Deformed Potential Energy of Super Heavy Element Z = 120 in a Generalized Liquid Drop Model

Abstract

The macroscopic deformed potential energy for super-heavy elementsZ = 120 is determined within a generalized liquid drop model (GLDM). Theshell correction is calculated with the Strutinsky method and themicroscopic single particle energies are derived from the shell model inan axially deformed Woods–Saxon potential with the same quasi-molecularshape. The total potential energy of a nucleus is calculated by themacro-microscopic method as the summation of the liquid-drop energy andthe Strutinsky shell correction. The theory is adopted to describe thedeformed potential energies in a set of cold reactions. The neck in thequasi-molecular shape is responsible to the deep valley of the fusionbarrier due to shell corrections. In the cold fusion path, thedouble-hump fusion barrier is predicted by the shell correction andcomplete fusion events may occur. The results show that some ofprojectile–target combinations in the entrance channel, such as50Ca+252Fm→ 302120* and58Fe+244Pu→ 302120*, favour the fusionreaction, which can be considered as candidates for the synthesis ofsuper heavy nuclei Z = 120 and the former might be the best cold fusionreaction to produce the nucleus 302120 among them.