10-1

Fission

• General Overview of Fission

• The Probability of Fission The Liquid Drop Model Shell Corrections Spontaneous Fission Spontaneously Fissioning Isomers The Transition Nucleus

• Fission Product Distributions Total Kinetic Energy Release Fission Product Mass Distributions Fission Product Charge Distributions

10-2

Fission• Nucleus absorbs energy

Excites and deforms Configuration “transition state”

or “saddle point” • Nuclear Coulomb energy decreases

during deformation nuclear surface energy increases

• At saddle point,the rate of change of the Coulomb energy is equal to the rate of change of the nuclear surface energy

• 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 10-20 s.

• Particles form more spherical shapes converting potential energy to

emission of “prompt” neutrons then gamma

10-3

Fission• Competes with evaporation of nucleons and small nucleon

clusters in region of high atomic numbers

• When enough energy is supplied by the bombarding particle for the Coulomb barrier to be surmountedas opposed to spontaneous fission, where tunneling

through barrier occurs• Nuclides with odd number of neutrons fissioned by thermal

neutrons with large cross sectionsfollow 1/v law at low energies, sharp resonances at

high energies• Usually asymmetric mass split

MH/ML1.4

due to shell effects, magic numbers

10-4

Fission• Primary fission products always on neutron-excess side

of stabilityhigh-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

• Probability of primary product having atomic number Z:

• Emission of several neutrons per fission crucial for maintaining chain reaction

• “Delayed neutron” emissions important in control of nuclear reactors

c

ZZexp

c

1)Z(P

2p

10-5

• Double-humped fission barrier at lower mass numbers, the second barrier is rate-determining,

whereas at larger A, inner barrier is symmetric shapes are the most stable at the two potential minima

and the first saddle, but some asymmetry lowers second saddleasymmetry moves second saddle toward larger h

(thinner neck), which leads to increased Coulomb repulsion energies for separating fragments

10-6

Fission Probability

• Based on balance of energy Coulomb energy (Ec) and surface energy of sphere

(Es)

x=Ec/2Es

* Ec=acZ2/A1/3

* Es=asA2/3

• From liquid drop model 239Pu is 36.97 209Bi is 32.96

10-7

Spontaneous Fission

• Rare decay mode discovered in 1940 Observed in light actinides increases in importance

with increasing atomic number until it is a stability limiting decay mode Z ≥ 98 Half-lives changed by

a factor 1029

* Uranium to Fermium

Decay to barrier penetration

10-8

10-9

Fission Fragments

10-10

Fission Fragments

10-11

Fission Fragments

• Asymmetric fission product distribution• thermal neutron induced fission of uranium and plutonium and 252Cf

MH/ML =1.3-1.5 liquid drop model would predict that the greatest energy release

and the most probable would be symmetric This situation is shown in Figure 11-

• Symmetric fission is suppressed by at least two orders of magnitude relative to asymmetric fission as mass of the fissioning system increases

Location of heavy peak in the fission remains constant position of the light peak increases Heavy fragment peak at A=132 preference for asymmetric fission due to stability at Z=50,

N=82, * a doubly magic spherical nucleus.

10-12

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

10-13

Energetics

• Determination of total kinetic energy Equation deviates at heavy actinides (Md, Fm)

• Consider fission of 238U Assume symmetric

Z=46, A=119

* E=462*1.440/(1.8(1191/3)2)=175 MeV and asymmetric fission

Z=35, A=91 Z=57, A=147

* E=(35)(57)*1.44/(1.8*(911/3+1471/3))=164 MeV