Iterative solutions of the ATDHFB equations to determine the nuclear collective inertia

TL;DR

This paper develops an iterative ATDHFB method within Skyrme density functional theory to compute nuclear collective inertia, incorporating time-odd mean fields and verifying results against dynamical cranking predictions.

Contribution

It introduces an iterative solution to the ATDHFB equations that avoids explicit stability matrix calculation and includes self-consistent time-odd mean field contributions.

Findings

The iterative method successfully computes the inertia tensor.

Results agree with dynamical cranking predictions.

The density-derivative term is effectively evaluated numerically.

Abstract

An iterative adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method is developed within the framework of Skyrme density functional theory. The ATDHFB equation is solved iteratively to avoid explicitly calculating the stability matrix. The contribution of the time-odd mean fields to the ATDHF(B) moment of inertia is incorporated self-consistently, and the results are verified by comparing them with the dynamical cranking predictions. The inertia mass tensor is calculated with the density-derivative term evaluated by numerical differentiation.