3D TDHFB theory with Gogny force and fission dynamicsof <sup>240</sup>Pu

Abstract

Nuclear fission is one of the most complex processes in nuclear physics, involving a strong interplay between nuclear structure and dynamics, as well as various many-body correlations and fluctuation effects. Systematically theoretical and experimental research on the fission problems is of great significance to clarify the fission mechanism, reveal the complexity of low-energy nuclear dynamics, and test the nuclear model theory based on the nuclear many-body theory. However, despite the huge theoretical effort pursued by several generations of physicists, many crucial facets of this process are still not understood at a fundamental level, warranting further exploration of its dynamics. This is more so when viewed from the microscopic theoretical point of view. In the subject of study on nuclear fission, scission dynamics represents one of the most challenging problems in many-body theory as it plays a crucial role for determining the main properties of fission fragments and the emitted light particles. In the scission and post-scission processes, the fragments can experience a rapid change in shape and thus trigger the non-adiabatic effects coming from couplings between collective and intrinsic degrees of freedom. Therefore, from microscopic point of view, a reasonable description of the entire fission process could be achieved with an adiabatic model describing the slow evolution across the barrier, followed by a non-adiabatic treatment of the scission and post-scission dynamics. In this paper, with the aid of the nuclear mean-field model and Gogny effective nucleon-nucleon interaction, a three-dimensional Cartesian mesh code of time-dependent Hartree-Fock-Bogoliubov theory (Gogny-TDHFB Code for Fission) has been developed for solving the static and/or dynamic equations with isolated or periodic boundary conditions and no further symmetry assumptions. In contrast with the Skyrme HFB, the particle-hole channel and the particle-particle channel are treated on an equal footing in the HFB calculations with the Gogny interaction (Gogny HFB). The code consists of two parts: One is the constrained HFB for calculating the adiabatic fission potential energy surface in the multi-dimensional collective phase space, the other is TDHFB for studying the dynamical process of nuclear fission. In order to describe the extremely large deformation of nuclei in the direction of fission, the basis functions in the spatial grid points of the Lagrange mesh are introduced with respect to the direction of the z -axis, and the deformation harmonic oscillator eigenfunctions are used as the basis functions in the ( x , y ) directions. In the calculation of multi-dimensional potential energy surfaces, the constraints are imposed on expectation values of the multi-pole moments Q lm and the augmented Lagrangian method (ALM) is exploited for multi-constrained calculations. A parallel interface using the message passing interface (MPI) library has been implemented for large-scale calculations on massively parallel computers. Under the help of Gogny-TDHFB Code for Fission and by mainly focusing on the scission process, various aspects including the nuclear fission processes, the multi-dimensional potential energy surface, the configuration of scission point, more importantly, the non-adiabatic dynamics in the course of deformation from saddle to scission and also in post-scission are microscopically investigated in order to make clarification on the fission mechanisms, the nature of scission and some other basic problems. As an example, the spontaneous fission process of 240Pu has been studied. The results on the non-adiabatic dynamics in the course of deformation from saddle to scission and also in post-scission show that the pairing correlation plays crucial roles in the scission dynamics of nuclear fission.