Analytically solvable model of charge dispersion in nuclear fission

Using the asymmetric two-center shell model potentials in parametrized forms, the time-dependent Schrödinger 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 ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$.