HT 2005 T8: Fission 1
Nuclear Fission• Historic Dates
• Fission Mechanism
• Binding Energy
• Liquid-Drop Model
• Classification of Heavy Nuclides
• Prompt Neutrons
• Delayed Neutrons
HT 2005 T8: Fission 2
Historic Introduction
• 1932: The neutron is discovered byJ.Chadwick → experiments with neutrons.
• 1939: Bombardment of U gives medium-heavy atoms (Ba), O.Hahn and F.Strassman; L.Meitner explains; E.Fermi and co-workers did not recognize fission.
• 1940: Spontaneous Fission (SF) is discovered by G.N.Flerov and K.A.Petrzhak.
• 1947: Ternary fission is discovered by Qian Sabqiang and He Zehui.
HT 2005 T8: Fission 3
Basic Notation
• Z is the number of protons, charge number or atomic number
• N is the number of neutrons
• A = Z + N is the number of nucleons,A is called the mass number
• is a specific nucleus, X – chem. sym.
• is in an excited state
XAZ
*XAZ
HT 2005 T8: Fission 4
Nuclides and Isotopes
• Isotope ≡ atoms with same Z and A
• Nuclide = atoms/nuclei with same Z and A and being in a specific energy state
• Isomer = long-lived excited states, 113
49 Inm
238 238 * 113 11392 92 49 49U U In Inm
Isotope Isotope
HT 2005 T8: Fission 5
Nuclear Energy Production
( ) ( )
1) 0
2)
A A
tot totb b
Q X X Q
E EQ
A AQ Q
HT 2005 T8: Fission 6
Fission Process1710 s 1710 s 1410 s
1 min
Ternary: 1/400
32
60
5.2 0.00650.7%
MeVE
MeVE
util
tot
200180
210190
fission
MeVf 200
( , ) ( , )th ffV
P E vn E dV r r
HT 2005 T8: Fission 7
Compound Nucleus
1 2
A+1A A+1 *
A A
XX X
Y
En
Z Q
A A+1 * A+1
A+1 A+1 * A
X X X
X X X : Photoelectric liberation
Detailed balance theorem: b
b
E
n E
E
E
n
HT 2005 T8: Fission 8
Binding Energy
2
2 2
2
totb n p
n p p n
totb
b n
E c Nm A N m M
c N m m Am M c Am M
E ME c m
A A
1MeV 9MeV
A 70: 8.6MeV(A=70) 7.5MeV(A=238)b
b
E
E
HT 2005 T8: Fission 9
Energy Release
1 2A AA A+1 *
21 2
2
2 1 21 1 2
X X Y
( 1) 1
f
f c
ib
i i n
cf b b b b c
n Z E
E c M M M
EM A m
c
E A E E A E E A A A A
HT 2005 T8: Fission 10
Fission Energy
0 50 100 150 200 250 3000
50
100
150
200
250
300
Mass number A
Ene
rgy
[Me
V]
fE
85
fE
1 2r r0
maxpE
r
THE
maxpE
THE
HT 2005 T8: Fission 11
Liquid-Drop Model
2
2 3 3 41 3
1 2
AZ p nM X Zm A Z m M
Z Z A ZM A A A
A A
Nuclear force
Surface force
Coulomb repulsion
Stability maximum
Spin factor
: 15.8; 17.8; 0.71; 23.7MeV 34,
0, or
34
Even Even
O E E O
Odd Odd
HT 2005 T8: Fission 12
Fissionable Ratio
2 1 3 2
2 3
2
223592
223994
Fissionable ratio:
50 does not exist
U: 35.9
Pu: 36.8
Coulomb
Surface
AZ
E Z A ZE A A
ZX
AZAZA
HT 2005 T8: Fission 13
Excitation Energy
2 2( ) 2 3
1 3 1 2
23.2( 2 ) 0.72 11.215.8 18.3
tot
b
A Z ZE A A D
A A A
kEAX A+1X* 1 ( ) ( )A tot A tot
ex Z b Z b kE E E E
2
2 3Fission: 0.17 5.2 0.117 MeVex TH
ZE E A
A
1 ( ) ( )
1 ( ) ( )
1 ( ) ( )
0
A tot A totex Z b Z b k TH
A tot A totk Z b Z b TH
A tot A totk TH Z b Z b
E E E E E
E E E E
E E E E
HT 2005 T8: Fission 14
Classification of Heavy Nuclides
233 235 239 24192 92 94 94
232 238 240 24290 92 94 94
232 23390 92
238 239 24192 94 94
241 2
Fertile
5294 98
Fissionable
Fissile
Fertil
0 U, U, Pu, Pu:
1MeV Th, U, Pu, Pu:
Th U
U Pu,
e:
Pu
Pu, CfSF:
k
k
E
E
HT 2005 T8: Fission 15
Examples of Fission
235 236 * 144 9192 55 37
235 236 * 140 9492 54 38
235 236 * 136 9992 53 38
U U Cs Rb 1
U U Xe Sr 2
U U I Y
n n
n n
n n
HT 2005 T8: Fission 16
Fission Product Yield
1 2
1 2
A AA
A A
X Y
1 Y
n Z
A M M Z
HT 2005 T8: Fission 17
Kinetic Energy Distribution1 2A AA
2 21 1 2 2
1 2
2 11 1 2 2
1 2
1 2 2 1
2
1
X Y
;2 2
95
140
n Z
M v M vE E
E MM v M v
E M
M M E E
EE
HT 2005 T8: Fission 18
Energy Released in FissionFission
fragmentsReleased energy
[MeV]Range [m]
235U 239PuLighter fragment 99.81 101.82 < 110-4
Heavier fragment 68 73.2 < 110-4
Prompt neutrons 4.8 5.8 *Prompt (t < 1 µs) 7.5 7.0 1.0
Decay products:
-particles 7.8 8.0 < 110-2
– rays (t > 1 s)
6.8 6.2 1.0
neutrino 12.0 12.0
210 215
HT 2005 T8: Fission 19
Prompt Neutrons239Pu
235U
233U
235
239
233
2.432 0.066
2.349 0.1
2.482 0.
50
075
2.41
2.8
2 0.136
44 0.138 E
E
E
E
E
E = 1
HT 2005 T8: Fission 20
Prompt Neutron Energy
1.036
3
0.1 10MeV
( ) 0.453 sinh 2.29
2( ) ; 1.29MeV
E
EkT
E
N E e E
EN E e T
T
HT 2005 T8: Fission 21
Delayed Neutron Precursors87Br
T½s
87Kr* 86Kr + n
β–
β–
87Kr
87Rb
87Sr
6 groups of precursors
decay constant of the -th group
fraction of all (prompt+delayed)
neutrons from the -th group
i
i
i
i
HT 2005 T8: Fission 22
Delayed Neutron Groups
HT 2005 T8: Fission 23
Delayed Neutron Spectra
23592
Delayed neutron fraction:
U 0.0065 0.7%
d
HT 2005 T8: Fission 24
Microscopic Cross Section
θ
x
Δx
cross section σ
Monoenergeticbeam of neutrons
I = n/(sm2 sec)
Reaction rate R = #/(sm2 sec)
detector
detector
Microscopic cross section σ is defined by
R = σ × I × NB
[#/(sm2 sec)] = [sm2] ×[#/(sm2 sec)]×[#/sm2]
Background material
σ/A = Probability per nucleus that a neutron in the beam will interact with it
2[ ]BR Nsm
I
HT 2005 T8: Fission 25
Fission Cross Section
10-3 10-2 10-1 100 101 102 103 104 105 106 107
Energy (eV)
10-2
10-1
100
101
102
103
104
(b
arns
)
235 U
capture
fission
10-3 10-2 10-1 100 101 102 103 104 105 106 107
Energy (eV)
10-2
10-1
100
101
102
103
104
(b
arns
)
239 Pu
capture
fission
10-3 10-2 10-1 100 101 102 103 104 105 106 107
Energy (eV)
10-2
10-1
100
101
102
103
104
(b
arns
)
233 U
capture
fission
10-3 10-2 10-1 100 101 102 103 104 105 106 107
Energy (eV)
10-2
10-1
100
101
102
103
104
(b
arns
)
241 Pu
fission
HT 2005 T8: Fission 26
Resonances
238 239 * 23992 92 92U U Un
2 238 2nm c Mc
( )a E
E
Incident n
23992 U
6.67kE eV
HT 2005 T8: Fission 27
235U vs. 238U
10-3 10-2 10-1 100 101 102 103 104 105 106 107
Energy (eV)
10-2
10-1
100
101
102
103
104
(b
arns
)
235 U
capture
fission
HT 2005 T8: Fission 28
The END