Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model**The project supported by National Natural Science Foundation of China under Grant Nos. 10235020, 10275094, 10175092, and 10075080 and the State Key Basic Research Program of China under Grant No. G2000077400

Abstract

The macroscopic deformed potential energies for super-heavy elements Z=110,112,114,116,118 are determined within a generalized liquid drop model (GLDM). A quasi-molecular mechanism is introduced to describe the deformation of a nucleus in the GLDM and the shell model simultaneously. The macroscopic energy of a two-center nuclear system in the GLDM includes the volume-, surface-, and Coulomb-energies, the proximity effect at each mass asymmetry, and accurate nuclear radius. The shell correction is calculated by the Strutinsky method and the microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with the quasi-molecular shape. The total potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is applied to predict the fusion barriers of the cold reactions 64Ni+208Pb→ 272110*, 70Zn + 208Pb→ 278112*, 76Ge+208Pb→ 284114*, 82Se+208Pb→ 290116*, 86Kr+208Pb→ 294118*. It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier. In the cold fusion path, double-hump fusion barriers could be predicted by the shell corrections and complete fusion events may occur.