Gauge angle dependence in TDHFB calculations of ${}^{20}$O + ${}^{20}$O head-on collisions with the Gogny interaction

TL;DR

This paper develops a numerical method to study how the initial gauge angle affects head-on collisions of superfluid ${}^{20}$O nuclei using TDHFB with the Gogny interaction, revealing a sine dependence in neutron flux.

Contribution

The paper introduces a hybrid basis numerical approach for TDHFB calculations of nuclear collisions, analyzing gauge angle effects with detailed dependence on initial conditions.

Findings

Neutron flux across a plane depends sinusoidally on twice the gauge angle.

Trajectories and pairing energies are sensitive to initial gauge angle.

The method effectively captures gauge angle dependence in superfluid nuclear collisions.

Abstract

A numerical method to solve the TDHFB equations by using a hybrid basis of the two-dimensional harmonic oscillator eigenfunctions and one-dimensional Lagrange mesh with the Gogny effective interaction is applied to the head-on collisions of the superfluid nuclei ${}^{20}$O's. Taking the energies around the barrier top energy, the trajectories, pairing energies, and numbers of transferred nucleons are displayed. Their dependence on the relative gauge angle at the initial time is studied by taking typical sample points of the gauge angle. It turned out that the functional form of the flux of the neutrons across a section plane is proportional to the sine of the two times of the gauge angle.