A2 Induced Fission 0

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A-2 Induced Fission 0 Introduction
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
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A-2 Induced Fission 1 Generalities
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
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A-2 Induced Fission 2 Liquid-drop picture
Fission can be qualitatively understood on the
basis of the liquid-drop model
electrical repulsion pushes the 2 lobes apart
fission fragment
n
n
n
n
235U
high excitation and strong oscillation
formation of a neck
fission fragment
Note fission liberates about 200 MeV per atom!
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A-2 Induced Fission 3 Chain 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.
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A-2 Induced Fission 4 Mass distribution
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 ? b
b ? 75s 140Cs 94Y 64s ? b b
? 19m 140Ba 94Zr 13d ?
b 140La 40h ? b 140Ca
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A-2 Induced Fission 5 Mass distribution
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A-2 Induced Fission 6 Fission barrier
Fission 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.
U
barrier
UB
1/r electric potential energy
r
r0
range of the nuclear force
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 260106Sg 7.2 ms
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A-2 Induced Fission 7 Double fission barrier

• 50s 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 lt
  A lt 190 and A gt 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

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A-2 Induced Fission 9
A-2 Induced Fission 8 Double 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 lt Epot gt 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.
Epot (MeV)
230Th
240Pu
252Cf
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Bn
0
deformation
with Bn binding energy of the neutron in the
considered nucleus
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A-2 Induced Fission 9 Double 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.

E
excited states spectroscopy
g
class II states
fission isomers
class I states
spontaneous fission
deformation
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A-2 Induced Fission 10 Double fission barrier
Fission isomers

• lowest class II states
• de-excitation through - fission (tunneling
  through the 2nd barrier)
• - g 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 lt T1/2 lt 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.

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A-2 Induced Fission 11 After 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 gs are emitted in a larger time
length which can reach few ms. 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.
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A-2 Induced Fission 12 Time scale in fission
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A-2 Induced Fission 13 Energies in 235U thermal
fission
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.
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A-2 Induced Fission 14 Neutron-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.
MeV
En lt 0.1 eV
L.E. Glendenin et al., Phys. Rev. C (1981) 2600
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A-2 Induced Fission 15 Energy dependence of
(n,f) cross sections
Case of 235U and 237Nb
thermal neutrons
235U neutron binding energy gt maximum fission
barrier ? large cross section 237Nb neutron
binding energy lt maximum fission barrier ? small
cross section ? when excitation energy E gt
maximum fission barrier ? sharp rise of sf
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A-2 Induced Fission 16 Neutron energy spectra
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 ltEngt 3/2 TM.
235U(n,f)
TM 1.352 MeV ltEngt 2.028 MeV
B.E. Watt, Phys. Rev. 2 (1952) 1037
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A-2 Induced Fission 17 Nuclear reactors
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.
Pressurized Water Reactor
Boiling Water Reactor
Liquid-Metal Fast-Breeder 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
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A-2 Induced Fission 18 Nuclear energy
Electricity production in 2001

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A-2 Induced Fission 19 A reactor for
fundamental research
Institute Laue-Langevin (Grenoble) a
french-german-english lab