A-2 Induced Fission – 0Introduction

• Generalities

• Liquid-drop picture

• Chain reactions

• Mass distribution

• Fission barrier

• Double fission barrier

• After the scission point

• Time scale in fission

• Neutron-induced fission

• Energy dependence of (n,f) cross sections

• Neutron energy spectra

• Nuclear reactors

• Nuclear energy

• A reactor for fundamental research

A-2 Induced Fission – 1Generalities

Nuclear fission Decay process in which an unstable nucleus splits into two fragments of comparable mass.

1932: discovery of neutrons

1939: official discovery by Otto Hahn and Fritz Strassmann fission of 235U

Lise Meitner! (109Mn)

1942: first “chain reacting pile” (E. Fermi)

1945: first nuclear explosion in Alamogordo (New Mexico, USA)

1972: discovery of Oklo (Gabon): unique natural nuclear reactor (1.8 106 y ago) very abnormal isotopic ratios of 235U/238U in uranium ores

A-2 Induced Fission – 2Liquid-drop picture

n235U

high excitation and strong oscillation

formation of a neck

electrical repulsion pushes the 2 lobes apart

fission fragment

nn

n

fission fragment

Fission can be qualitatively understood on the basis of the liquid-drop model

Note: fission liberates about 200 MeV per atom!

A-2 Induced Fission – 3Chain reactions

Chain reactions

If at least one neutron from each fission strikes another 235U nucleus and initiates fission, then the chain reaction is sustained.

If the reaction will sustain itself, it is said to be "critical", and the mass of 235U required to produced the critical condition is said to be a "critical mass". A critical chain reaction can be achieved at low concentrations of 235U if the neutrons from fission are moderated in water to lower their speed, since the probability for fission with slow neutrons is greater.

A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction.

When 235U undergoes fission, the average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 and 137. Most of these fission fragments are highly unstable, and some of them such as 137Cs and 90Sr are extremely dangerous when released to the environment.

235U + n 236U* 140Xe + 94Sr + 2n

T1/2 = 14s 75s

140Cs 94Y

64s 19m

140Ba 94Zr

13d 140La

40h 140Ca

A-2 Induced Fission – 4Mass distribution

A-2 Induced Fission – 5Mass distribution

Fission barrier

A-2 Induced Fission – 6Fission barrier

U

UB

1/r electric potential energy

rr0range of the nuclear force

barrier

Fission occurs if there is an excitation energy greater than UB

or an appreciable probability for tunneling through the potential energy barrier.

Spontaneous fission occurs via a quantum mechanical tunneling through the fission barrier.

Fissibility parameter:

x = Z2/A

Spontaneous fission is possible only for elements with A 230 and x 45.

Ground states spontaneous fission half-lives for

235U: (9.8 2.8) x 1018 y 238Pu: (4.70 0.08) x 1010 y 256Fm: 2.86 h 238U: (8.2 0.1) x 1015 y 254Cf: 60.7 y 260

106Sg: 7.2 ms

50’s: enhancement in the study of the nuclear deformations for stable nuclei in between shell closures.

the spherical shell model is unable to explain the large quadrupolar moments of nuclei at 150 < A < 190 and A > 220

unified model of A. Bohr and B. Mottelson: macroscopic + individual aspects

1955: S.G. Nilsson develops a deformed shell model

the potential is defined by oscillation frequencies, functions of deformation parameters

if the nucleus is deformed, the degeneracy of the energy levels of the spherical potential is partially lifted

the spreading in energy of these levels increase with the deformation

for small deformations, this spreading leads to an uniform repartition of the levels

for large deformations, on can observe the appearance of shell effects due to the gatherings of Nilsson levels coming from different shells initially

The presence of these level gatherings, because they lower the level density, is at the origin of the permanent deformation of some nuclei in their ground state.

But, the total energy is overestimated for the high energies…

A-2 Induced Fission – 7Double fission barrier

A-2 Induced Fission – 9A-2 Induced Fission – 8Double fission barrier

The method proposed by Strutinski is the synthesis of the liquid drop model and the deformed shell model in order to describe simultaneously the mean value of the potential energy < Epot > and its local fluctuations as a function of the nucleon number and the nucleus deformation.

macroscopic – microscopic model of fission

The oscillating aspects of the shell corrections in this model leads to the prediction of a fission barrier with two bumps: the double fission barrier.

Ep

ot (

MeV

)

deformation

5

0

230Th 240Pu 252Cf

Bn

with Bn: binding energy of the neutron in the considered nucleus

A-2 Induced Fission – 9Double fission barrier

Experimental consequences

hierarchy of the states of the fissioning nucleus as a function of deformation:

compound states of class I: normally deformed and very dense (level density D = 0.1-1 eV)

compound states of class II: superdeformed with a reduced excitation energy E* ~ 2-3 MeV with a smaller level density (D = 0.05-10 KeV)

These states have comparable properties: their presence and coupling with tunnel effect through the intermediate barrier have allowed a coherent interpretation of numerous experimental results in disagreement with the predictions of the liquid drop model.

class Istates

class IIstates

fission isomers

excited states spectroscopy

spontaneous fission

E

deformation

A-2 Induced Fission – 10Double fission barrier

Fission isomers

lowest class II states

de-excitation through: - fission (tunneling through the 2nd barrier) - emission after tunneling to the 1st well through the 1st barrier

these “form isomers” have a greater deformation than the ground state in the 1st well

1st discovery in 1962 (Polikanov), ~ 30 isomers have been observed in the U-Bk region

E* = Eg.s. + 2-3 MeV few tens of ps < T1/2 < 14ms

one measures the variation with the incident energy of the ratio between the number of delayed fissions (coming from the isomer) and the number of prompt fissions

A statistical model allows generally to extract the height of the second well and the shape of the second barrier.

6410 10delayed

prompt

NR

N

A-2 Induced Fission – 11After the scission point

Beyond the barriers, the system evolves irreversibly towards the scission. This transition is very fast (few 10-22 s).

During the scission, the system gets a large amount of energy (~20-30 MeV) that is used as deformation energy of the fragments.

Just after the scission, the fragments convert their Coulomb energy in translation kinetic energy. They reach then 90% of their final kinetic energy in 1.3 10-20 s. As soon as the distance between the two fragments is larger than the nuclear force range (~ 2.5 10-13 cm), they get a deformation energy that they convert rapidly in internal excitation energy (this conversion is done with a damping of the collective vibrations in ~ 10-21 s).

The prompt neutron emission is performed in 10-14 s (the distance between fragments is then 2. 10-8 cm).

The ’s are emitted in a larger time length which can reach few s.

The formed fragments are unstable because too rich in neutrons. The delayed neutrons represent only 1% of the total neutron emission but they are of great importance for the reactivity of reactors.

A-2 Induced Fission – 12Time scale in fission

A-2 Induced Fission – 13Energies in 235U thermal fission

< prompt energy >

fragment Ekin 169.0

neutron emission 4.8

g emission 7.0

180.8

< delayed energy >

- energy 6.4

delayed neutron emission 0.01

emission 6.2

emission 10.0

22.61

< total energy > 203.41

The total kinetic energy of the fragments increases with the mass and the charge of the fissioning nucleus as Z2/A1/3. In the contrary, it is independent of the excitation energy of the fissioning system due to the effect of the Coulomb repulsion of the fragments formed at the scission.

A-2 Induced Fission – 14Neutron-induced fission

In the history of fission research, neutron-induced fission has always played the most important role (Hahn & Strassmann).

The neutrons do not feel the Coulomb repulsion, only the nuclear attraction. Therefore nuclear reactions can be induced by neutrons of arbitrarily low energies.

The asymmetric fission is largely favoured. The light mass peak goes towards heavier fragments when the mass of the fissioning nucleus increases.

L.E. Glendenin et al., Phys. Rev. C (1981) 2600

En < 0.1 eV

MeV

A-2 Induced Fission – 15Energy dependence of (n,f) cross sections

Case of 235U and 237Nb

235U: neutron binding energy > maximum fission barrier large cross section237Nb: neutron binding energy < maximum fission barrier small cross section

when excitation energy E* > maximum fission barrier sharp rise of f

thermal neutrons

A-2 Induced Fission – 16Neutron energy spectra

B.E. Watt, Phys. Rev. 2 (1952) 1037

235U(n,f)

The most prominent neutron emission source is the evaporation from the fully accelerated fragments.

The integral neutron spectrum can be fitted with a Maxwellian distribution:

With TM the only parameter characterizing the distribution. The average neutron energy is given by <En> = 3/2 TM.

1/ 2

1/ 2 3/ 2

2( ) .expM

M M

E EN E

T T

TM = 1.352 MeV<En> = 2.028 MeV

It takes 1011 fissions per second to produce one watt of electrical power. As a result, about one gram of fuel is consumed per day per megawatt of electrical energy produced. This means that one gram of waste products is produced per megawatt per day, which includes 0.5 grams of 239Pu.

A-2 Induced Fission – 17Nuclear reactors

Liquid-Metal Fast-Breeder Reactor

Boiling Water Reactor Pressurized Water Reactor

BWR: the most common in case of a leak the water can become radioactive

PWR: the moderating and turbine waters are separated more expensive

LMFBR: liquid sodium is used as moderator and heat transfer medium

A-2 Induced Fission – 18Nuclear energy

0

20

40

60

80

100

EU-15

Euro-zone

B DK D EL E F IRL I L NL A P FIN S UK

conventional thermal nuclear hydro and other

%

Electricity production in 2001

A-2 Induced Fission – 19A reactor for fundamental research

Institute Laue-Langevin (Grenoble): a french-german-english lab