S-pairing in neutron matter. I. Correlated Basis Function Theory

TL;DR

This paper extends correlated basis function theory to include realistic nuclear forces and pairing correlations in neutron matter, deriving and solving correlated gap equations to analyze the effects of tensor correlations and many-body effects on superfluid pairing.

Contribution

It develops a generalized correlated BCS framework incorporating tensor and short-range correlations, providing new insights into neutron matter superfluidity.

Findings

Tensor correlations reduce the pairing gap.

Many-body effects decrease the gap compared to simple BCS.

Realistic potentials influence the magnitude of the pairing gap.

Abstract

S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of Ref. [Nucl. Phys. A363 (1981) 383], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two--body order of the cluster expansion, but considering the one--body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated non linear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne v_{14} and Argonne v_{8'}) to stress the role of the tensor correlations and of the many--body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many--body contributions.