Moments of inertia of rare-earth nuclei and the nuclear time-odd mean fields within exact solutions of the adiabatic theory

TL;DR

This paper presents a systematic analysis of nuclear moments of inertia using Skyrme and Gogny density functional theories, employing a novel exact iterative solution of the ATDHFB equations, showing good agreement with experimental data without adjustable parameters.

Contribution

Introduces a new exact iterative method for solving ATDHFB equations to accurately determine time-odd mean fields and moments of inertia in nuclei.

Findings

Calculated moments of inertia agree with experimental data.

Time-odd mean fields significantly influence rotational properties.

Effective mass correlates with impact of time-odd fields in Skyrme functionals.

Abstract

We systematically analyse the nuclear moments of inertia determined within the Skyrme and Gogny density functional theories. The time-odd mean fields generated by collective rotation are self-consistently determined by a novel exact iterative solution of the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) equations. Although details of the results depend on the functional used, the calculated moments of inertia are in good overall agreement with the experimental data, with no adjustable parameters. To show the essential importance of the time-odd mean fields, we compared the ATDHFB moments of inertia with those obtained from the Inglis-Belyaev formula. For Skyrme density functionals, we find strong correlations between the effective mass and the impact of the time-odd mean fields on the rotational and vibrational collective inertia.