Nuclear pairing from microscopic forces: singlet channels and higher-partial waves

TL;DR

This paper investigates nuclear pairing gaps across various angular momentum channels using realistic chiral potentials, employing a stable numerical method to improve understanding of superfluidity in neutron stars.

Contribution

It applies Khodel's method to calculate pairing gaps in all relevant channels, including singlet and coupled states, with improved numerical stability and agreement with other ab-initio approaches.

Findings

Successful application of Khodel's method to multiple pairing channels

Agreement with existing ab-initio calculations

Provides key data for superfluid neutron star models

Abstract

Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $\chi(p)$ defined by $\Delta(p) = \Delta_F \chi(p)$ and a non-linear algebraic equation for the gap magnitude $\Delta_F = \Delta(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave. Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.