Nuclear Fission
elementary principles
BNEN 2012-2013 Intro
William D’haeseleer
Mass defect & Binding energy
ΔE = Δm c2
Nuclear Fission
• Heavy elements may tend to split/fission
• But need activation energy to surmount
potential barrier
• Absorption of n sufficient in
233U 235U 239Pu … fissile nuclei
• Fission energy released ~ 200 MeV
• Energetic fission fragments
• 2 à 3 prompt neutrons released upon fission
Nuclear fission
Nuclear Fission + products
Ref: Duderstadt & Hamilton
Practical Fission Fuels
1
0
n
A1
z
X   Az X  → fission
Ref: Lamarsh NRT
fissile U-233
fissile U-235
fissile Pu-239
BNEN NRT 2009-2010
William D’haeseleer
6
Practical Fission Fuels
From these,
235
only 92
U appears in nature (0.71%)
The other fissile isotopes must be “bred”
out of
out of
Th-232
U-238
(for U-233)
(for Pu-239)
7
Practical Fission Fuels
Fertile nuclei
Nuclei that are not easily “fissile” (see further)
but that produce fissile isotopes
after absorption of a neutron
8
Practical Fission Fuels
* Thorium-uranium
n  23290Th   + 23390Th
1
0
β (22 min)
233
91
- not much used so far
- but large reserves of Th-232
Pa
β (27 d)
233
92
U
Fissile by slow (thermal) neutron
- new interest because of ADS
(cf. Rubbia)
9
Practical Fission Fuels
* Uranium-Plutonium
239
n  238
U


+
92
92 U
1
0
β (23 min)
239
93
Np
β (2.3 d)
- up till now mostly used for weapons
- is implicitly present in U-reactors
- now also used as MOX fuels
239
94
Pu
Fissile by slow
(thermal) neutron
- the basic scheme for “breeder reactors”
10
Practical Fission Fuels
Fissionable nuclei
Th-232 and U-238 fissionable with threshold
energy
U-233, U-235 & Pu 239 easily fissionable = “fissile”
-- see Table 3.1 -11
Practical Fission Fuels
1
0
n
A1
z
X   Az X  → fission
Eth=1.4 MeV
Th-232
fissionable
U-238
fissionable
Eth=0.6MeV
BNEN NRT 2009-2010
William D’haeseleer
12
Fission Chain Reaction
Chain reaction
235
U
Fission Chain Reaction
• k= multiplication factor
• k= (# neutrons in generation i) /
(# neutrons in generation i-1)
• k= 1  critical reactor
• k>1  supercritical
• k<1 subcritical
Critical mass
• Critical mass is amount of mass of fissile
material, such that
Neutron gain due to fission
=
Neutron losses due to leakage & absorption
• Critical mass
= minimal mass for stationary fission regime
Probability for fission
Logarithmic
scale !
Comparison fission cross section U-235 and U-238 [Ref Krane]
BNEN NRT 2009-2010
William D’haeseleer
16
Cross Section of Fissionable Nuclei
• Thermal cross section
Important for “fissile” nuclei, is the so-called
thermal cross section
 at 0.025 eV
th
f
-- See Table 3.2 -17
Cross Section of Fissionable Nuclei
18
Cross Section of Fissionable Nuclei
• Absorption without fission
σγ for these nuclei ~ other nuclei
 behaves like 1/v for small v
at low En, inelastic scattering non existing
 only competition between
-fission
-radiative capture
19
Cross Section of Fissionable Nuclei
Define


capture to fission ratio
f
20
Cross Section of Fissionable Nuclei
α > 1 more chance for radiative capture
U-235
α < 1 more chance for fission
21
Cross Section of Fissionable Nuclei


f
Note
 a     f
22
Cross Section of Fissionable Nuclei
Then with


f
Relative probability fission =
f
1

 f   1 
Relative probability rad. capture =



 f   1 
23
Thermal reactors
• Belgian fission reactors are “thermal
reactors”
• Neutrons, born with <E>=2MeV to be
slowed down to ~ 0.025 eV
• By means of moderator:
– Light material: hydrogen, deuterium, water
graphite
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products
generally radioactive
Dominantly
neutron rich
Mostly β- decay
The products of fission: neutrons
→ Besides fission also absorption

capture to fission ratio
Recall  
f

In U-235:
15% for low En
1
Therefore:
f
v
v

a 1 
See table 3.2
    f
η=number of n ejected per n absorbed in the “fuel”
30
The products of fission: neutrons
f
v
v

a 1 
31
The products of fission: neutrons
f
v
v

a 1 
η(E) for
U-233, U-235, Pu-239 &
Pu-241
Ref: Duderstadt & Hamilton
BNEN NRT 2009-2010
William D’haeseleer
32
The products of fission: neutrons
f
v
v

a 1 
To be compared with
curve for α (cfr before)
33
Ref: Duderstadt & Hamilton
The products of fission: neutrons
η usually also defined for mixture U-235 and U-238

v(25)  f (25)
a (25)  a (28)
 
f
i
 Ni  f i
 a i  Ni  a i
for material i
for material i
34
Enrichment
• Natural U consist of 99.3% 238U & 0.7% 235U
• NU alone cannot sustain chain reaction
• NU in heavy water moderator D2O can be
critical (CANDU reactors)
• Light water (H2O) moderated reactors need
enrichment of fissile isotope 235U
• Typically in thermal reactors 3-5% 235U
enrichment
• For bombs need > 90% enrichment
Production of transurans
Evolution
of 235U content
and Pu isotopes
in typical LWR
Production of transurans
Reactor power & burn up
● Fission Rate
= # fissions per second
given: a reactor producing P MW
fission rate
P 106 J / s

ER 106 1.6 1019 J
 P
 6.25 1018 
 ER
 1
s

 P 
 5.4 1023 
 fissions/day
 ER 
Reactor power & burn up
● Burn up
= amount of mass fissioned per unit time
 Burn up = fission rate * mass of 1 atom
 PA 
Burn up = 0.895 
 gram/day
 ER 
 A 6.0210  gram
23
for A = 235 ; ER = 200 MeV … Burn Up = 1P gram/day
! For a reactor of 1 MW, 1 gram/day U-235 will be fissioned !
Reactor power & burn up
Hence, burn up
0.895
PA
gram/day
ER
Amount of fuel fissioned
But fuel consumption is larger
→ because of radiative capture
a
Total absorption rate =
 fission rate
f
 1    fission rate
Reactor power & burn up
consumption rate
PA
0.895 1   
gram/day
ER
Energy “production” per fissioned amount of fuel:
MWD/tonne
- assume pure U-235, and assume that all U-235 is fissioned;
- then: energy “production” 1MWD/g = 106 MWD/tonne
- but also radiative capture only 8 x 105 MWD/tonne
- but also U-238 in “fuel”  in practice ~ 20 to 30 x 10³ MWD/tonne
(however, recently more)
~ 50 to 60 x 103 MWD/tonne
Actinide Buildup [Ref: CLEFS CEA Nr 53]
Total U
Total Pu
955 746
941 026
923 339
9 737
11 338
13 000
Composition of spent fuel
• Typical for LWR:
Fission Products [Ref: CLEFS CEA Nr 53]
TOTAL
33,6
46,1
61,4
Fission Products [Ref: CLEFS CEA Nr 53]
Category
UOX 33 GWa/tUi
Enr 3.5%
Amount kg/tUi
Uranium
Plutonium
UOX 45 GWa/tUi
Enr: 3.7%
Amount kg/tUi
UOX 60 GWa/tUi
Enr: 4,5%
Amount kg/tUi
955.746
941.026
923.339
9.737
11.338
13.0
61.4
FP
33.6
46.1
TOTAL
999.083
998.464
997.739
Remainder converted to energy via E=∆m c2
Delayed neutrons
• Recall 2 à 3 prompt neutrons, released
after ~10-14 sec
• Thermalized after ~1 μsec
• Absorption after ~200 μs ~ 10-4 s
• Difficult to control
• Nature has foreseen solution!
Delayed Neutrons
• Recall β decay from some fission products
Neutron emission after β decay
After β decay, if energy excited state daughter
larger than “virtual energy” (binding energy
weakest bound neutron) in neighbor:
Then
n emission
rather than
γ emission
Called “delayed neutrons”
Delayed neutrons
• Small amount of delayed neutrons suffices
(fraction ~0.0065) to allow appropriate
control of reactor
• Easy to deal with perturbations