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.” àtwo highly charged, deformed fragments in contact large Coulomb repulsion accelerates fragments to 90% final kinetic energy within 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 surmounted §as opposed to spontaneous fission, where tunneling through barrier occurs 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 Usually asymmetric mass split §M H /M L  1.4 §due to shell effects, magic numbers

10-4 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 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

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 saddle àasymmetry 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 (E c ) and surface energy of sphere (E s ) àx=E c /2E s * E c =a c Z 2 /A 1/3 *E s =a s A 2/3 From liquid drop model § 239 Pu is § 209 Bi 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 àZ ≥ 98 àHalf-lives changed by a factor *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 252 Cf §MH/ML = § 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 àLocation of heavy peak in the fission remains constant àposition of the light peak increases àHeavy fragment peak at A=132 àpreference 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 238 U §Assume symmetric à Z=46, A=119 *E=46 2 *1.440/(1.8(119 1/3 )2)=175 MeV §and asymmetric fission àZ=35, A=91 àZ=57, A=147 *E=(35)(57)*1.44/(1.8*(91 1/ /3 ))=164 MeV