Nuclear Science Minor ProgramNuclear Science Minor Program

14 upper division units from the following:

• CHEM 482 Directed Study in Advanced Topics of Chemistry

• NUSC 341 Introduction to Radiochemistry• NUSC 342 Introduction to Nuclear Science• NUSC 344 Nucleosynthesis and Distribution of the

Elements• NUSC 346 Radiochemistry Laboratory• NUSC 444 Special Topics in Nuclear Science• NUSC 485 Particle Physics• PHYS 385 Quantum Physics

What we’ve discussed last timeWhat we’ve discussed last time

• History of radioactivity

• Interactions and Force Carriers

• Standard Model and Subatomic Particles

• Structure of Matter

• Nucleus

• Chart of Nuclides

Forces in Matter Forces in Matter and and

the Subatomic Particlesthe Subatomic Particles

Chapter 1Chapter 1

Natural Decay ChainsNatural Decay Chains

http://hyperphysics.phy-astr.gsu.edu/

(4n + 0)

6 α particles4 β- particles

http://hyperphysics.phy-astr.gsu.edu/

(4n + 2)

8 α particles6 β particles

(4n + 3)

7 α particles4 β particles

The members of this series are not presently found in nature because the half-life of the longest lived isotope in the series is short compared to the age of the earth.

< 4.7 109 y

7 α particles4 β- particles

Types of Radioactive DecayTypes of Radioactive Decay

Chapter 2

Radioactive DecayRadioactive Decay

• Statistical process• Spontaneous emission of particle or

electromagnetic radiation from the atom • Unaffected by temperature, pressure,

physical state, etc• Exoergic process• Conserves total energy, linear and angular

momentum, charge, mass number, lepton number, etc.

Units of EnergyUnits of Energy

• Mass and energy are interchangeable –

E = mc2

where energy usually expressed in MeV

• 1 eV = 1.602 x 10-19 J = 1.60219 x 10-12 erg

• 1 MeV = 1.602 x 10-13 J = 1.60219 x 10-6 erg

• 1 u = 931.5 MeV/c2

Decay ModesDecay Modes• Alpha decay• Beta decay • Gamma decay• Spontaneous fission• Delayed neutron and proton emission• Two-proton decay• Composite particle emission• Double beta decay• Prompt proton decay (new)

Molecular Rotations and Vibrations Molecular Rotations and Vibrations (Bjerrum 1912)(Bjerrum 1912)

01 ħ2/I

10 ħ2/I

L= 0L= 1L= 2

L= 3

L= 4

L= 5

3 ħ2/I

6 ħ2/I

15 ħ2/I

rota

tion

axis

r1r2

r

m1

m2CM

Absorption spectrum of HCl(note the double peaking caused

by two isotopes of Cl)

λ = 3 μm = 3 x 10-4 cm, IR

moments of inertiabond and force length

VibrationsVibrations

http://wwwnsg.nuclear.lu.se

RotationRotation

http://wwwnsg.nuclear.lu.se

prolate rotor oblate rotor

Reflection Asymmetric ShapeReflection Asymmetric Shape

http://wwwnsg.nuclear.lu.se

octupole

Gamma-Ray Radiation and NucleiGamma-Ray Radiation and Nuclei

γγGermanium detector

Num

ber

of c

ount

s

Gamma-ray energy (keV)

29Cu3059

γ-rayenergy, keV

Excitationenergy, keV

Angularmomentum, ħ

γγ

γγ

Alpha DecayAlpha Decay

• 210Po 4He + 206Pb + γ

• t1/2 (210Po) = 138.4 d; Eα= 5.304 MeV

• Typically for A>150; Z > 83 (144Nd, 147Sm)

• Geiger-Nuttall rule:

Et

log

1 log 2/1

HeXX N

AZN

AZ

422

42

216Rn; 8.05 MeV, 45μs144Nd; 1.83 MeV, 2.1 x 1015 y

Conservation of Energy Conservation of Energy for Alpha Decayfor Alpha Decay

Etrans= Eα+ Erecoil

E = ½ mv2

2mE = m2v2 = (mv)2

p = mv; p2 = m2v2 = (mv)2 = 2mE

pα= precoil

2m αE α= 2mrecoilErecoil

Erecoil = (m α/mrecoil)E α

Alpha SpectrumAlpha Spectrum

NAZ X

242

N

AZ Y

Parent

Daughter

α1(20%)

α2(40%)

α3(40%)γ1

γ3 γ2 5.0 5.5 6.0 6.5 7.0 7.5

HeXX N

AZN

AZ

422

42

What we have learned last timeWhat we have learned last time

• Natural decay chains

• Excited molecules and nuclei

• Alpha decay

Alpha DecayAlpha Decay

NAZ X

242

N

AZ Y

Parent

Daughter

α1(20%)

α2(40%)

α3(40%)γ1

γ3 γ2

5.0 5.5 6.0 6.5 7.0 7.5

HeXX N

AZN

AZ

422

42

Counts

Eα (MeV)

238U 234Th + 4He2+

238U 234Th + 4He

Beta DecayBeta Decay

change a neutron to a proton

change a proton to a neutron

EC: electron capture, change a proton to a neutron

is an electron

11 N

AZN

AZ YX

11 N

AZN

AZ YX

11 NA

ZNAZ YeX

β+ is an anti-electron or positron

(negatron decay)

Unlike alpha decay, which occurs primarily among nuclei in specific areas The periodic table, beta decay is possible for certain isotopes of all elements

Negatron (Negatron (ββ--) Decay) Decay

dtSP

ytYSr

3.14

1.29

2/13216

3215

2/19039

9038

YAZ 1Daughter

β1

β2

γ

XAZParent

11 N

AZN

AZ YX

NAZ X

11 NA

Z Y

Neutron rich nuclei; Large N/Z ratio t1/2

Beta decay – Energy Beta decay – Energy spectrumspectrum

• Emax

• Antineutrino in β-

– No charge– No magnetic moment– Near zero rest mass– Spin ½– Conservation of lepton

number

β-

β+

Beta-particle energy

Num

ber

of b

eta

part

icle

s

Etrans = Enegatron + Eantineutrino + Erecoil

Antineutrino discoveryAntineutrino discovery np

1953 by F. Reines and C.L. Cowan Jr.

Positron (Positron (ββ++) Decay) Decay change a proton to a neutron

11 N

AZN

AZ YX

β+ is an anti-electron, or positron

min 3.20

605.2

2/1115

116

2/12210

2211

tBC

ytNeNa

• Proton rich nuclei• Similar spectrum as in negatron decay • Change a proton to a neutron positive electron is emitted by the nucleus and an orbital electron originally present in the parent atom is lost to form a neutral daughter atom.• equivalent to the creation of a positron-electron pair from the available transition energy• 2 x 0.511 MeV = 1.02 MeV necessary to create 2 electrons• β+ decay is possible only when the energy of the transition is greater than 1.02 MeV

The fate of the positronThe fate of the positron• Conversion to pure energy by

positron annihilation

• After the positron slows down to energies comparable to that of surroundings

• Formation of 1, 3, or 0 annihilation photons, depending on the spin orientation of the electron-positron pair

• If the spins are parallel triple state

• If the spins are anti-parallel a single state

• Positronium “atom” light “isotope” of hydrogen, with the positron substituting for the nuclear proton

• Ortho positronium; paralell spins10-7 s

• Para positronium; anti-parallel spins 10-10 s

Electron Capture (EC orElectron Capture (EC orεε))

EC: electron capture, change a proton to a neutron

11 NA

ZNAZ YeXexcited nucleus

+ x-rays or Auger electrons + inner bremsstrahlung

dtIrPt

dtYbLu

2.10 ; electronsAuger raysx

70.6 ; electronsAuger raysx

2/118877

18878

2/1172

7017271

Gamma DecayGamma Decay

• Pure γ decay

• Internal conversion (IC)

• Pair production (PP)

h 5.4

d 8.249

2/111549

11549

2/111047

11047

*

tInIn

tAgAg

XX

m

m

AZ

AZ

Pure Gamma-Ray EmissionPure Gamma-Ray Emission

γ99.8%

β1, t1/2 = 1.17 m

0.2%β2, t1/2 = 6.70 h

92U91Pa

234U

234mPa

234gPa

2 keV < E < 7 MeV; monoenergetic

Internal ConversionInternal Conversion

The excited nucleus transfers the energy to an orbital electron, which is then ejected from the atom (monoenergetic).

EIC electron = Etrans – BEatomic electron

IC and gamma decay are competing processes

Internal conversion coefficient (α)

α= Fraction of decays occurring by gamma emission/Fraction of decays occurring by IC

Pair ProductionPair Production

• E > 1.02 MeV

16mO 16O

Etrans = 6.05 MeV

t1/2 = 7 x 10-11 s

eeXX AZ

AZ

*

Spontaneous Fission DecaySpontaneous Fission Decay

neutrons 215260

9838

25298 NdSrCf

Induced Fission ReactionInduced Fission Reaction

neutrons 29436

14056

123592 KrBanU

Oklo, Gabon – Oklo, Gabon – A natural fission reactorA natural fission reactor

• 235U natural abundance is well known: 0.00720 ± 0.00001

• Uranium deposit where self-sustained nuclear chain reactions have occurred.

• 235U abundance 0.00717, about 3 standard deviations below the accepted value.

• The only process which can lead to reduction of U is fission by low-energy neutrons.

• 2 x 109 y, 235U (~3%) reactor moderated by groundwater.

• Fission product isotope signatures Nd, Ru

Geological Situation in Gabon leading to natural nuclear fission reactors:

1. Nuclear reactor zones2. Sandstone3. Ore layer4. Granite

Fossil Reactor 15, located in Oklo, Gabon. Uranium oxide remains are visible as the yellowish rock.

Source: NASA

OkloOklo

Estimations

• 5 tonnes of 235U were fissioned.

• Total energy released 2 x 1030 MeV or 108 MW∙h. A contemporary power reactor can operate at 103 MW.

• Average power 0.01 MW, operating for 106 y.

Important feature:

the fission products are still in place in the reactor zone and have migrated very little. Despite climate changes, no substantial movement of the fission products has taken place over the past 2 x 109 y.

Confirmation: Nd signatureConfirmation: Nd signature

• natural neodymium contains 27% 142Nd• the Nd at Oklo contained less than 6% but contained more 143Nd• the isotopic composition matched that produced by the fissioning of 235U.

Delayed-Neutron EmissionDelayed-Neutron Emission

• Following beta decay of fission products such as 140Ba and 94Kr

• 87Br 87Kr 86Kr + n + β-

neutron rich

Delayed-Proton EmissionDelayed-Proton Emission

• Production of precursor: 54Fe(p,2n)53Co

• Decay by proton emission: 53Co 52Fe +p

Double-Beta DecayDouble-Beta Decay

• 130Te, 82Se stable to ordinary beta decay, but unstable toward 2-beta decay

• Simultaneous 2 beta emission

2

28236

y 104.18234

13054

y 105.213052

20

21

KrSe

XeTex

x

Two-Proton DecayTwo-Proton Decay

• 22Al (1960), 54Zn (2005)

• 45Fe (2003, 2007)

• 48Ni

End of Chapter 2End of Chapter 2

Questions?