Neutron--Proton Pairing Correlations in a Single $l$-shell Model

A Márquez Romero,J Dobaczewski,A Pastore

doi:10.5506/aphyspolb.49.347

Abstract

The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.

Highlights

In an analogous way to electrons in superconducting metals, nucleons in nuclei form Cooper pairs, and pairing is a significant feature of nuclear structure [1]
A suitable mean-field description of pairing correlations is given by the Hartree–Fock– Bogoliubov (HFB) method, where the particle–hole and particle–particle channels are treated on the same footing [4]
The article is organized as follows: in Section 2 we present the theoretical background of an exact algebraic model for the pairing correlations, HFB formalism, and isocranking technique

Summary

Introduction

In an analogous way to electrons in superconducting metals, nucleons in nuclei form Cooper pairs, and pairing is a significant feature of nuclear structure [1]. Only pairing correlations among like-particles are considered. Pastore wave-functions at the Fermi surfaces of both species, cf [2, 3]. A suitable mean-field description of pairing correlations is given by the Hartree–Fock– Bogoliubov (HFB) method, where the particle–hole and particle–particle channels are treated on the same footing [4]. Because of the affinity of the orbitals that protons and neutrons occupy at the Fermi surface, their wave-functions overlap and a consistent meanfield theory needs to include the np mixing in both the particle–hole [5, 6] and particle–particle channels. The article is organized as follows: in Section 2 we present the theoretical background of an exact algebraic model for the pairing correlations, HFB formalism, and isocranking technique.

Formalism

HFB formalism with neutron–proton mixing

Cranking in isospin space

Results

Conclusions and perspectives