fission

Classification of Neutron
Interaction with Matter
Neutron Interaction
Scattering
Elastic
Inelastic
Absorption
Fission
Capture N. mult.
(n,2n)
(n,γ)
(n,3n)
...
Fission Process
(n,p)
(n,α)
Page 1
FISSION
Otto Hahn and Fritz Strassman, 1938 - Berlin
Otto Frisch and Lisa Meitner explanation, 1939
235
92
235
U + n → ( 92
U ) → X + Y + neutrons
235
92
235
U + n → ( 92
U) →
144
56
Ba +
89
36
235
92
235
U + n → ( 92
U) →
140
54
Xe +
94
38
*
*
*
Fission Process
Kr + 3 10 n
Sr + 2 10 n
Page 2
Fission: Process – Liquid Drop Model
• Neutron collides with a 235U
nucleus to form an excited state
that decays into two smaller
nuclei (plus neutrons) plus
ENERGY!
• Example: 235U + n →
142Ba + 2n + 180 MeV
92Kr
+
Fission Process
Page 3
•
Nucleus absorbs energy
– Excites and deforms
– Configuration “transition state” or “saddle point”
•
Nuclear Coulomb energy decreases during deformation
– nuclear surface energy increases
•
At saddle point,the rate of change of the Coulomb energy is equal to the rate
of change of the nuclear surface energy
•
If the nucleus deforms beyond this point it is committed to fission
– neck between fragments disappears
– nucleus divides into two fragments at the “scission point.”
• two highly charged, deformed fragments in contact
•
large Coulomb repulsion accelerates fragments to 90% final kinetic energy
within 10-20 s.
•
Particles form more spherical shapes
– converting potential energy to emission of “prompt” neutrons then
gamma
Fission Process
Page 4
Fission: Chain Reaction
• Use neutrons from fission process to initiate other fissions!
• 1942: Fermi achieved first self-sustaining chain reaction.
• For nuclear bomb, need
more than one neutron
from first fission event
causing a second event.
• For nuclear power plant,
need less than one
neutron causing a
second event.
Fission Process
Page 5
Fission: Sustainable Chain Reaction
Fission Process
Page 6
Neutron Sources
• Spontaneous Fission
• Installed Sources
Fission Process
Page 7
Fission
• When enough energy is supplied by the bombarding particle for
the Coulomb barrier to be surmounted
– as opposed to spontaneous fission, where tunneling through
barrier occurs
• Nuclides with odd number of neutrons fissioned by thermal
neutrons with large cross sections
– follow 1/v law at low energies, sharp resonances at high
energies
• Usually asymmetric mass split
– MH/ML≈1.4
– due to shell effects, magic numbers
Fission Process
Page 8
Spontaneous Fission
•
Rare decay mode discovered in
1940
– Observed in light actinides
– increases in importance with
increasing atomic number until it
is a stability limiting decay mode
• Z ≥ 98
• Half-lives changed by a
factor 1029 Uranium to
Fermium
– Decay to barrier penetration
Fission Process
Page 9
Fission Probability
• Based on balance of energy
– Coulomb energy (Ec) and surface energy of sphere (Es)
• x=Ec/2Es
– Ec=acZ2/A1/3
– Es=asA2/3
• From liquid drop model
– 239Pu is 36.97
– 209Bi is 32.96
Fission Process
Page 10
Different Fission Modes
Fission Process
Page 11
Uranium-235 Fission
y
235 U
92
200MeV
x
1 n
0
238 U
92
Fisija: ΔEvezanja > Eaktivacije
2.43
1 n
0
239 Pu
94
235 U
92
ΔEvezanja.jezgre = Ev.nastale – Ev.početne
Eactivation = needed to start fission
Fission energy distribution
U235 – fissile
U238 – fertile
Fission fragmenats
1 eV = 1,60219E-19 J
200 Mev = 3,204E-11 J
Fission Process
83.5%
Prompt γ-rays
2.5%
Neutrons
2.5%
β-decay from fragmenats
3.5%
γ− decay fragments
3.0%
Neutrino energy
5.0%
Page 12
Fission
•
Primary fission products always on neutron-excess side of β stability
– high-Z elements that undergo fission have much larger
neutron-proton ratios than the stable nuclides in fission
product region
– primary product decays by series of successive β- processes to
its stable isobar
•
Probability of primary product having atomic number Z:
2
⎡
⎤
(
)
Z
−
Z
1
p
P ( Z) =
exp ⎢−
⎥
c
cπ
⎢⎣
⎥⎦
•
Emission of several neutrons per fission crucial for maintaining chain
reaction
•
“Delayed neutron” emissions important in control of nuclear reactors
Fission Process
Page 13
ν ≈ 2.5 n/fiss
εf ≈ 200 MeV/fiss
MeV = 1.602 x 10-13 J
Pthermal = Nfission • εf • MeV
[W]
= [#fiss/s] • [MeV/fiss] • [J/MeV]
Fission Process
Page 14
Fissionable Material
• Fissile Material – fission is possible with neutrons of any energy
• Fissionable Material – fission with neutrons is possible
• Fertile Material – after transmutations can give fissile material
Fission Process
Page 15
Cross section
Fission Process
Page 16
104
104
235
238
U
10
102
σ (barns)
σ (barns)
10
3
fission
10
1
100
3
102
10
U
capture
1
100
capture
10-1
10-1
10-2 -3
10
10-2 -3
10
fission
10-2
10-1
100
101
102
103
104
105
106
107
Energy (eV)
10-2
10-1
100
101
102
103
104
105
106
107
Energy (eV)
Fission Process
Page 17
Uranium Fission
1
0
94
140
1
n + 235
U
→
Sr
+
Xe
+
2
92
38
54
0n
94
1
→139
Ba
+
Kr
+
3
56
36
0n
Fission products + neutrons
1
0
n( > 1Mev ) + 238
92 U → fission ⋅ products, neutrons
1
0
β−
β−
n + U → U t1/ 2 =24 min → Npt1 / 2 =2, 4 days →239
94 Pu
238
92
239
92
1
0
239
93
240
n+ 239
Pu
→
94
94 Pu
Less than 1% neutrons are delayed neutrons from fission products
decay
Up to 40 different ways of splitting – 80 different fission products.
Fission Process
Page 18
Conversion of Fertile Nuclides to
Fissile Nuclides
Fission Process
Page 19
104
238
3
U
10
102
total
101
100
3
102
Pu
capture
101
100
capture
10-1
10-2 -3
10
239
fission
σ (barns)
σ (barns)
10
104
10-1
10-2
10-1
100
101
102
103
104
105
106
107
10-2 -3
10
10-2
Energy (eV)
10-1
100
101
102
103
104
105
106
107
Energy (eV)
Fission Process
Page 20
104
104
232
233
Th
3
10
102
σ (barns)
σ (barns)
10
3
101
U
102
101
fission
capture
100
100
fission
10-1
10-2 -3
10
10-2
10-1
100
101
102
103
104
105
106
capture
10-1
107
10-2 -3
10
10-2
Energy (eV)
10-1
100
101
102
103
104
105
106
107
Energy (eV)
Fission Process
Page 21
Distribution of Fission Energy
Fission Process
Page 22
Energetics
•
Determination of total kinetic energy
– Equation deviates at heavy actinides (Md, Fm)
•
Consider fission of 238U
– Assume symmetric
• Z=46, A=119
– E=462*1.440/(1.8(1191/3)2)=175 MeV
– and asymmetric fission
• Z=35, A=91
• Z=57, A=147
– E=(35)(57)*1.44/(1.8*(911/3+1471/3))=164 MeV
Fission Process
Page 23
Fission Process
Page 24
Prompt Fission Neutron Energy Spectrum
•
The neutrons produced by fission are high energy neutrons, and almost
all fission neutrons have energies between 0.1 MeV and 10 MeV.
•
Most probable neutron energy is about 0.7 MeV
•
Average energy of fission neutrons is about 2 MeV.
Fission Process
Page 25
Fission Fragments
•
Asymmetric fission product distribution
•
thermal neutron induced fission of uranium and plutonium and 252Cf
– MH/ML =1.3-1.5
– liquid drop model would predict that the greatest energy release
and the most probable would be symmetric
– magic numbers and shell corrections explain differences
•
Symmetric fission is suppressed by at least two orders of magnitude
relative to asymmetric fission
– as mass of the fissioning system increases
• Location of heavy peak in the fission remains constant
• position of the light peak increases
• Heavy fragment peak at A=132
• preference for asymmetric fission due to stability at Z=50, N=82,
– a doubly magic spherical nucleus.
Fission Process
Page 26
Fission Process
Page 27
Fission products
Decay heat (Ostatna toplina):
P0 – power after shutdown
t0 – operation time
τ - time after shutdown
[
P = P0 ⋅ 0,0061 ⋅ (τ − t0 )
−0 , 2
−τ
−0 , 2
]
Fission Process
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Fission Process
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Fission Process
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Fission Process
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Fission Process
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Fission Process
Page 33
Decay heat power and energy release
after shutdown as a function of time.
Fission Process
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Fission Process
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Fission Process
Page 36
Prompt and Delayed Neutrons
•
Prompt neutrons are released directly from fission within 1e-13 seconds of the
fission event.
•
Delayed neutrons are released from the decay of fission products that are called
delayed neutron precursors. Delayed neutron precursors are grouped according
to half-life. Half-lives vary from fractions of a second to almost a minute.
•
The fraction of neutrons born as delayed neutrons is different for different fuel
materials. Following are values for some common fuel materials.
– Uranium-235 0.0065
– Plutonium-239 0.0021
•
Delayed neutrons are produced by a classification of fission products known as
delayed neutron precursors. When a delayed neutron precursor undergoes a
decay, it results in an excited daughter nucleus which immediately ejects a
neutron. Therefore, these delayed neutrons appear with a half-life of the delayed
neutron precursor.
Fission Process
Page 37
Prompt and Delayed Neutrons
•
The delayed neutron generation time is the total time from the birth of the fast
neutron to the emission of the delayed neutron in the next generation. Delayed
neutron generation times are dominated by the half-life of the delayed neutron
precursor. The average delayed neutron generation time is about 12.5 seconds.
•
A prompt neutron generation time is the sum of the amount of time it takes a
fast neutron to thermalize, the amount of time the neutron exists as a thermal
neutron before it is absorbed, and the amount of time between a fissionable
nuclide absorbing a neutron and fission neutrons being released. Prompt
neutron generation time is about 5.e -5
•
The average neutron generation time can be calculated from the prompt and
delayed neutron generation times and the delayed neutron fraction using
Equation
Fission Process
Page 38
Neutron Reproduction Factor (Faktor umnožavanja neutrona)
Fission Process
Page 39
Fission Process
Page 40
Physical Principles of a Nuclear Reactor
E
Leakage
N2
2 MeV
≡
N
N
2
N1
1
ν n/fission
Energy
Fast fission
Resonance abs.
ν ≈ 2.5
Non-fissile abs.
1 eV
Slowing down
k
Non-fuel abs.
Fission
200 MeV/fission
Leakage
Fission Process
Page 41
Neutron Cycle in Thermal Reactor
Fission Process
Page 42
Neutron Life Cycle
Fission Process
Page 43
Effective Multiplication Factor
•
Value of keff for a self-sustaining chain reaction of fissions, where the neutron
population is neither increasing nor decreasing, is one. The condition where the
neutron chain reaction is self-sustaining and the neutron population is neither
increasing nor decreasing is referred to as the critical condition and can be
expressed by the simple equation keff = 1 .
•
If the neutron production is greater than the absorption and leakage, the reactor
is called supercritical. In a supercritical reactor, keff is greater than one, and the
neutron flux increases each generation.
•
If the neutron production is less than the absorption and leakage, the reactor is
called subcritical. In a subcritical reactor, keff is less than one, and the flux
decreases each generation.
Fission Process
Page 44
Neutron Life Cycle with keff=1
Fission Process
Page 45
Thermal and Fast Reactor Neutron Spectra
Fission Process
Page 46
Neutron Slowing Down and Thermalization
•
Fission neutrons are produced at an average energy level of 2 MeV and
immediately begin to slow down as the result of numerous scattering reactions
with a variety of target nuclei.
•
After a number of collisions with nuclei, the speed of a neutron is reduced to
such an extent that it has approximately the same average kinetic energy as the
atoms (or molecules) of the medium in which the neutron is undergoing elastic
scattering. This energy, which is only a small fraction of an electron volt at
ordinary temperatures (0.025 eV at 20(C), is frequently referred to as the
thermal energy, since it depends upon the temperature.
•
Neutrons whose energies have been reduced to values in this region (< 1 eV)
are designated thermal neutrons.
•
The process of reducing the energy of a neutron to the thermal region by elastic
scattering is referred to as thermalization, slowing down, or moderation.
•
The material used for the purpose of thermalizing neutrons is called a
moderator.
Fission Process
Page 47
Neutron Slowing Down and Thermalization
• A good moderator reduces the speed of neutrons in a small
number of collisions, but does not absorb them to any great extent.
• Slowing the neutrons in as few collisions as possible is desirable
in order to reduce the amount of neutron leakage from the core
and also to reduce the number of resonance absorptions in nonfuel materials.
• The ideal moderating material (moderator) should have the
following nuclear properties.
– large scattering cross section
– small absorption cross section
– large energy loss per collision
Fission Process
Page 48
Neutron Slowing Down and Thermalization
•
The macroscopic slowing down power (MSDP) is the product of the
logarithmic energy decrement and the macroscopic cross section for scattering
in the material. (Sposobnost usporavanja)
•
The moderating ratio is the ratio of the macroscopic slowing down power to the
macroscopic cross section for absorption. (Odnos moderacije)
Fission Process
Page 49
Natural Nuclear Reactors
Fission Process
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Fission Process
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Fission Process
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Fission Process
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Fission Process
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Fission Process
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