Linear Responses in Time-dependent Hartree-Fock-Bogoliubov Method with Gogny Interaction

TL;DR

This paper introduces a numerical method for integrating the time-dependent Hartree-Fock-Bogoliubov equations with Gogny interaction, demonstrating its effectiveness through applications to small amplitude vibrations in various isotopes.

Contribution

A new numerical approach for TDHFB equations with Gogny interaction is developed and validated on nuclear vibrational modes.

Findings

Conservation of energy, particle number, and center-of-mass confirmed.

Successfully applied to multiple isotopes for quadrupole and dipole vibrations.

Calculated strength functions match expected vibrational properties.

Abstract

A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.