)

Composed from quarks strong interaction

Bosons - integral spinFermions - half integral spin

Four known interactions

Leveling of coupling constants for high transferred momentum (high energies)

Exchange character of interactions

Interaction intensity given by interaction coupling constant ndash its magnitude changes with increasing of transfer momentum (energy) Variously for different interactions rarr equalizing of coupling constant for high transferred momenta (energies)

Interaction intermediate boson interaction constant range

Gravitation graviton 2middot10-39 infinite

Weak W+ W- Z0 7middot10-14 ) 10-18 m

Electromagnetic γ 7middot10-3 infinite

Strong 8 gluons 1 10-15 m

) Effective value given by large masses of W+ W- a Z0 bosons

Mediate particle ndash intermedial bosons

Range of interaction depends on mediate particle massMagnitude of coupling constant on their properties (also mass)

Example of graphical representation of exchange interaction nature during inelastic electron scattering on proton with charm creation using Feynman diagram

Inte

ract

ion

inte

nsi

ty α

Energy E [GeV]

strong SU(3)

unifiedSU(5)

electromagnetic U(1)

weak SU(2)

Introduction to collision kinematicStudy of collisions and decays of nuclei and elementary particles ndash main method of microscopic properties investigation

Elastic scattering ndash intrinsic state of motion of participated particles is not changed during scattering particles are not excited or deexcited and their rest masses are not changed

Inelastic scattering ndash intrinsic state of motion of particles changes (are excited) but particle transmutation is missing

Deep inelastic scattering ndash very strong particle excitation happens big transformation of the kinetic energy to excitation one

Nuclear reactions (reactions of elementary particles) ndash nuclear transmutation induced by external action Change of structure of participated nuclei (particles) and also change of state of motion Nuclear reactions are also scatterings Nuclear reactions are possible to divide according to different criteria

According to history ( fission nuclear reactions fusion reactions nuclear transfer reactions hellip)

According to collision participants (photonuclear reactions heavy ion reactions proton induced reactions neutron production reactions hellip)

According to reaction energy (exothermic endothermic reactions)

According to energy of impinging particles (low energy high energy relativistic collision ultrarelativistic hellip)

Set of masses energies and moments of objects participating in the reaction or decay is named as process kinematics Not all kinematics quantities are independent Relations are determined by conservation laws Energy conservation law and momentum conservation law are the most important for kinematics

Transformation between different coordinate systems and quantities which are conserved during transformation (invariant variables) are important for kinematics quantities determination

Nuclear decay (radioactivity) ndash spontaneous (not always ndash induced decay) nuclear transmutation connected with particle production

Elementary particle decay - the same for elementary particles

Rutherford scattering

Target thin foil from heavy nuclei (for example gold)

Beam collimated low energy α particles with velocity v = v0 ltlt c after scattering v = vα ltlt c

The interaction character and object structure are not introduced

tt0 vmvmvm

Momentum conservation law (11)

and so hellip (11a)

square hellip (11b)

2

t

2

tt

t220 v

m

mvv

m

m2vv

Energy conservation law (12a)2tt

220 vm

2

1vm

2

1vm

2

1 and so (12b)

2t

t220 v

m

mvv

Using comparison of equations (11b) and (12b) we obtain helliphelliphelliphellip (13) tt2

t vv2m

m1v

For scalar product of two vectors it holds so that we obtaincosbaba

tt

0 vm

mvv

If mtltltmα

Left side of equation (13) is positive rarr from right side results that target and α particle are moving to the original direction after scattering rarr only small deviation of α particle

If mtgtgtmα

Left side of equation (13) is negative rarr large angle between α particle and reflected target nucleus results from right side rarr large scattering angle of α particle

Concrete example of scattering on gold atommα 37middot103 MeVc2 me 051 MeVc2 a mAu 18middot105 MeVc2

1) If mt =me then mtmα 14middot10-4

We obtain from equation (13) ve = vt = 2vαcos le 2vα

We obtain from equation (12b) vα v0

Then for magnitude of momentum it holds meve = m(mem) ve le mmiddot14middot10-4middot2vα 28middot10-4mv0

Maximal momentum transferred to the electron is le 28middot10-4 of original momentum and momentum of α particle decreases only for adequate (so negligible) part of momentum

cosvv2vv2m

m1v tt

t2t

Reminder of equation (13)

2t

t220 v

m

mvv

Reminder of equation (12b)

Maximal angular deflection α of α particle arise if whole change of electron and α momenta are to the vertical direction Then (α 0)

α rad tan α = mevemv0 le 28middot10-4 α le 0016o

2) If mt =mAu then mAumα 49

We obtain from equation (13) vAu = vt = 2(mαmt)vα cos 2(mαvα)mt

We introduce this maximal possible velocity vt in (12b) and we obtain vα v0

Then for momentum is valid mAuvAu le 2mvα 2mv0

Maximal momentum transferred on Au nucleus is double of original momentum and α particle can be backscattered with original magnitude of momentum (velocity)

Maximal angular deflection α of α particle will be up to 180o

Full agreement with Rutherford experiment and atomic model

1) weakly scattered - scattering on electrons2) scattered to large angles ndash scattering on massive nucleus

Attention remember we assumed that objects are point like and we didnt involve force character


2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because

Inclusion of force character ndash central repulsive electric field

20

A r

Q

4

1)RE(r

Thomson model ndash positive charged cloud with radius of atom RA

Electric field intensity outside

Electric field intensity inside3A0

A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e

The strongest field is on cloud surface and force acting on particle (Q = 2e) is

This force decreases quickly with distance and it acts along trajectory L 2RA t = L v0 2RA v0 Resulting change of particle

momentum = given transversal impulse

0A0MAX vR4

eQ4tFp

Maximal angle is 20A0 vmR4

eQ4pptan

Substituting RA 10-10m v0 107 ms Q = 79e (Thomson model)rad tan 27middot10-4 rarr 0015o only very small angles

Estimation for Rutherford model

Substituting RA = RJ 10-14m (only quantitative estimation)tan 27 rarr 70o also very large scattering angles

Thomson atomic model

Electrons

Positive charged cloud

Electrons

Positive charged nucleus

Rutherford atomic model

Possibility of achievement of large deflections by multiple scattering

Foil at experiment has 104 atomic layers Let assume

1) Thomson model (scattering on electrons or on positive charged cloud)2) One scattering on every atomic layer3) Mean value of one deflection magnitude 001o Either on electron or on positive charged nucleus

Mean value of whole magnitude of deflection after N scatterings is (deflections are to all directions therefore we must use squares)

N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)

We deduce equation (1) Scattering takes place in space but for simplicity we will show problem using two dimensional case

Multiple particle scattering

Deflections i are distributed both in positive and negative

directions statistically around Gaussian normal distribution for studied case So that mean value of particle deflection from original direction is equal zero

0N

1ii

N

1ii

the same type of scattering on each atomic layer i22 i

2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii

Then we can derive given relation (1)

ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii

Because it is valid for two inter-independent random quantities a and b with Gaussian distribution

And already showed relation is valid N

We substitute N by mentioned 104 and mean value of one deflection = 001o Mean value of deflection magnitude after multiple scattering in Geiger and Marsden experiment is around 1o This value is near to the real measured experimental value

Certain very small ratio of particles was deflected more then 90o during experiment (one particle from every 8000 particles) We determine probability P() that deflection larger then originates from multiple scattering

If all deflections will be in the same direction and will have mean value final angle will be ~100o (we accent assumption each scattering has deflection value equal to the mean value) Probability of this is P = (12)N =(12)10000 = 10-3010 Proper calculation will give

2 eP We substitute 350081002

190 1090 eePooo

Clear contradiction with experiment ndash Thomson model must be rejected

Derivation of Rutherford equation for scattering

Assumptions1) particle and atomic nucleus are point like masses and charges2) Particle and nucleus experience only electric repulsion force ndash dynamics is included3) Nucleus is very massive comparable to the particle and it is not moving

Acting force Charged particle with the charge Ze produces a Coulomb potential r

Ze

4

1rU

0

Two charged particles with the charges Ze and Zlsquoe and the distance rr

experience a Coulomb force giving rice to a potential energy r

eZZ

4

1rV

2

0

Coulomb force is

1) Conservative force ndash force is gradient of potential energy rVrF

2) Central force rVrVrV

Magnitude of Coulomb force is and force acts in the direction of particle join 2

2

0 r

eZZ

4

1rF

Electrostatic force is thus proportional to 1r2 trajectory of particle is a hyperbola with nucleus in its external focus

We define

Impact parameter b ndash minimal distance on which particle comes near to the nucleus in the case without force acting

Scattering angle - angle between asymptotic directions of particle arrival and departure

Geometry of Rutheford scattering

Momenta in Rutheford scattering

First we find relation between b and

Nucleus gives to the particle impulse particle momentum changes from original value p0 to final value p

dtF

dtFppp 0

helliphelliphelliphellip (1)

Using assumption about target fixation we obtain that kinetic energy and magnitude of particle momentum before during and after scattering are the same

p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF

Because impulse is in the same direction as the change of momentum it is valid

where is running angle between and along particle trajectory F

p

helliphelliphellip (2)

helliphelliphelliphelliphellip (3)

We substitute (2) and (3) to (1) dtcosF2

sinvm20

0

helliphelliphelliphelliphelliphellip(4)

We change integration variable from t to

d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)

where ddt is angular velocity of particle motion around nucleus Electrostatic action of nucleus on particle is in direction of the join vector force momentum do not act angular momentum is not changing (its original value is mv0b) and it is connected with angular velocity = ddt mr2 = const = mr2 (ddt) = mv0b

0Fr

then bv

r

d

dt

0

2

we substitute dtd at (5)

21

21

220 cosFr

2sinbvm2 d hellip (6)

2

2

0 r

2Ze

4

1F

We substitute electrostatic force F (Z=2)

We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d

We substitute to the relation (6)

2cos

Ze

2sinbvm2

0

220

Scattering angle is connected with collision parameter b by relation

bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)

The smaller impact parameter b the larger scattering angle

Energy and momentum conservation law Just these conservation laws are very important They determine relations between kinematic quantities It is valid for isolated system

Conservation law of whole energy

Conservation law of whole momentum

if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM

Nonrelativistic approximation (m0c2 gtgt EKIN) EKIN = p2(2m0)

2i0

2f0 cMcM i

0f0 MM

Together it is valid for elastic scattering iKIN

fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p

Ultrarelativistic approximation (m0c2 ltlt EKIN) E asymp EKIN asymp pc

if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp

We obtain for elastic scattering

Using momentum conservation law

sinpsinp0 21 and cospcospp 211

We obtain using cosine theorem cosp2pppp 1121

21

22

Nonrelativistic approximation

Using energy conservation law2

22

1

21

1

21

2m

p

2m

p

2m

p

We can eliminated two variables using these equations The energy of reflected target particle ElsquoKIN

2 and reflection angle ψ are usually not measured We obtain relation between remaining kinematic variables using given equations

0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN

Ultrarelativistic approximation

112

12

12

2211 pp2pppppp Using energy conservation law

We obtain using this relation and momentum conservation law cos 1 and therefore 0

Conception of cross section

1) Base conceptions ndash differential integral cross section total cross section geometric interpretation of cross section

2) Macroscopic cross section mean free path

3) Typical values of cross sections for different processes

Chamber for measurement of cross sections of different astrophysical reactions at NPI of ASCR

Ultrarelativistic heavy ion collisionon RHIC accelerator at Brookhaven

Introduction of cross section

Formerly we obtained relation between Rutherford scattering angle and impact parameter ( particles are scattered)

bZe

E4

2cotg

2KIN0

helliphelliphelliphelliphelliphelliphellip (1)

The smaller impact parameter b the bigger scattering angle

Impact parameter is not directly measurable and new directly measurable quantity must be define We introduce scattering cross section for quantitative description of scattering processes

Derivation of Rutherford relation for scattering

Relation between impact parameter b and scattering angle particle with impact parameter smaller or the same as b (aiming to the area b2) is scattered to a angle larger than value b given by relation (1) for appropriate value of b Then applies

(b) = b2 helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip (2)

(then dimension of is m2 barn = 10-28 m2)

We assume thin foil (cross sections of neighboring nuclei are not overlapping and multiple scattering does not take place) with thickness L with nj atoms in volume unit Beam with number NS of particles are going to the area SS (Number of beam particles per time and area units ndash luminosity ndash is for present accelerators up to 1038 m-2s-1)

2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS

Fraction f(b) of incident particles scattered to angle larger then b is

We substitute of b from equation (1)

2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb

Sketch of the Rutherford experiment Angular distribution of scattered particles

The number of target nuclei on which particles are impinging is Nj = njLSS Sum of cross sections for scattering to angle b and more is

(b) = njLSS


bZe

E4

2cotg

2KIN0

Reminder of equation (2)(b) = b2


We can write for detector area in distance r from the target

d2

cos2

sinr4dsinr2)rd)(sinr2(dS 22

d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S

Number N() of particles going to the detector per area unit is

2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S

Such relation is known as Rutherford equation for scattering

d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j

During real experiment detector measures particles scattered to angles from up to +d Fraction of incident particles scattered to such angular range is

Reminder of pictures

2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)

Different types of differential cross sections

angular )(d

d

)(d

d spectral )E(

dE

d spectral angular )E(dEd

d

double or triple differential cross section

Integral cross sections through energy angle

Values of cross section

Very strong dependence of cross sections on energy of beam particles and interaction character Values are within very broad range 10-47 m2 divide 10-24 m2 rarr 10-19 barn divide 104 barn

Strong interaction (interaction of nucleons and other hadrons) 10-30 m2 divide 10-24 m2 rarr 001 barn divide 104 barn

Electromagnetic interaction (reaction of charged leptons or photons) 10-35 m2 divide 10-30 m2 rarr 01 μbarn divide 10 mbarn

Weak interaction (neutrino reactions) 10-47 m2 = 10-19 barn

Cross section of different neutron reactions with gold nucleus

Macroscopic quantities

Particle passage through matter interacted particles disappear from beam (N0 ndash number of incident particles)

dxnN

dNj

x

0

j

N

N

dxnN

dN

0

ln N ndash ln N0 = ndash njσx xn0

jeNN

Number of touched particles N decrease exponential with thickness x

Number of interacting particles )e(1NNN xn00

j

For xrarr0 xn1e jxn j

N0 ndash N N0 ndash N0(1-njx) N0njx

and then xnN

NN

N

dNj

0

0

Absorption coefficient = nj

Mean free path l = is mean distance which particle travels in a matter before interaction

jn

1l

Quantum physics all measured macroscopic quantities l are mean values (l is statistical quantity also in classical physics)

Phenomenological properties of nuclei

1) Introduction - nucleon structure of nucleus

2) Sizes of nuclei

3) Masses and bounding energies of nuclei

4) Energy states of nuclei

5) Spins

6) Magnetic and electric moments

7) Stability and instability of nuclei

8) Nature of nuclear forces

Introduction ndash nucleon structure of nuclei Atomic nucleus consists of nucleons (protons and neutrons)

Number of protons (atomic number) ndash Z Total number nucleons (nucleon number) ndash A

Number of neutrons ndash N = A-Z NAZ Pr

Different nuclei with the same number of protons ndash isotopes

Different nuclei with the same number of neutrons ndash isotones

Different nuclei with the same number of nucleons ndash isobars

Different nuclei ndash nuclidesNuclei with N1 = Z2 and N2 = Z1 ndash mirror nuclei

Neutral atoms have the same number of electrons inside atomic electron shell as protons inside nucleusProton number gives also charge of nucleus Qj = Zmiddote

(Direct confirmation of charge value in scattering experiments ndash from Rutherford equation for scattering (dσdΩ) = f(Z2))

Atomic nucleus can be relatively stable in ground state or in excited state to higher energy ndash isomers (τ gt 10-9s)

2300155A198

AZ

Stable nuclei have A and Z which fulfill approximately empirical equation

Reliably known nuclei are up to Z=112 in present time (discovery of nuclei with Z=114 116 (Dubna) needs confirmation)Nuclei up to Z=83 (Bi) have at least one stable isotope Po (Z=84) has not stable isotope Th U a Pu have T12 comparable with age of Earth

Maximal number of stable isotopes is for Sn (Z=50) - 10 (A =112 114 115 116 117 118 119 120 122 124)

Total number of known isotopes of one element is till 38 Number of known nuclides gt 2800

Sizes of nucleiDistribution of mass or charge in nucleus are determined

We use mainly scattering of charged or neutral particles on nuclei

Density ρ of matter and charge is constant inside nucleus and we observe fast density decrease on the nucleus boundary The density distribution can be described very well for spherical nuclei by relation (Woods-Saxon)

where α is diffusion coefficient Nucleus radius R is distance from the center where density is half of maximal value Approximate relation R = f(A) can be derived from measurements R = r0A13

where we obtained from measurement r0 = 12(1) 10-15 m = 12(2) fm (α = 18 fm-1) This shows on

permanency of nuclear density Using Avogardo constant

or using proton mass 315

27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3

High energy electron scattering (charge distribution) smaller r0Neutron scattering (mass distribution) larger r0

Distribution of mass density connected with charge ρ = f(r) measured by electron scattering with energy 1 GeV

Larger volume of neutron matter is done by larger number of neutrons at nuclei (in the other case the volume of protons should be larger because Coulomb repulsion)

)Rr(0

e1)r(

Deformed nuclei ndash all nuclei are not spherical together with smaller values of deformation of some nuclei in ground state the superdeformation (21 31) was observed for highly excited states They are determined by measurements of electric quadruple moments and electromagnetic transitions between excited states of nuclei

Neutron and proton halo ndash light nuclei with relatively large excess of neutrons or protons rarr weakly bounded neutrons and protons form halo around central part of nucleus

Experimental determination of nuclei sizes

1) Scattering of different particles on nuclei Sufficient energy of incident particles is necessary for studies of sizes r = 10-15m De Broglie wave length λ = hp lt r

Neutrons mnc2 gtgt EKIN rarr rarr EKIN gt 20 MeVKIN2mEh

Electrons mec2 ltlt EKIN rarr λ = hcEKIN rarr EKIN gt 200 MeV

2) Measurement of roentgen spectra of mion atoms They have mions in place of electrons (mμ = 207 me) μe ndash interact with nucleus only by electromagnetic interaction Mions are ~200 nearer to nucleus rarr bdquofeelldquo size of nucleus (K-shell radius is for mion at Pb 3 fm ~ size of nucleus)

3) Isotopic shift of spectral lines The splitting of spectral lines is observed in hyperfine structure of spectra of atoms with different isotopes ndash depends on charge distribution ndash nuclear radius

4) Study of α decay The nuclear radius can be determined using relation between probability of α particle production and its kinetic energy

Masses of nuclei

Nucleus has Z protons and N=A-Z neutrons Naive conception of nuclear masses

M(AZ) = Zmp+(A-Z)mn

where mp is proton mass (mp 93827 MeVc2) and mn is neutron mass (mn 93956 MeVc2)

where MeVc2 = 178210-30 kg we use also mass unit mu = u = 93149 MeVc2 = 166010-27 kg Then mass of nucleus is given by relative atomic mass Ar=M(AZ)mu

Real masses are smaller ndash nucleus is stable against decay because of energy conservation law Mass defect ΔM ΔM(AZ) = M(AZ) - Zmp + (A-Z)mn

It is equivalent to energy released by connection of single nucleons to nucleus - binding energy B(AZ) = - ΔM(AZ) c2

Binding energy per one nucleon BA

Maximal is for nucleus 56Fe (Z=26 BA=879 MeV)

Possible energy sources

1) Fusion of light nuclei2) Fission of heavy nuclei

879 MeVnucleon 14middot10-13 J166middot10-27 kg = 87middot1013 Jkg

(gasoline burning 47middot107 Jkg) Binding energy per one nucleon for stable nuclei

Measurement of masses and binding energies

Mass spectroscopy

Mass spectrographs and spectrometers use particle motion in electric and magnetic fields

Mass m=p22EKIN can be determined by comparison of momentum and kinetic energy We use passage of ions with charge Q through ldquoenergy filterrdquo and ldquomomentum filterrdquo which are realized using electric and magnetic fields

EQFE

and then F = QE BvQFB

for is FB = QvBvB

The study of Audi and Wapstra from 1993 (systematic review of nuclear masses) names 2650 different isotopes Mass is determined for 1825 of them

Frequency of revolution in magnetic field of ion storage ring is used Momenta are equilibrated by electron cooling rarr for different masses rarr different velocity and frequency

Electron cooling of storage ring ESR at GSI Darmstadt

Comparison of frequencies (masses) of ground and isomer states of 52Mn Measured at GSI Darmstadt

Excited energy statesNucleus can be both in ground state and in state with higher energy ndash excited state

Every excited state ndash corresponding energyrarr energy level

Energy level structure of 66Cu nucleus (measured at GANIL ndash France experiment E243)

Deexcitation of excited nucleus from higher level to lower one by photon irradiation (gamma ray) or direct transfer of energy to electron from electron cloud of atom ndash irradiation of conversion electron Nucleus is not changed Or by decay (particle emission) Nucleus is changed

Scheme of energy levels

Quantum physics rarr discrete values of possible energies

Three types of nuclear excited states

1) Particle ndash nucleons at excited state EPART

2) Vibrational ndash vibration of nuclei EVIB

3) Rotational ndash rotation of deformed nuclei EROT (quantum spherical object can not have rotational energy)

it is valid EPART gtgt EVIB gtgt EROT

Spins of nucleiProtons and neutrons have spin 12 Vector sum of spins and orbital angular momenta is total angular momentum of nucleus I which is named as spin of nucleus

Orbital angular momenta of nucleons have integral values rarr nuclei with even A ndash integral spin nuclei with odd A ndash half-integral spin

Classically angular momentum is define as At quantum physic by appropriate operator which fulfill commutating relations

prl

lˆ

ilˆ

lˆ

There are valid such rules

2) From commutation relations it results that vector components can not be observed individually Simultaneously and only one component ndash for example Iz can be observed 2I

3) Components (spin projections) can take values Iz = Iħ (I-1)ħ (I-2)ħ hellip -(I-1)ħ -Iħ together 2I+1 values

4) Angular momentum is given by number I = max(Iz) Spin corresponding to orbital angular momentum of nucleons is only integral I equiv l = 0 1 2 3 4 5 hellip (s p d f g h hellip) intrinsic spin of nucleon is I equiv s = 12

5) Superposition for single nucleon leads to j = l 12 Superposition for system of more particles is diverse Extreme cases

slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where

1) Eigenvalues are where number I = 0 12 1 32 2 52 hellip angular momentum magnitude is |I| = ħ [I(I-1)]12

2I

22 1)I(II

Magnetic and electric momenta

Ig j

Ig j

Magnetic dipole moment μ is connected to existence of spin I and charge Ze It is given by relation

where g is gyromagnetic ratio and μj is nuclear magneton 114

pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e

For point like particle g = 2 (for electron agreement μe = 10011596 μB) For nucleons μp = 279 μj and μn = -191 μj ndash anomalous magnetic moments show complicated structure of these particles

Magnetic moments of nuclei are only μ = -3 μj 10 μj even-even nuclei μ = I = 0 rarr confirmation of small spins strong pairing and absence of electrons at nuclei

Electric momenta

Electric dipole momentum is connected with charge polarization of system Assumption nuclear charge in the ground state is distributed uniformly rarr electric dipole momentum is zero Agree with experiment

)aZ(c5

2Q 22

Electric quadruple moment Q gives difference of charge distribution from spherical Assumption Nucleus is rotational ellipsoid with uniformly distributed charge Ze(ca are main split axles of ellipsoid) deformation δ = (c-a)R = ΔRR

Results of measurements

1) Most of nuclei have Q = 10-29 10-30 m2 rarr δ le 01

2) In the region A ~ 150 180 and A ge 250 large values are measured Q ~ 10-27 m2 They are larger than nucleus area rarr δ ~ 02 03 rarr deformed nuclei

Stability and instability of nucleiStable nuclei for small A (lt40) is valid Z = N for heavier nuclei N 17 Z This dependence can be express more accurately by empirical relation

2300155A198

AZ

For stable heavy nuclei excess of neutrons rarr charge density and destabilizing influence of Coulomb repulsion is smaller for larger number of neutrons

Even-even nuclei are more stable rarr existence of pairing N Z number of stable nucleieven even 156 even odd 48odd even 50odd odd 5

Magic numbers ndash observed values of N and Z with increased stability

At 1896 H Becquerel observed first sign of instability of nuclei ndash radioactivity Instable nuclei irradiate

Alpha decay rarr nucleus transformation by 4He irradiationBeta decay rarr nucleus transformation by e- e+ irradiation or capture of electron from atomic cloudGamma decay rarr nucleus is not changed only deexcitation by photon or converse electron irradiationSpontaneous fission rarr fission of very heavy nuclei to two nucleiProton emission rarr nucleus transformation by proton emission

Nuclei with livetime in the ns region are studied in present time They are bordered by

proton stability border during leave from stability curve to proton excess (separative energy of proton decreases to 0) and neutron stability border ndash the same for neutrons Energy level width Γ of excited nuclear state and its decay time τ are connected together by relation τΓ asymp h Boundery for decay time Γ lt ΔE (ΔE ndash distance of levels) ΔE~ 1 MeVrarr τ gtgt 6middot10-22s

Nature of nuclear forces

The forces inside nuclei are electromagnetic interaction (Coulomb repulsion) weak (beta decay) but mainly strong nuclear interaction (it bonds nucleus together)

For Coulomb interaction binding energy is B Z (Z-1) BZ Z for large Z non saturated forces with long range

For nuclear force binding energy is BA const ndash done by short range and saturation of nuclear forces Maximal range ~17 fm

Nuclear forces are attractive (bond nucleus together) for very short distances (~04 fm) they are repulsive (nucleus does not collapse) More accurate form of nuclear force potential can be obtained by scattering of nucleons on nucleons or nuclei

Charge independency ndash cross sections of nucleon scattering are not dependent on their electric charge rarr For nuclear forces neutron and proton are two different states of single particle - nucleon New quantity isospin T is define for their description Nucleon has than isospin T = 12 with two possible orientation TZ = +12 (proton) and TZ = -12 (neutron) Formally we work with isospin as with spin

In the case of scattering centrifugal barier given by angular momentum of incident particle acts in addition

Expect strong interaction electric force influences also Nucleus has positive charge and for positive charged particle this force produces Coulomb barrier (range of electric force is larger then this of strong force) Appropriate potential has form V(r) ~ Qr

Spin dependence ndash explains existence of stable deuteron (it exists only at triplet state ndash s = 1 and no at singlet - s = 0) and absence of di-neutron This property is studied by scattering experiments using oriented beams and targets

Tensor character ndash interaction between two nucleons depends on angle between spin directions and direction of join of particles

Models of atomic nuclei

1) Introduction

2) Drop model of nucleus

3) Shell model of nucleus

Octupole vibrations of nucleus(taken from H-J Wolesheima

GSI Darmstadt)

Extreme superdeformed states werepredicted on the base of models

IntroductionNucleus is quantum system of many nucleons interacting mainly by strong nuclear interaction Theory of atomic nuclei must describe

1) Structure of nucleus (distribution and properties of nuclear levels)2) Mechanism of nuclear reactions (dynamical properties of nuclei)

Development of theory of nucleus needs overcome of three main problems

1) We do not know accurate form of forces acting between nucleons at nucleus2) Equations describing motion of nucleons at nucleus are very complicated ndash problem of mathematical description3) Nucleus has at the same time so many nucleons (description of motion of every its particle is not possible) and so little (statistical description as macroscopic continuous matter is not possible)

Real theory of atomic nuclei is missing only models exist Models replace nucleus by model reduced physical system reliable and sufficiently simple description of some properties of nuclei

Phenomenological models ndash mean potential of nucleus is used its parameters are determined from experiment

Microscopic models ndash proceed from nucleon potential (phenomenological or microscopic) and calculate interaction between nucleons at nucleus

Semimicroscopic models ndash interaction between nucleons is separated to two parts mean potential of nucleus and residual nucleon interaction

B) According to how they describe interaction between nucleons

Models of atomic nuclei can be divided

A) According to magnitude of nucleon interaction

Collective models (models with strong coupling) ndash description of properties of nucleus given by collective motion of nucleons

Singleparticle models (models of independent particles) ndash describe properties of nucleus given by individual nucleon motion in potential field created by all nucleons at nucleus

Unified (collective) models ndash collective and singleparticle properties of nuclei together are reflected

Liquid drop model of atomic nucleiLet us analyze of properties similar to liquid Think of nucleus as drop of incompressible liquid bonded together by saturated short range forces

Description of binding energy B = B(AZ)

We sum different contributions B = B1 + B2 + B3 + B4 + B5

1) Volume (condensing) energy released by fixed and saturated nucleon at nuclei B1 = aVA

2) Surface energy nucleons on surface rarr smaller number of partners rarr addition of negative member proportional to surface S = 4πR2 = 4πA23 B2 = -aSA23

3) Coulomb energy repulsive force between protons decreases binding energy Coulomb energy for uniformly charged sphere is E Q2R For nucleus Q2 = Z2e2 a R = r0A13 B3 = -aCZ2A-13

4) Energy of asymmetry neutron excess decreases binding energyA

2)A(Za

A

TaB

2

A

2Z

A4

5) Pair energy binding energy for paired nucleons increases + for even-even nuclei B5 = 0 for nuclei with odd A where aPA-12

- for odd-odd nucleiWe sum single contributions and substitute to relation for mass

M(AZ) = Zmp+(A-Z)mn ndash B(AZ)c2

M(AZ) = Zmp+(A-Z)mnndashaVA+aSA23 + aCZ2A-13 + aA(Z-A2)2A-1plusmnδ

Weizsaumlcker semiempirical mass formula Parameters are fitted using measured masses of nuclei

(aV = 1585 aA = 929 aS = 1834 aP = 115 aC = 071 all in MeVc2)

Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy

Shell model of nucleusAssumption primary interaction of single nucleon with force field created by all nucleons Nucleons are fermions one in every state (filled gradually from the lowest energy)

Experimental evidence

1) Nuclei with value Z or N equal to 2 8 20 28 50 82 126 (magic numbers) are more stable (isotope occurrence number of stable isotopes behavior of separation energy magnitude)2) Nuclei with magic Z and N have zero quadrupol electric moments zero deformation3) The biggest number of stable isotopes is for even-even combination (156) the smallest for odd-odd (5)4) Shell model explains spin of nuclei Even-even nucleus protons and neutrons are paired Spin and orbital angular momenta for pair are zeroed Either proton or neutron is left over in odd nuclei Half-integral spin of this nucleon is summed with integral angular momentum of rest of nucleus half-integral spin of nucleus Proton and neutron are left over at odd-odd nuclei integral spin of nucleus

Shell model

1) All nucleons create potential which we describe by 50 MeV deep square potential well with rounded edges potential of harmonic oscillator or even more realistic Woods-Saxon potential2) We solve Schroumldinger equation for nucleon in this potential well We obtain stationary states characterized by quantum numbers n l ml Group of states with near energies creates shell Transition between shells high energy Transition inside shell law energy3) Coulomb interaction must be included difference between proton and neutron states4) Spin-orbital interaction must be included Weak LS coupling for the lightest nuclei Strong jj coupling for heavy nuclei Spin is oriented same as orbital angular momentum rarr nucleon is attracted to nucleus stronger Strong split of level with orbital angular momentum l

without spin-orbitalcoupling

with spin-orbitalcoupling

Ene

rgy

Numberper level

Numberper shell

Totalnumber

Sequence of energy levels of nucleons given by shell model (not real scale) ndash source A Beiser

Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series

Detection system GAMASPHERE for study rays from gamma decay

IntroductionTransmutation of nuclei accompanied by radiation emissions was observed - radioactivity Discovery of radioactivity was made by H Becquerel (1896)

Three basic types of radioactivity and nuclear decay 1) Alpha decay2) Beta decay3) Gamma decay

and nuclear fission (spontaneous or induced) and further more exotic types of decay

Transmutation of one nucleus to another proceed during decay (nucleus is not changed during gamma decay ndash only energy of excited nucleus is decreased)

Mother nucleus ndash decaying nucleus Daughter nucleus ndash nucleus incurred by decay

Sequence of follow up decays ndash decay series

Decay of nucleus is not dependent on chemical and physical properties of nucleus neighboring (exception is for example gamma decay through conversion electrons which is influenced by chemical binding)

Electrostatic apparatus of P Curie for radioactivity measurement (left) and present complex for measurement of conversion electrons (right)

Radioactivity decay law

Activity (radioactivity) Adt

dNA

where N is number of nuclei at given time in sample [Bq = s-1 Ci =371010Bq]

Constant probability λ of decay of each nucleus per time unit is assumed Number dN of nuclei decayed per time dt

dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0

Both sides are integrated

ln N ndash ln N0 = -λt t0NN e

Then for radioactivity we obtaint

0t

0 eAeNdt

dNA where A0 equiv -λN0

Probability of decay λ is named decay constant Time of decreasing from N to N2 is decay half-life T12 We introduce N = N02 21T

00 N

2

N e

2lnT 21

Mean lifetime τ 1

For t = τ activity decreases to 1e = 036788

Heisenberg uncertainty principle ΔEΔt asymp ħ rarr Γ τ asymp ħ where Γ is decay width of unstable state Γ = ħ τ = ħ λ

Total probability λ for more different alternative possibilities with decay constants λ1λ2λ3 hellip λM

M

1kk

M

1kk

Sequence of decay we have for decay series λ1N1 rarr λ2N2 rarr λ3N3 rarr hellip rarr λiNi rarr hellip rarr λMNM

Time change of Ni for isotope i in series dNidt = λi-1Ni-1 - λiNi

We solve system of differential equations and assume

t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee

For coefficients Cij it is valid i ne j ji

1ij1iij CC

Coefficients with i = j can be obtained from boundary conditions in time t = 0 Ni(0) = Ci1 + Ci2 + Ci3 + hellip + Cii

Special case for τ1 gtgt τ2τ3 hellip τM each following member has the same

number of decays per time unit as first Number of existed nuclei is inversely dependent on its λ rarr decay series is in radioactive equilibrium

Creation of radioactive nuclei with constant velocity ndash irradiation using reactor or accelerator Velocity of radioactive nuclei creation is P

Development of activity during homogenous irradiation

dNdt = - λN + P

Solution of equation (N0 = 0) λN(t) = A(t) = P(1 ndash e-λt)

It is efficient to irradiate number of half-lives but not so long time ndash saturation starts

Alpha decay

HeYX 42

4A2Z

AZ

High value of alpha particle binding energy rarr EKIN sufficient for escape from nucleus rarr

Relation between decay energy and kinetic energy of alpha particles

Decay energy Q = (mi ndash mf ndashmα)c2

Kinetic energies of nuclei after decay (nonrelativistic approximation)EKIN f = (12)mfvf

2 EKIN α = (12) mαvα2

v

m

mv

ff From momentum conservation law mfvf = mαvα rarr ( mf gtgt mα rarr vf ltlt vα)

From energy conservation law EKIN f + EKIN α = Q (12) mαvα2 + (12)mfvf

2 = Q

We modify equation and we introduce

Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff

Kinetic energy of alpha particle QA

4AQ

mm

mE

f

fKIN

Typical value of kinetic energy is 5 MeV For example for 222Rn Q = 5587 MeV and EKIN α= 5486 MeV

Barrier penetration

Particle (ZA) impacts on nucleus (ZA) ndash necessity of potential barrier overcoming

For Coulomb barier is the highest point in the place where nuclear forces start to act R

ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e

Barrier height is VCB asymp 25 MeV for nuclei with A=200

Problem of penetration of α particle from nucleus through potential barrier rarr it is possible only because of quantum physics

Assumptions of theory of α particle penetration

1) Alpha particle can exist at nuclei separately2) Particle is constantly moving and it is bonded at nucleus by potential barrier3) It exists some (relatively very small) probability of barrier penetration

Probability of decay λ per time unit λ = νP

where ν is number of impacts on barrier per time unit and P probability of barrier penetration

We assumed that α particle is oscillating along diameter of nucleus

212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N

Probability P = f(EKINαVCB) Quantum physics is needed for its derivation

bound statequasistationary state

Beta decay

Nuclei emits electrons

1) Continuous distribution of electron energy (discrete was assumed ndash discrete values of energy (masses) difference between mother and daughter nuclei) Maximal EEKIN = (Mi ndash Mf ndash me)c2

2) Angular momentum ndash spins of mother and daughter nuclei differ mostly by 0 or by 1 Spin of electron is but 12 rarr half-integral change

Schematic dependence Ne = f(Ee) at beta decay

rarr postulation of new particle existence ndash neutrino

mn gt mp + mν rarr spontaneous process

epn

neutron decay τ asymp 900 s (strong asymp 10-23 s elmg asymp 10-16 s) rarr decay is made by weak interaction

inverse process proceeds spontaneously only inside nucleus

Process of beta decay ndash creation of electron (positron) or capture of electron from atomic shell accompanied by antineutrino (neutrino) creation inside nucleus Z is changed by one A is not changed

Electron energy

Rel

ativ

e el

ectr

on in

ten

sity

According to mass of atom with charge Z we obtain three cases

1) Mass is larger than mass of atom with charge Z+1 rarr electron decay ndash decay energy is split between electron a antineutrino neutron is transformed to proton

eYY A1Z

AZ

2) Mass is smaller than mass of atom with charge Z+1 but it is larger than mZ+1 ndash 2mec2 rarr electron capture ndash energy is split between neutrino energy and electron binding energy Proton is transformed to neutron YeY A

Z-A

1Z

3) Mass is smaller than mZ+1 ndash 2mec2 rarr positron decay ndash part of decay energy higher than 2mec2 is split between kinetic energies of neutrino and positron Proton changes to neutron

eYY A

ZA

1ZDiscrete lines on continuous spectrum

1) Auger electrons ndash vacancy after electron capture is filled by electron from outer electron shell and obtained energy is realized through Roumlntgen photon Its energy is only a few keV rarr it is very easy absorbed rarr complicated detection

2) Conversion electrons ndash direct transfer of energy of excited nucleus to electron from atom

Beta decay can goes on different levels of daughter nucleus not only on ground but also on excited Excited daughter nucleus then realized energy by gamma decay

Some mother nuclei can decay by two different ways either by electron decay or electron capture to two different nuclei

During studies of beta decay discovery of parity conservation violation in the processes connected with weak interaction was done

Gamma decay

After alpha or beta decay rarr daughter nuclei at excited state rarr emission of gamma quantum rarr gamma decay

Eγ = hν = Ei - Ef

More accurate (inclusion of recoil energy)

Momenta conservation law rarr hνc = Mjv

Energy conservation law rarr 2

j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE

where ΔER is recoil energy

Excited nucleus unloads energy by photon irradiation

Different transition multipolarities Electric EJ rarr spin I = min J parity π = (-1)I

Magnetic MJ rarr spin I = min J parity π = (-1)I+1

Multipole expansion and simple selective rules

Energy of emitted gamma quantum

Transition between levels with spins Ii and If and parities πi and πf

I = |Ii ndash If| pro Ii ne If I = 1 for Ii = If gt 0 π = (-1)I+K = πiπf K=0 for E and K=1 pro MElectromagnetic transition with photon emission between states Ii = 0 and If = 0 does not exist

Mean lifetimes of levels are mostly very short ( lt 10-7s ndash electromagnetic interaction is much stronger than weak) rarr life time of previous beta or alpha decays are longer rarr time behavior of gamma decay reproduces time behavior of previous decay

They exist longer and even very long life times of excited levels - isomer states

Probability (intensity) of transition between energy levels depends on spins and parities of initial and end states Usually transitions for which change of spin is smaller are more intensive

System of excited states transitions between them and their characteristics are shown by decay schema

Example of part of gamma ray spectra from source 169Yb rarr 169Tm

Decay schema of 169Yb rarr 169Tm

Internal conversion

Direct transfer of energy of excited nucleus to electron from atomic electron shell (Coulomb interaction between nucleus and electrons) Energy of emitted electron Ee = Eγ ndash Be

where Eγ is excitation energy of nucleus Be is binding energy of electron

Alternative process to gamma emission Total transition probability λ is λ = λγ + λe

The conversion coefficients α are introduced It is valid dNedt = λeN and dNγdt = λγNand then NeNγ = λeλγ and λ = λγ (1 + α) where α = NeNγ

We label αK αL αM αN hellip conversion coefficients of corresponding electron shell K L M N hellip α = αK + αL + αM + αN + hellip

The conversion coefficients decrease with Eγ and increase with Z of nucleus

Transitions Ii = 0 rarr If = 0 only internal conversion not gamma transition

The place freed by electron emitted during internal conversion is filled by other electron and Roumlntgen ray is emitted with energy Eγ = Bef - Bei

characteristic Roumlntgen rays of correspondent shell

Energy released by filling of free place by electron can be again transferred directly to another electron and the Auger electron is emitted instead of Roumlntgen photon

Nuclear fission

The dependency of binding energy on nucleon number shows possibility of heavy nuclei fission to two nuclei (fragments) with masses in the range of half mass of mother nucleus

2AZ1

AZ

AZ YYX 2

2

1

1

Penetration of Coulomb barrier is for fragments more difficult than for alpha particles (Z1 Z2 gt Zα = 2) rarr the lightest nucleus with spontaneous fission is 232Th Example

of fission of 236U

Energy released by fission Ef ge VC rarr spontaneous fission

Energy Ea needed for overcoming of potential barrier ndash activation energy ndash for heavy nuclei is small ( ~ MeV) rarr energy released by neutron capture is enough (high for nuclei with odd N)

Certain number of neutrons is released after neutron capture during each fission (nuclei with average A have relatively smaller neutron excess than nucley with large A) rarr further fissions are induced rarr chain reaction

235U + n rarr 236U rarr fission rarr Y1 + Y2 + ν∙n

Average number η of neutrons emitted during one act of fission is important - 236U (ν = 247) or per one neutron capture for 235U (η = 208) (only 85 of 236U makes fission 15 makes gamma decay)

How many of created neutrons produced further fission depends on arrangement of setup with fission material

Ratio between neutron numbers in n and n+1 generations of fission is named as multiplication factor kIts magnitude is split to three cases

k lt 1 ndash subcritical ndash without external neutron source reactions stop rarr accelerator driven transmutors ndash external neutron sourcek = 1 ndash critical ndash can take place controlled chain reaction rarr nuclear reactorsk gt 1 ndash supercritical ndash uncontrolled (runaway) chain reaction rarr nuclear bombs

Fission products of uranium 235U Dependency of their production on mass number A (taken from A Beiser Concepts of modern physics)

After supplial of energy ndash induced fission ndash energy supplied by photon (photofission) by neutron hellip

Decay series

Different radioactive isotope were produced during elements synthesis (before 5 ndash 7 miliards years)

Some survive 40K 87Rb 144Nd 147Hf The heaviest from them 232Th 235U a 238U

Beta decay A is not changed Alpha decay A rarr A - 4

Summary of decay series A Series Mother nucleus

T 12 [years]

4n Thorium 232Th 1391010

4n + 1 Neptunium 237Np 214106

4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108

Decay life time of mother nucleus of neptunium series is shorter than time of Earth existenceAlso all furthers rarr must be produced artificially rarr with lower A by neutron bombarding with higher A by heavy ion bombarding

Some isotopes in decay series must decay by alpha as well as beta decays rarr branching

Possibilities of radioactive element usage 1) Dating (archeology geology)2) Medicine application (diagnostic ndash radioisotope cancer irradiation)3) Measurement of tracer element contents (activation analysis)4) Defectology Roumlntgen devices

Nuclear reactions

1) Introduction

2) Nuclear reaction yield

3) Conservation laws

4) Nuclear reaction mechanism

5) Compound nucleus reactions

6) Direct reactions

Fission of 252Cf nucleus(taken from WWW pages of group studying fission at LBL)

IntroductionIncident particle a collides with a target nucleus A rarr different processes

1) Elastic scattering ndash (nn) (pp) hellip2) Inelastic scattering ndash (nnlsquo) (pplsquo) hellip3) Nuclear reactions a) creation of new nucleus and particle - A(ab)B b) creation of new nucleus and more particles - A(ab1b2b3hellip)B c) nuclear fission ndash (nf) d) nuclear spallation

input channel - particles (nuclei) enter into reaction and their characteristics (energies momenta spins hellip) output channel ndash particles (nuclei) get off reaction and their characteristics

Reaction can be described in the form A(ab)B for example 27Al(nα)24Na or 27Al + n rarr 24Na + α

from point of view of used projectile e) photonuclear reactions - (γn) (γα) hellip f) radiative capture ndash (n γ) (p γ) hellip g) reactions with neutrons ndash (np) (n α) hellip h) reactions with protons ndash (pα) hellip i) reactions with deuterons ndash (dt) (dp) (dn) hellip j) reactions with alpha particles ndash (αn) (αp) hellip k) heavy ion reactions

Thin target ndash does not changed intensity and energy of beam particlesThick target ndash intensity and energy of beam particles are changed

Reaction yield ndash number of reactions divided by number of incident particles

Threshold reactions ndash occur only for energy higher than some value

Cross section σ depends on energies momenta spins charges hellip of involved particles

Dependency of cross section on energy σ (E) ndash excitation function

Nuclear reaction yieldReaction yield ndash number of reactions ΔN divided by number of incident particles N0 w = ΔN N0

Thin target ndash does not changed intensity and energy of beam particles rarr reaction yield w = ΔN N0 = σnx

Depends on specific target

where n ndash number of target nuclei in volume unit x is target thickness rarr nx is surface target density

Thick target ndash intensity and energy of beam particles are changed Process depends on type of particles

1) Reactions with charged particles ndash energy losses by ionization and excitation of target atoms Reactions occur for different energies of incident particles Number of particle is changed by nuclear reactions (can be neglected for some cases) Thick target (thickness d gt range R)

dN = N(x)nσ(x)dx asymp N0nσ(x)dx

(reaction with nuclei are neglected N(x) asymp N0)

Reaction yield is (d gt R) KIN

R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa

Higher energies of incident particle and smaller ionization losses rarr higher range and yieldw=w(EKIN) ndash excitation function

Mean cross section R

0

(x)dxR

1 Rnw rarr

2) Neutron reactions ndash no interaction with atomic shell only scattering and absorption on nuclei Number of neutrons is decreasing but their energy is not changed significantly Beam of monoenergy neutrons with yield intensity N0 Number of reactions dN in a target layer dx for deepness x is dN = -N(x)nσdxwhere N(x) is intensity of neutron yield in place x and σ is total cross section σ = σpr + σnepr + σabs + hellip

We integrate equation N(x) = N0e-nσx for 0 le x le d

Number of interacting neutrons from N0 in target with thickness d is ΔN = N0(1 ndash e-nσd)

Reaction yield is )e1(N

Nw dnRR

0

3) Photon reactions ndash photons interact with nuclei and electrons rarr scattering and absorption rarr decreasing of photon yield intensity

I(x) = I0e-μx

where μ is linear attenuation coefficient (μ = μan where μa is atomic attenuation coefficient and n is

number of target atoms in volume unit)

dnI

Iw

a0

For thin target (attenuation can be neglected) reaction yield is

where ΔI is total number of reactions and from this is number of studied photonuclear reactions a

I

We obtain for thick target with thickness d )e1(I

Iw nd

aa0

a

σ ndash total cross sectionσR ndash cross section of given reaction

Conservation laws

Energy conservation law and momenta conservation law

Described in the part about kinematics Directions of fly out and possible energies of reaction products can be determined by these laws

Type of interaction must be known for determination of angular distribution

Angular momentum conservation law ndash orbital angular momentum given by relative motion of two particles can have only discrete values l = 0 1 2 3 hellip [ħ] rarr For low energies and short range of forces rarr reaction possible only for limited small number l Semiclasical (orbital angular momentum is product of momentum and impact parameter)

pb = lħ rarr l le pbmaxħ = 2πR λ

where λ is de Broglie wave length of particle and R is interaction range Accurate quantum mechanic analysis rarr reaction is possible also for higher orbital momentum l but cross section rapidly decreases Total cross section can be split

ll

Charge conservation law ndash sum of electric charges before reaction and after it are conserved

Baryon number conservation law ndash for low energy (E lt mnc2) rarr nucleon number conservation law

Mechanisms of nuclear reactions Different reaction mechanism

1) Direct reactions (also elastic and inelastic scattering) - reactions insistent very briefly τ asymp 10-22s rarr wide levels slow changes of σ with projectile energy

2) Reactions through compound nucleus ndash nucleus with lifetime τ asymp 10-16s is created rarr narrow levels rarr sharp changes of σ with projectile energy (resonance character) decay to different channels

Reaction through compound nucleus Reactions during which projectile energy is distributed to more nucleons of target nucleus rarr excited compound nucleus is created rarr energy cumulating rarr single or more nucleons fly outCompound nucleus decay 10-16s

Two independent processes Compound nucleus creation Compound nucleus decay

Cross section σab reaction from incident channel a and final b through compound nucleus C

σab = σaCPb where σaC is cross section for compound nucleus creation and Pb is probability of compound nucleus decay to channel b

Direct reactions

Direct reactions (also elastic and inelastic scattering) - reactions continuing very short 10-22s

Stripping reactions ndash target nucleus takes away one or more nucleons from projectile rest of projectile flies further without significant change of momentum - (dp) reactions

Pickup reactions ndash extracting of nucleons from nucleus by projectile

Transfer reactions ndash generally transfer of nucleons between target and projectile

Diferences in comparison with reactions through compound nucleus

a) Angular distribution is asymmetric ndash strong increasing of intensity in impact directionb) Excitation function has not resonance characterc) Larger ratio of flying out particles with higher energyd) Relative ratios of cross sections of different processes do not agree with compound nucleus model

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Three size levels of submicroscopic domain studiesVariety of our ordinary surroundings (macroscopic world) is consisted of atoms and molecules originating in chemical bonding of atoms

Description of the submicroscopic domain

Atomic physics ndash physics of an electron cloud of an atom chemical bonding of atoms to molecules only electromagnetic interaction

Nuclear physics ndash physics of atomic nuclei and interactions inside interaction of a nucleus and electron shells interaction of nucleus and elementary particles physics of nuclear matter strong weak and electromagnetic interactions

Subnuclear physics (elementary particle physics or also high energy physics) ndash physics of elementary particles and interactions - strong weak and electromagnetic

Scale Size Energy 1) Interaction Momentum 2)

[m] [MeV] [MeVc] Atomic ~10-10 ~ 000001 elmg (molecul) 0002Nuclear ~10-14 ~ 8 strong (nuclear) 20Subnuclear ~10-15 ~ 200 strong 200

1) Bonding energy of an electron in a atom or energy of molecular bonding nucleon bonding energy energy needed for elementary particles creation (comparable with their rest energies ndash masses)

2) Calculated using characteristics size and Heisenberg uncertainty principle ΔpmiddotΔx ~ ħ

Scale in Scale in

Atom

Nucleus

Proton

Quark Electron

































































0 cpcmE


Structure of matter











Weak W+ W- Z0 7middot10-14 ) 10-18 m







Inte

ract

ion

inte

nsi

ty α

Energy E [GeV]

strong SU(3)

unifiedSU(5)


weak SU(2)


















tt0 vmvmvm


and so hellip (11a)

square hellip (11b)

2

t

2

tt

t220 v

m

mvv

m

m2vv


220 vm

2

1vm

2

1vm

2

1 and so (12b)

2t

t220 v

m

mvv


t vv2m

m1v


tt

0 vm

mvv

If mtltltmα


If mtgtgtmα








cosvv2vv2m

m1v tt

t2t


2t

t220 v

m

mvv














2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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0 cpcmE


Structure of matter











Weak W+ W- Z0 7middot10-14 ) 10-18 m







Inte

ract

ion

inte

nsi

ty α

Energy E [GeV]

strong SU(3)

unifiedSU(5)


weak SU(2)


















tt0 vmvmvm


and so hellip (11a)

square hellip (11b)

2

t

2

tt

t220 v

m

mvv

m

m2vv


220 vm

2

1vm

2

1vm

2

1 and so (12b)

2t

t220 v

m

mvv


t vv2m

m1v


tt

0 vm

mvv

If mtltltmα


If mtgtgtmα








cosvv2vv2m

m1v tt

t2t


2t

t220 v

m

mvv














2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Slide 63

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Slide 65

Slide 66

Slide 67

Slide 68







Weak W+ W- Z0 7middot10-14 ) 10-18 m







Inte

ract

ion

inte

nsi

ty α

Energy E [GeV]

strong SU(3)

unifiedSU(5)


weak SU(2)


















tt0 vmvmvm


and so hellip (11a)

square hellip (11b)

2

t

2

tt

t220 v

m

mvv

m

m2vv


220 vm

2

1vm

2

1vm

2

1 and so (12b)

2t

t220 v

m

mvv


t vv2m

m1v


tt

0 vm

mvv

If mtltltmα


If mtgtgtmα








cosvv2vv2m

m1v tt

t2t


2t

t220 v

m

mvv














2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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Slide 54

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Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68


















tt0 vmvmvm


and so hellip (11a)

square hellip (11b)

2

t

2

tt

t220 v

m

mvv

m

m2vv


220 vm

2

1vm

2

1vm

2

1 and so (12b)

2t

t220 v

m

mvv


t vv2m

m1v


tt

0 vm

mvv

If mtltltmα


If mtgtgtmα








cosvv2vv2m

m1v tt

t2t


2t

t220 v

m

mvv














2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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Slide 65

Slide 66

Slide 67

Slide 68

If mtltltmα


If mtgtgtmα








cosvv2vv2m

m1v tt

t2t


2t

t220 v

m

mvv














2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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Slide 49

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Slide 51

Slide 52

Slide 53

Slide 54

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Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68











2t

t220 v

m

mvv


cosvv2vv2m

m1v tt

t2t

222

2

t

ααt22t

t220 vv

m

4mv

m

v2m

m

mvv

m

mvv

t

because


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

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Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68


20

A r

Q

4

1)RE(r




A R

Qr

4

1)RE(r

2A0

AMAX R4

Q2)R2eE(rF

e




0A0MAX vR4

eQ4tFp


eQ4pptan





Electrons


Electrons







N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68





N2N

1i

2

2N

1ii

2 N

i

helliphellip (1)





0N

1ii

N

1ii


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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Slide 64

Slide 65

Slide 66

Slide 67

Slide 68


2N

1i

2i

1

1 11

2N

1i

1N

1i

N

1ijji

2

2N

1ii N22

N

i

N

ijji

N

iii


ababMN

1ba

MN

1b

M

1a

N

1ba

MN

1kk

M

1jj

N

1ii

M

1jj

N

1ii







190 1090 eePooo





Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

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Slide 9

Slide 10

Slide 11

Slide 12

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Slide 68




Ze

4

1rU

0



eZZ

4

1rV

2

0

Coulomb force is




2

0 r

eZZ

4

1rF


We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

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Slide 6

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Slide 9

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Slide 46

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Slide 49

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Slide 51

Slide 52

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Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

We define







dtF

dtFppp 0



p0 = p = mv0=mv

We see from figure

2sinv2mp

2sinvm p

2

100

dtcosF



p




sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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Slide 68


sinvm20

0



d

d

dtcosF

2sinvm2

21

21-

0

hellip (5)


0Fr

then bv

r

d

dt

0

2


21

21

220 cosFr


2

2

0 r

2Ze

4

1F


We obtain

2cos

Zedcos

4

2dcosFr

0

221

210

221

21

2

Ze

because it is valid

2

cos222

sin2sincos 2121

21

21

d


2cos

Ze

2sinbvm2

0

220


bZe

E4

Ze

bvm2

2cotg

2KIN0

2

200

hellip (7)





if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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if n

1jj

n

1kk pp

if n

1jj

n

1kk EE

jf

n

1jjKIN

20

n

1kkKIN

20 EcmEcm

jif f

n

1jjKIN

n

1jj

20

n

1k

n

1kkKINk

20 EcmEcm i

KIN2i

0fKIN

2f0 EcMEcM


2i0

2f0 cMcM i

0f0 MM


fKIN EE

if n

1j j0

2n

1k k0

2

2m

p

2m

p


if EE iKIN

fKIN EE

f in

1k

n

1jjk cpcp

f in

1k

n

1jjk pp





21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

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21

22



22

1

21

1

21

2m

p

2m

p

2m

p



0cosppm

m2

m

m1p

m

m1p 11

2

1

2

121

2

121

0cosEE

m

m2

m

m1E

m

m1E 1 KIN1 KIN

2

1

2

11 KIN

2

11 KIN


112

12

12











bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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bZe

E4

2cotg

2KIN0









2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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2j

jbb bLn

S

LSn

SN

)(N)f(

S

S

SS



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb



(b) = njLSS


bZe

E4

2cotg

2KIN0




d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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d2

cos2


d2

cos2

sinr4

d2

sin2

cotgE4

ZeLnN

dS

dfN

dS

dN

2

2

2

KIN0

2

jS

S


2sinEr8

eLZnN

dS

dN

42KIN

220

42j

S


d2

sin2

cotgE4

ZeLndf 2

2

KIN0

2

j



2gcot

E4

ZeLn)(f 2

2

KIN0

2

jb


hellip (4)


angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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angular )(d

d

)(d

d spectral )E(

dE


d











dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Slide 68



dxnN

dNj

x

0

j

N

N

dxnN

dN

0


jeNN



j



and then xnN

NN

N

dNj

0

0



jn

1l




2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68



2) Sizes of nuclei



5) Spins














2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 17

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Slide 27

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Slide 33

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Slide 35

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Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68











2300155A198

AZ












27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68








27

30

p

3

p

m102134

kg10671

r34

m

R34

Am

we obtain 1017 kgm3




)Rr(0

e1)r(










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 19

Slide 20

Slide 21

Slide 22

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Slide 35

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Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

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Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68










Masses of nuclei


M(AZ) = Zmp+(A-Z)mn












Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

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Slide 51

Slide 52

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Slide 54

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Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68


Mass spectroscopy



EQFE


for is FB = QvBvB



















prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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prl

lˆ

ilˆ

lˆ






slˆ

jˆ

i

ii

i sSlˆ

LSLI

LS-coupling where i

ijˆ

Ijj-coupling where


2I

22 1)I(II


Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Ig j

Ig j



pj MeVT10153

c2m

e

Bohr magneton 111

eB MeVT10795

c2m

e



Electric momenta


)aZ(c5

2Q 22






2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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2300155A198

AZ



















1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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1) Introduction




GSI Darmstadt)























2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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2)A(Za

A

TaB

2

A

2Z

A4







Volume energy

Surface energy

Coulomb energy

Asymmetry energy

Binding energy




Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Shell model




Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Ene

rgy

Numberper level

Numberper shell

Totalnumber


Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Radioactivity

1) Introduction

2) Decay law

3) Alpha decay

4) Beta decay

5) Gamma decay

6) Fission

7) Decay series












dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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dNA



dN = -Nλdt dtN

dN

t

0

N

N

dtN

dN

0




0t

0 eAeNdt



00 N

2

N e

2lnT 21

Mean lifetime τ 1




M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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M

1kk

M

1kk




t111

1CN et

22t

21221 CCN ee

hellipt

MMt

M1M2M1 CCN ee


1ij1iij CC






dNdt = - λN + P



Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Alpha decay

HeYX 42

4A2Z

AZ






v

m

mv



2 = Q


Qm

mmE1

m

mvm

2

1vm

2

1v

m

mm

2

1

f

fKIN

f

22

2

ff


4AQ

mm

mE

f

fKIN


Barrier penetration



ZeZ

4

1

)A(Ar

ZZ

4

1V

2

03131

0

2

0C

α

e








212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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212

0

2KI

2KIN 10

R2E

cE

Rm2

E

2R

v

N



Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Beta decay







epn




Electron energy

Rel

ativ

e el

ectr

on in

ten

sity



eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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eYY A1Z

AZ


Z-A

1Z


eYY A

ZA







Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Gamma decay


Eγ = hν = Ei - Ef




j

2jfi c

h

2M

1hvM

2

1hEE

Rfi2j

22

fi EEEcM2

hEEhE















Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Internal conversion











Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Nuclear fission


2AZ1

AZ

AZ YYX 2

2

1

1


of fission of 236U











Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Decay series





T 12 [years]



4n + 2 Uranium 238U 451109

4n + 3 Actinium 235U 71108




Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Nuclear reactions

1) Introduction





6) Direct reactions





















R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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R

0

E

0 KIN

KIN

0

dE

dx

dE)(E

n(x)dxnN

ΔNw

KINa



0

(x)dxR

1 Rnw rarr





Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Nw dnRR

0


I(x) = I0e-μx



dnI

Iw

a0



I


Iw nd

aa0

a


Conservation laws







ll










Direct reactions







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Conservation laws







ll










Direct reactions







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Direct reactions







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introduction to subatomic physics "revolution in the science can be done only by excellent,...

Documents

atomic physics physics

physics of nuclear matter

concepts of modern physics

subatomic physics revolution

interaction of nucleus

nuclear forces

interactions strong

microscopic domain description