Axially deformed relativistic Hartree Bogoliubov with separable pairing force

TL;DR

This paper extends a separable pairing interaction to axially deformed relativistic Hartree Bogoliubov theory, demonstrating fast convergence and computational efficiency while accurately describing ground states of deformed nuclei.

Contribution

It introduces a separable pairing force into deformed RHB theory, enabling efficient calculations with maintained accuracy compared to the Gogny force.

Findings

Fast convergence of the separable expansion in deformed nuclei

Reduced computational time for RHB calculations

Good agreement with experimental data for Sm isotopes

Abstract

A separable form of pairing interaction in the $^{1}S_{0}$ channel has been introduced and successfully applied in the description of both static and dynamic properties of superfluid nuclei. By adjusting the parameters to reproduce the pairing properties of the Gogny force in nuclear matter, this separable pairing force is successful in depicting the pairing properties of ground states and vibrational excitations of spherical nuclei on almost the same footing as the original Gogny force. In this article, we extend these investigations for Relativistic Hartree Bogoliubov theory in deformed nuclei with axial symmetry (RHBZ) using the same separable pairing interaction. In order to preserve translational invariance we construct one- and two-dimensional Talmi-Moshinsky brackets for the cylindrical harmonic oscillator basis. We show that the matrix elements of this force can then be expanded in a series of separable terms. The convergence of this expansion is investigated for various deformations. We observe a relatively fast convergence. This allows for a considerable reduction in computing time as compared to RHBZ-calculations with the full Gogny force in the pairing channel. As an example we solve the RHBZ equations with this separable pairing force for the ground states of the chain of Sm-isotopes. Good agreement with the experimental data as well as with other theoretical results is achieved.