Finite-range separable pairing interaction in Cartesian coordinates

A M Romero,A Pastore,J Dobaczewski

doi:10.1088/1742-6596/1643/1/012144

Abstract

Within a simple SO(8) algebraic model, the coexistence between isoscalar and isovector pairing modes can be successfully described using a mean-field method plus restoration of broken symmetries. In order to port this methodology to real nuclei, we need to employ realistic density functionals in the pairing channel. In this article, we present an analytical derivation of matrix elements of a separable pairing interaction in Cartesian coordinates and we correct errors of derivations available in the literature. After implementing this interaction in the code HFODD, we study evolution of pairing gaps in the chain of deformed Erbium isotopes, and we compare the results with a standard density-dependent contact pairing interaction.

Highlights

Pairing correlations play a crucial role in understanding nuclear phenomena, such as, for example, the odd-even mass staggering [1]
We present an analytical derivation of matrix elements of a separable pairing interaction in Cartesian coordinates and we correct errors of derivations available in the literature
In a recent article [4], using the mean-field approximation [5] applied to a simple SO(8) model [6, 7], we showed that it is possible to obtain the coexistence of the two types of condensate

Summary

Introduction

Pairing correlations play a crucial role in understanding nuclear phenomena, such as, for example, the odd-even mass staggering [1]. The main conclusion of our work is that the crucial ingredient to observe such a coexistence is to apply the variational principle for a projected (symmetry-restored) mean-field states This encouraging result motivated us to implement the same technique within a realistic nuclear density-functional theory (DFT). The first step in this direction is to choose a realistic pairing functional that is capable of reproducing basic properties of the isovector pairing and at the same time allows for opening the isoscalar pairing channel To this end, in this article we discuss derivations and implementations related to the finite-range separable pairing interaction [8, 9]. 3. Separable pairing interaction we present a detailed derivation of the matrix elements of the separable interaction in a Cartesian basis. An alternative derivation of the analogous matrix elements of more general separable interactions was given in Ref. [16]

Pairing gaps

Findings

Conclusions