Theory of Charge Dispersion in Nuclear Fissioii

F o r the distribution of nuclear charge in fission, a number of empirical hypotheses such a s that of equal charge distribution, unchanged charge density, and minimum potential energy have been proposed in the past by various authors.' Only recently, Holub, Mustafa, and Schmitt2 have calculated the potential energy sur face fo r the charge vibration in 236U by using the two-spheroid liquid-drop model of Nix and Swiatecki and including the shell effects calculated in the Strutinsky p r e ~ c r i p t i o n . ~ The single-particle s ta tes used to calculate the shell correction a r e those of a one-center Nilsson-type oscillator. In this paper we develop a theory fo r the charge dispersion in nuclear fission by using the concept of the charge-asymmetry coordinate treated a s a dynamical coordinate in the asymmetr ic two-cent e r shell model7ATCSM). The theory is applied to the fission of 236U and there is no f r e e parame t e r to be fitted. We consider the protons and neutrons a s moving in two separate single-particle potentials of the ATCSM (Fig. 1) and define the protonand neutron-asymmetry coordinates, respectively, a s