Scission-point model of nuclear fission based on deformed-shell effects

Abstract

A static model of nuclear fission is proposed based on the assumption of statistical equilibrium among collective degrees of freedom at the scission point. The relative probabilities of formation of complementary fission fragment pairs are determined from the relative potential energies of a system of two nearly touching. coaxial spheroids with quadrupole deformations. The total potential energy of the system at the scission point is calculated as the sum of liquid-drop and shell- and pairing-correction terms for each spheroid, and Coulomb and nuclear potential terms describing the interaction between them. The fissioning system at the scission point is characterized by three parameters---the distance between the tips of the spheroids ($d$), the intrinsic excitation energy of the fragments (${\ensuremath{\tau}}_{\mathrm{int}}$), and a collective temperature (${T}_{\mathrm{coll}}$). No attempt is made to adjust these parameters to give optimum fits to experimental data, but rather, a single choice of values for $d$, ${\ensuremath{\tau}}_{\mathrm{int}}$ and ${T}_{\mathrm{coll}}$ is used in the calculations for all fissioning systems. The general trends of the distributions of mass, nuclear charge, and kinetic energy in the fission of a wide range of nuclides from Po to Fm are well reproduced in the calculations. The major influence of the deformed-shell corrections for neutrons is indicated and provides a convenient framework for the interpretation of observed trends in the data and for the prediction of new results. The scission-point configurations derived from the model provide an interpretation of the saw-tooth neutron emission curve as well as previously unexplained observations on the variation of $\stackrel{-}{\mathrm{TKE}}$ for isotopes of U, Pu, Cm, and Cf; structure in the width of total kinetic energy release as a function of fragment mass ratio; and a difference in threshold energies for symmetric and asymmetric mass splits in the fission of Ra and Ac isotopes. In spite of a number of recognized simplifications in the model, quantitative fits to the data are generally within expected errors of the shell corrections determined by the Strutinski prescription.NUCLEAR REACTIONS, FISSION Po, Ra, U, Cm, Cf, Fm; calculated $A$, $Z$, and KE distribution of fragments. Liquid-drop model. Deformed-shell corrections. Strutinski prescription. Asymmetric and symmetric fission.