Fission
• Readings: Modern Nuclear Chemistry,
Chapter 11; Nuclear and Radiochemistry,
Chapter 3
• General Overview of Fission
• Energetics
• The Probability of Fission
• Fission Product Distributions
 Total Kinetic Energy Release
 Fission Product Mass Distributions
 Fission Product Charge Distributions
• Fission in Reactors
 Delayed neutron
• Proton induced fission
7-1
Nuclear Fission
• Fission discovered by Otto Hahn and Fritz
Strassman, Lisa Meitner in 1938
 Demonstrated neutron irradiation of
uranium resulted in products like Ba
and La
 Chemical separation of fission
products
• For induced fission, odd N
 Addition of neutron to form even N
 Pairing energy
• In 1940 G. N. Flerov reported that 238U
undergoes fission spontaneously
 half life of round 1016 y
 Several other spontaneous fission
isotopes found
 Z > 90
 Partial fission half lives from
nanoseconds to 2E17 years
7-2
Fission
•
Can occur when enough energy is supplied by the bombarding particle for the Coulomb
barrier to be surmounted

Fast neutron

Proton
• Spontaneous fission occurs by tunneling through barrier
 Similar to alpha decay
• Thermal neutron induced fission from pairing of unpaired neutron

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
7-3
Energetics
Calculations
• Why does 235U undergo neutron
induced fission for thermal
energies?

Where does energy come
from?
• Generalized energy equation
AZ + n A+1Z + E

• For 235U

E=(40.914+8.071)-42.441

E=6.544 MeV
• For 238U

E=(47.304+8.071)-50.569

E=4.806 MeV
• For 233U

E=(36.913+8.071)-38.141

E=6.843 MeV
• Fission requires around 5-6 MeV
7-4
Fission Process
•
•
•
•
•
•
Usually asymmetric mass split
 MH/ML1.4 for uranium and plutonium
 due to shell effects, magic numbers
 Heavy fragment peak near A=132, Z=50, N=82
 Symmetric fission is suppressed by at least two orders of magnitude relative to
asymmetric fission
Occurs in nuclear reactions

Competes with evaporation of nucleons in region of high atomic numbers
As mass of the fissioning system increases

Location of heavy peak in the fission remains constant

position of the light peak increases
Fission Process
Nucleus absorbs energy

Excites and deforms

Configuration “transition state” or “saddle point”
Nuclear Coulomb energy decreases during deformation

Nuclear surface energy increases
Saddle point key condition

rate of change of the Coulomb energy is equal to the rate of change of the
nuclear surface energy

Induces instability that drives break up of nucleus
7-5
Fission Process
• 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%
-20
final kinetic energy within 10 s
7-6
Fission Products
• Fission yield curve varies with fissile isotope
• 2 peak areas for U and Pu thermal neutron induced fission
• Variation in light fragment peak
235U fission yield
• Influence of neutron energy observed
7-7
7-8
Fission
•
•
•
Primary fission products
always on neutron-excess side
of  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 processes to its stable
isobar
Yields can be determined

Independent yield:
specific for a nuclide

Cumulative yield: yield
of an isobar
 Beta decay to
valley of stability

Data for independent
and cumulative yields
can be found or
calculated
For reactors

Emission of several
neutrons per fission
crucial for maintaining
chain reaction

“Delayed neutron”
emissions important in
control of nuclear
reactors
Comparison of cumulative and
independent yields for A=141
http://www-nds.iaea.org/sgnucdat/c2.htm
7-9
Fission products
• Particles form more spherical
shapes
 Converting potential energy
to emission of “prompt”
neutrons
 Gamma emission after
neutrons
 Then  decay
Occasionally one of these
 decays populates a high
lying excited state of a
daughter that is unstable
with respect to neutron
emission
 “delayed” neutrons
 0.75 % of total neutrons
 137-139I and 87-90Br as
examples
7-10
Delayed Neutrons
•
Fission fragments are neutron rich

More neutron rich, more energetic decay

In some cases available energy high enough for leaving the residual
nucleus in such a highly excited state
 Around 5 MeV
 neutron emission occurs
7-11
Delayed Neutrons in Reactors
• Control of fission
 0.1 msec for neutron from fission to react
Need to have tight control
0.1 % increase per generation
* 1.001^100, 10 % increase in 10 msec
• Delayed neutrons useful in control
 Longer than 0.1 msec
 0.65 % of neutrons delayed from 235U
0.26 % for 233U and 0.21 % for 239Pu
• Fission product poisons influence reactors
 135Xe capture cross section 3E6 barns
7-12
Nuclear reactors
• Probable neutron energy from fission is 0.7 MeV
 Fast reactors
 High Z reflector
 Thermal reactors need to slow neutrons
 Water, D2O, graphite
* Low Z and low cross section
• Power proportional to number of available neutrons
 Should be kept constant under changing
conditions
 Control elements and burnable poisons
 k=1 (multiplication factor)
 Ratio of fissions from one generation to the
next
7-13
* k>1 at startup
Fission Process and Damage
•
•
•
•
Neutron spatial distribution is along the direction of motion of the fragments
Energy release in fission is primarily in the form of the kinetic energies
Energy is “mass-energy” released in fission due to the increased stability of the
fission fragments
Recoil length about 10 microns, diameter of 6 nm

About size of UO2 crystal

95 % of energy into stopping power
 Remainder into lattice defects
* Radiation induced creep

High local temperature from fission
 3300 K in 10 nm diameter
7-14
Energetics
• Any nucleus of A> 100 into two nuclei of
approximately equal size is exoergic.
 Why fission at A>230
• Separation of a heavy nucleus into two positively
charged fragments is hindered by Coulomb
barrier
 Treat fission as barrier penetration
Barrier height is difference between
* Coulomb energy between the two
fragments when they are just touching
* the energy released in the fission
process
• Near uranium both these quantities have values
close to 200 MeV
7-15
Energetics
•
200Hg
give 165 MeV for Coulomb energy
between the fragments and 139 MeV for energy
release
 Lower fission barriers for U when
compared to Hg
• Barrier height increases more slowly with
increasing nuclear size compared to fission
decay energy
• Spontaneous fission is observed only among the
very heaviest elements
• Half lives generally decrease rapidly with
increasing Z
7-16
7-17
Energetics
•
Generalized Coulomb barrier equation

Compare with Q value for fission
Vc 
•
•
•
Z 1Z 2e
2
R1  R 2
 0 . 96
Z 1Z 2
1/ 3
1
A
 A
1/ 3
2
MeV
Vc 
Z 1 Z 2 1 . 44
1/ 3
1 . 8 ( A1
 A2 )
1/ 3
Determination of total kinetic energy

Equation deviates at heavy actinides (Md, Fm)
Consider fission of 238U

Assume symmetric
238U119Pd + 119Pd + Q

 Z=46, A=119
* Vc=462*1.440/(1.8(1191/3)2)=175 MeV
* Q=47.3087-(2*-71.6203) = 190.54 MeV

asymmetric fission
238U91Br + 147La + Q

 Z=35, A=91
 Z=57, A=147
* Vc=(35)(57)*1.44/(1.8*(911/3+1471/3))=164 MeV
* Q=47.3087-(-61.5083+-66.8484) = 175.66 MeV
Realistic case needs to consider shell effects
7-18
Fission Isomers
• Some isomeric states in
heavy nuclei decay by
spontaneous fission with
very short half lives

Nano- to
microseconds
• Fissioning isomers are
states in these second
potential wells

Also called shape
isomers

Exists because
nuclear shape
different from that of
the ground state,
• Around 30 fission isomers
are known, from U to Bk
• Induced by neutrons,
protons, deuterons, and a
particles
7-19
Fission Isomers: Double-humped fission
barrier
• At lower mass numbers, the second barrier is ratedetermining, whereas at larger A, inner barrier is rate
determining
• Symmetric shapes are the most stable at two potential
minima and the first saddle, but some asymmetry lowers
second saddle
7-20
Proton induced fission
• Energetics impact fragment
distribution
• excitation energy of the
fissioning system increases

Influence of ground
state shell structure of
fragments would
decrease

Fission mass
distributions shows
increase in symmetric
fission
7-21
Topic Review
• Mechanisms of fission
 What is occurring in the nucleus during fission
• Understand the types of fission
 Particle induced
 Spontaneous
• Energetics of fission
 Q value and coulomb barrier
• The Probability of Fission
 Cumulative and specific yields
• Fission Product Distributions
 Total Kinetic Energy Release
 Fission Product Mass Distributions
7-22
Questions
• Compare energy values for the symmetric and
asymmetric fission of 242Am.
• What is the difference between prompt and
delayed neutrons in fission.
• What is the difference between induced and
spontaneous fission.
• What influences fission product distribution?
• Compare the Coulomb barrier and Q values for
the fission of Pb, Th, Pu, and Cm.
• Describe what occurs in the nucleus during fission.
• Compare the energy from the addition of a neutron
to 242Am and 241Am. Which isotope is likely to
fission from an additional neutron.
7-23
Pop Quiz
• Provide calculations showing why 239Pu can be
fissioned by thermal neutron but not 240Pu.
• Compare the Q value and Coulomb energy (Vc)
from the fission of 239Pu resulting in 138Ba and
101Sr. Is this energetically favored?
7-24