Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model

The macroscopic deformed potential energies for super-heavyelements Z=110,112,114,116,118 are determined within ageneralized liquid drop model (GLDM). A quasi-molecular mechanismis introduced to describe the deformation of a nucleus in the GLDMand the shell model simultaneously. The macroscopic energy of atwo-center nuclear system in the GLDM includes the volume-,surface-, and Coulomb-energies, the proximity effect at each massasymmetry, and accurate nuclear radius. The shell correction iscalculated by the Strutinsky method and the microscopic singleparticle energies are derived from a shell model in an axiallydeformed Woods-Saxon potential with the quasi-molecular shape. Thetotal potential energy of a nucleus can be calculated by themacro-microscopic method as the summation of the liquid-dropenergy and the Strutinsky shell correction. The theory is appliedto predict the fusion barriers of the cold reactions⁶⁴Ni+²⁰⁸Pbrightarrow ²⁷²110^*,⁷⁰Zn+²⁰⁸Pbrightarrow ²⁷⁸112^*,⁷⁶Ge+²⁰⁸Pbrightarrow ²⁸⁴114^*,⁸²Se+²⁰⁸Pbrightarrow ²⁹⁰116^*,⁸⁶Kr+²⁰⁸Pbrightarrow ²⁹⁴118^*.It is found that the neck in the quasi-molecular shape is responsiblefor the deep valley of the fusion barrier. In the cold fusion path,double-hump fusion barriers could be predicted by the shellcorrections and complete fusion events may occur.