A transport model description of Time-Dependent Generator Coordinate under Gaussian overlap approximation

TL;DR

This paper derives a novel transport equation based on the time-dependent generator coordinate method under the Gaussian overlap approximation, enabling the inclusion of non-adiabatic effects and dynamical fluctuations in nuclear fission modeling.

Contribution

It introduces a new transport equation that couples s-body phase space densities with s+1-body densities, advancing the modeling of nuclear dynamics beyond adiabatic approximations.

Findings

The transport equation incorporates non-adiabatic effects and fluctuations.

It couples multiple body phase space densities for detailed dynamics.

Future work includes numerical simulations for fission nuclei.

Abstract

In this work, we derived a transport equation based on a generalized equation of time-dependent generator coordinate method (TDGCM) under the Gaussian overlap approximation (GOA). The transport equation is obtained by using quantum-mechanics phase space distributions under a ``quasi-particle" picture and strategy of Bogoliubov-Born-Green-Kirkood-Yvon (BBGKY) hierarchy. The theoretical advantage of this transport equation is that time evolution of $s$-body phase space density distribution is coupled with $s+1$-body phase space density distributions, and thus, non-adiabatic effects and dynamical fluctuations could be involved by more collective degrees and entanglement of phase space trajectories. In future, we will perform the numerical calculations for fission nuclei after obtaining collective inertia and potential energy surface (PES).