CHEM 312 Lecture 7: 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 bombarding particle for Coulomb
barrier to be surmounted

Fast neutron

Proton
• Spontaneous fission occurs by tunneling through barrier
• Thermal neutron induces fission from pairing of unpaired neutron, energy gain

Nuclides with odd number of neutrons fissioned by thermal neutrons with large
cross sections

follows1/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 + Q

• For 235U

Q=(40.914+8.071)-42.441

Q=6.544 MeV
• For 238U

Q=(47.304+8.071)-50.569

Q=4.806 MeV
• For 233U

Q=(36.913+8.071)-38.141

Q=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
• Location of heavy peak in fission
remains constant for 233,235U and 239Pu
 position of light peak increases
• 2 peak areas for U and Pu thermal
neutron induced fission
• Influence of neutron energy observed
235U
fission yield
7-5
•
•
•
Fission yield distribution varies with
fissile isotope
Heavier isotopes begin to demonstrate
symmetric fission

Both fission products at Z=50 for
Fm
As mass of fissioning system increases

Location of heavy peak in fission
remains constant

position of light peak increases
Fission Process
7-6
Fission products
• Primary fission products
always on neutron-excess
side of  stability
 high-Z elements that
undergo fission have
much larger neutronproton ratios than
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
Comparison of cumulative and
independent yields for A=141
http://www-nds.iaea.org/sgnucdat/c2.htm
7-7
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 Coulomb energy is equal to rate of change of nuclear surface energy

Induces instability that drives break up of nucleus
If nucleus deforms beyond this point it is committed to fission

Neck between fragments disappears

Nucleus divides into two fragments at “scission point.”
 two highly charged, deformed fragments in contact
Large Coulomb repulsion accelerates fragments to 90% final kinetic energy within 10 -20 s
7-8
Fission Process: Delayed Neutrons
•
•
Fission fragments are neutron rich

More neutron rich, more energetic
decay

In some cases available energy high
enough for leaving residual nucleus
in such a highly excited state
 Around 5 MeV
 neutron emission occurs
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 from
fission
 137-139I and 87-90Br as examples
7-9
Delayed Neutron Decay Chains
• For reactors
 Emission of several neutrons per
fission crucial for maintaining chain
reaction
 “Delayed neutron” emissions
important in control of nuclear
reactors
7-10
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
 0.75 % 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
7-11
Nuclear reactors and Fission
• Probable neutron energy from fission is
0.7 MeV

Average energy 2 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 next
* k>1 at startup
7-12
Fission Process and Damage
•
•
•
•
Neutron spatial distribution is along direction of motion of fragments
Energy release in fission is primarily in form of kinetic energies
Energy is “mass-energy” released in fission due to increased stability of 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
7-13
Fission 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
following
* Coulomb energy between two fragments
when they are just touching
* energy released in fission process
• Near uranium both these quantities have values
close to 200 MeV
7-14
Energetics
•
Generalized Coulomb barrier equation

Compare with Q value for fission
Z1Z 2e 2
Z1Z 2
Vc 
 0.96 1/ 3
MeV
1/ 3
R1  R2
A1  A2
•
•
•
Z1Z 21.44
Vc 
1.8( A11/ 3  A21/ 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

Fission would favor symmetric distribution without shell
7-15
Energetics
•
200Hg
give 165 MeV for Coulomb energy
between fragments and 139 MeV for energy
release
 Lower fission barriers for U when
compared to Hg
• Coulomb barrier height increases more slowly
with increasing nuclear size compared to fission
decay energy
• Spontaneous fission is observed only among
very heaviest elements
• Half lives generally decrease rapidly with
increasing Z
7-16
Half lives generally decrease rapidly with increasing Z
7-17
•
•
•
•
Some isomeric states in heavy
nuclei decay by spontaneous
fission with very short half lives

Nano- to microseconds

De-excite by fission process
rather than photon
emission
Fissioning isomers are states in
these second potential wells

Also called shape isomers

Exists because nuclear
shape different from that
of ground state

Proton distribution results
in nucleus unstable to
fission
Around 30 fission isomers are
known

from U to Bk
Can be induced by neutrons,
protons, deuterons, and a
particles

Can also result from decay
Fission Isomers
7-18
Fission Isomers: Doublehumped fission barrier
• At lower mass numbers,
second barrier is ratedetermining, whereas at
larger A, inner barrier is
rate determining
• Symmetric shapes are most
stable at two potential
minima and first saddle, but
some asymmetry lowers
second saddle
7-19
Proton induced fission
• Energetics impact fragment
distribution
• excitation energy of fissioning
system increases

Influence of ground
state shell structure of
fragments would
decrease

Fission mass
distributions shows
increase in symmetric
fission
7-20
Topic Review
• Mechanisms of fission
 What occurs 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
7-21
Questions
• Compare energy values for
the symmetric and
asymmetric spontaneous
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 Q value and Vc
Fission
products
Q (MeV)
Vc (MeV) Q-Vc
(MeV)
121Ag
+
210.95
182.46
28.49
+
203.49
178.28
25.21
121Cd
137Cs
105Zr
Z1Z 21.44
Vc 
1.8( A11/ 3  A21/ 3 )
7-22
Questions
• 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.
• Provide calculations
showing why 239Pu can
be fissioned by thermal
neutrons but not 240Pu
7-23
Questions
• Provide comments on blog
• Respond to PDF Quiz 7
7-24