Analytically solvable model of charge dispersion in nuclear fission

Abstract

Using the asymmetric two-center shell model potentials in parametrized forms, the time-dependent Schr\"odinger equation is solved analytically for the charge dispersion yields. We obtain a Gaussian function, characterized by a most probable charge and the width of the distribution. The hypothesis of an unchanged charge density and a minimum potential energy are given as limiting cases. Calculations are made for $^{236}\mathrm{U}$ and $^{252}\mathrm{Cf}$.NUCLEAR REACTIONS Nuclear fission, fragmentation theory, two-center shell model, time-dependent Schr\"odinger equation, analytical solution, Gaussian charge distribution, most-probable charge, unchanged charge density and minimum potential energy postulates, $^{236}\mathrm{U}$, $^{252}\mathrm{Cf}$.