1. 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

2. 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

3. 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

4. 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=( )
E=6.544 MeV
For 238U
E=( )
E=4.806 MeV
For 233U
E=( )
E=6.843 MeV
Fission requires around 5-6 MeV

5. Fission Process As mass of the fissioning system increases
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

6. 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% final kinetic energy within s

7. 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
Influence of neutron energy observed
235U fission yield

9. Comparison of cumulative and independent yields for A=141
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

10. 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
I and 87-90Br as examples

11. 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

12. 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

13. 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
k>1 at startup

14. 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

15. 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

16. 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

18. Energetics Generalized Coulomb barrier equation
Compare with Q value for fission
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= (2* ) = 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= ( ) = MeV
Realistic case needs to consider shell effects

19. 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

20. Fission Isomers: Double-humped fission barrier
At lower mass numbers, the second barrier is rate-determining, 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

21. 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

22. 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

23. 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.

24. 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?