Macro-microscopic Calculation of Five-dimensional Potential Energy Surface for 234U Fission

Abstract

A key question about the fission process of a heavy nucleus is to probe the nuclear potential energy landscape and its evolution from the single groundstate compound nucleus over the top of the fission barrier and further to the scission point, finally terminating in the formation of fission fragments. In this work, a macromicroscopic model was established to calculate the fission properties for uranium elements. The total potential energy as a function of deformation parameters was divided into a smoothly varying macroscopic part and a microscopic part representing quantum effect correction. The nuclear shape was described by the SwiateckiNix threequadraticsurface (3QS) parametrization, which could accurately represent the nuclear shape evolution all the way from the ground state to the scission configuration. The macroscopic part of the nuclear potential energy was calculated by the LSD (LublinStrasbourg drop) model. In the microscopic part, the foldedYukawa potential was used as the independent particle potential, whereas the shell correction method of Strutinsky and the smooth BCS pairing model were used to calculate the deformation energy of the compound nucleus. For the 234U compound nucleus, a potential energy surface (PES) with 5 906 250 lattice points was calculated and analyzed in a fivedimensional deformation space given by the 3QS parametrization. The watershed algorithm was used to search the fission paths on the fivedimensional PES for 234U. For different nuclear shapes, there are two well separated fission paths, asymmetric and symmetric, which share the same inner barrier and deviate at the point of second minimum, and finally end at two different points of the PES. During reaching scission points, the asymmetric fission pass will cross a new barrier with lower height than the outer barrier, but the height of the new barrier needs to be crossed is higher than the outer barrier for the symmetric fission path. The heights of fission potential barrier and the nuclear shapes at special positions, such as the saddle point and the scission point, were given for 234U. The comparison of our results, the inner barrier height and outer barrier height, with available experimental data and other’s theoretical results confirms the reliability of our calculations. The calculated results of this work, especially the outer barrier in the large deformation area, are in good agreement with the experimental data of RIPL library and Moller’s calculation, which means that the 3QS parametrization might be closer to the real nuclear shape than the generalized Lawrence shape description specially in the large deformation region.

Keywords

• macro-microscopic model
• barrier height
• saddle point