1
Fission
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
2
Nuclear Fission
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3
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DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
4
Fission timeline - I
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5
Fission timeline - II
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
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which nuclei become fission unstable,
i.e.,Induced
the point
How Does
Fission Occur?
pulsion of the protons outweights the attractive nature
More detailed calculation of fission process using liquid drop model:
Nuclear Fission
6
dering the surface and the Coulomb energy during the
is the activation energy: height of barrier above ground
deformed the surface energy increases, whileEfthe
state
ormation leads to an energetically more favourable
Liquid drop models provides intuitive picture of fission
Activation energy creates a deformation of the nucleus
ifferent stages of a fission reaction:
Deformation becomes extreme
Results in nucleus splitting into 2
aneously
e
tial in the
eous
for
the
hed line.
deformation
11
Dr Eram Rizvi
Nuclear Physics and Astrophysics - Lecture 15
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DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
7
7
Fission activation energy
del
mo
rop
id d
liqu
238U
(~6 MeV)
?
shell closure effects
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission barrier
8
Fission activation energy
V=Ec+Es
Fission energy QF
Fission parameter Z2/A
U
Fission barrier U:
U(r)
V |max V |r
0
e.g. 235U
U
U
Qf > 0:
Fission is energetically favoured
nuclei with Z > 114 and A > 270
deformation
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13
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
9
Nuclear Fission:
nuclear vs. Coulomb
1. The fission of a heavy nucleus requires a total
input energy of about 7 to 8 MeV to initially
overcome the strong force which holds the
nucleus into a spherical or nearly spherical
shape
2. A deformation it into a two-lobed ("peanut")
shape
3. The lobes separate from each other, pushed by
their mutual positive charge to a critical
distance, beyond which the short range strong
force can no longer hold them together
4. The process of their separation proceeds by the
energy of the (longer range) electromagnetic
repulsion between the fragments. The result is
two fission fragments moving away from each
other ( + a few neutrons )
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Liquid drop model
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10
© Ichikawa
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission barrier
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
11
© Ichikawa
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission barrier
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
12
© Ichikawa
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
13
Nuclear Fission:
octupole
shapes
18 of nuclear surfaces
II. The Fission Barrier
0.0
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
0.4
0.8
1.2
a2
1.6
2.0
2.4
quadrupole
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Global Properties of Atomic Nuclei
spontaneous fission
Fissibility parameter (Bohr & Wheeler, 1939)
[
ELDM ( def ) = E S ( 0) BS ( def ) ! 1+ 2x ( BC ( def ) ! 1)
ES (def )
BS ( def ) =
,
ES ( 0)
]
EC (def )
BC (def ) =
EC (cross
0) sections
Fission
EC ( 0)
Z2 / A
Z2
x = Spontaneous
= 2
"fission
2ES (0) ( Z / A)crit 50 A
Fission cross sections
half-life systematics vs. x
fissibility
Spontaneous fission half-life systematics
vs. x
parameter
The classical droplet stays
stable and spherical for x<1.
For x>1, it fissions immediately.
For 238U, x=0.8.
V(s)
EB
5–10 MeV
Sh e
ll
de
o
m
l
several
hundred n
tio
MeV
rec
cor
deformation
NUCS 342 (Lecture 28)
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
14
April 4,
2011 28)
13 / 29
NUCS 342
(Lecture
(Sw
ki)
c
e
iat
The LDM alone
cannot produce
stable deformations!
Shell correction!!!
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Lifetimes for spontaneous fission
15
For neutron-rich nuclei
Tsf can drastically change
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
16
Mass distribution of fission fragments
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
discrepancies are probably caused by shortcomings of the evaluated files due to
insufficient experimental information, e.g. for 229Th(nth,f) and 255Fm(nth,f).
17
Mass distribution of fission fragments
Nuclear mass distributions of fission fragments from
thermal neutron-induced fission. Measured or
evaluated data (black lines) are compared with
predictions (red and green lines).
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5
U fission fragment yields
Number of protons Z
Fission fragments for
18
235U
239
235
Pu
U
238
232
U
Th
Number of neutrons N
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Distribution of fission neutrons
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19
© Krane, Introductory nuclear physics
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20
Neutron spectrum distribution for thermal fission
235U
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Delayed neutrons from decay of
E
37
93Rb
21
38
Z
6 (MeV)
Neutron emission
0
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission cross sections for thermal neutrons
22
A+1 Activation
energy (MeV)
Cross section (b)
FISSILE
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission cross sections for thermal neutrons
Cross section (b)
23
A+1 Activation
energy (MeV)
FERTILE
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Effect of pairing on excitation energies
24
The binding energy of 236U is increased by an amount δ (~ 0.56 MeV); the excitation
energy is correspondingly increased by δ over what it would be in the absence of
pairing. In the case of 238U, the energy of the ground-state before capture is lowered
by δ, and as a result the energy of the capture state is correspondingly lower. The
excitation energy is therefore reduced by δ relative to its value without the pairing
force term. The difference in excitation energies between 235U + n and 238U + n is
therefore 2δ or 1.1 MeV
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Energy distribution of fission fragments for
thermal fission of 235U
25
light
fragments
heavy
fragments
T1
m2
=
T2
m1
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
26
Mass distribution of fission fragments for thermal
fission of transuranic elements
linear increase
shell closure effects
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Dependence of average masses of heavy and light
fission fragments on mass of fissioning nucleus
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27
© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Shell effects on thePupotential barrier
28
240
Energy
240Pu
1938 - Hahn & Strassmann
1939 Meitner & Frisch
1939 Bohr & Wheeler
1940 Petrzhak & Flerov
Distortion ε
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Energy
Shell effects on the potential barrier
29
Distortion ε
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© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission isomers
30
Energy
Fission isomers are states in the
secondary potential well. They
have a higher probability to
fission compared with the
ordinary ground state
because they must penetrate a
much thinner potential barrier.
fission
γ
Distortion ε
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Energy
31
fission resonances
There are many closely spaced states in the
first well and a few broad widely separated
states in the second well. Fission resonances
occur where states in the first well match in
energy (and in spin-parity) with states in the
second well. If we reach these selected states
in the first well, we will observe them to
fission with high probability.
CORSO DI FISICA NUCLEARE - PAOLO FINELLI
Distortion ε
© Krane, Introductory nuclear physics
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
32
Fission barriers
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33
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© Ichikawa
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
34
Two fission paths exist: one
asymmetric path and one
symmetric path. The
symmetric path has a higher
fission saddle point and the
more elongated shapes in
the valley beyond the saddle
point indicate that total
fragment kinetic energies in
the symmetric mode are
lower than in the
asymmetric mode. For
excitation energies just
above the symmetric saddle
the ridge separating the two
valleys is high enough to
keep the two modes well
separated.
Two fission paths exist: one asymmetric path
and one symmetric path. The symmetric path
has a higher fission saddle point and the more
elongated shapes in the valley beyond the saddle
point indicate that total fragment kinetic
energies in the symmetric mode are lower than
in the asymmetric mode. The ridge separating
the two valleys is certainly not high enough to
permit two well-separated modes to evolve.
Möller et al., Nature 409, 785 (2001)
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35
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© Ichikawa
DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
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