Calculation of Fission Potential Energy Surface and Fragment Mass Distribution Based on Fourier Nuclear Shape Parametrization

The fission potential energy surface is the basis of describing structural properties and dynamics of fission nuclei. The shape parameters constructed by Fourier series were used to describe the nuclear shape from ground state to the scission configuration in fission process. Multidimensional fission potential energy surfaces of 236U were calculated with the macroscopicmicroscopic method, in which the macroscopic energy part was obtained by the LublinStrasbourg Drop (LSD) model and the microscopic shell and pairing energy correction part were calculated based on the YukawaFolded (YF) single particle potential. The evolutions of the potential energy surface with different collective degrees of freedom (elongation of the nucleus, massasymmetry of leftright fragments and the neck thickness) were studied. The results show that the neck degree of freedom plays an important role in the evolution of nucleus from one fission path to two fission paths. With the calculated potential energy surface, the fission fragment mass distributions were obtained by using a three-dimensional collective model based on the BornOppenheimer approximation with two adjustable parameters zeropoint energy and half width of neck breaking probability. The calculated results are in good agreement with the experimental data, especially, the peak positions of the light and heavy fragments mass distribution are consistent with the experimental results. The effects of zeropoint energy and half width of neck breaking probability on fission fragment mass distributions also have been analyzed. The results show that zeropoint energy mainly affects the mass distribution width of fission fragment and the half width of neck breaking probability has an effect on the peak position of fragment mass distribution. The effect of temperature on potential energy surface of 236U has also been investigated in the Fourier nuclear shape parametrization framework. The height of the fission inner and outer barrier in symmetric fission path reduced with temperature increasing. The general topography of potential energy surface changes obviously as temperature increases and the main reason is the effect of microcorrection energy gradually decreases with the increasing of temperature. Finally, the higher temperature will lead to the disappearance of asymmetric fission valley on the potential energy surface. The dynamic calculated results based on the temperaturedependent potential energy surface show that the asymmetric fission contribution of fission fragment mass distribution gradually reduces and the symmetric fission contribution gradually dominates the fission fragment mass distribution with higher temperature, and these dynamic calculated results are consistent with the trend of temperaturedependent potential energy surface, as well as in accordance with the experimental observation.