Theoretical Investigation on Shell and Deformation Effects on Most Probable Charge in Nuclear Fission

Abstract

The most probable charge Z_P is obtained from Myers & Swiatecki mass formula by analytical method and the Z_P is expressed in terms of the part of simple liquid drop model, the shell and deformation effects. The deviation of the predicted Z_P- value from the Z_P ^UCD based on the unchanged charge distribution can be well interpreted by these terms. The shell effect shows the saw-tooth curve and the deformation effect shows a hump on the range of mass numbers where the shell function S(N, Z) exceeds the critical value Scrit introduced by Myers & Swiatecki. The predicted Z_p- values fairly well agree with the semi-empirical result obtained by Wahl and the fine structure is well reproduced. The magnitudes of the shell and deformation effects in the thermal neutron fission of ²³⁵U are about 0.7 and 0.25 charge units, respectively and both effects act so as to cancell each other.

KEYWORDS:

• fission
• thermal neutron fission
• uranium 235
• most probable charge
• shell effects
• deformation effects
• liquid drop model