$^1S_0$ pairing for neutrons in dense neutron matter induced by a soft pion

TL;DR

This paper investigates neutron pairing in dense neutron matter near the pion condensation point, showing that soft neutral pions induce a pairing gap with unique oscillatory potential characteristics.

Contribution

It introduces a model where soft neutral pions induce a pairing force, leading to $^1S_0$ neutron pairing in dense matter near the pion condensation threshold.

Findings

Neutron pairing gap $$ occurs near the pion condensation point.

Soft pion induced potential exhibits oscillatory behavior in coordinate space.

The pairing gap shows strong momentum dependence.

Abstract

The possibility of neutron pairing in the $^1S_0$ channel is studied for dense neutron matter in a vicinity of the $\pi^0$ condensation point. The $^1S_0$ pairing gap $\Delta$ is shown to occur in a model with a pairing force induced by the exchange of a soft neutral pionic mode. The soft pion induced potential $V_{\pi}(r)$ is characterized by an attenuating oscillatory behavior in coordinate space, while in momentum space all $S$-wave matrix elements $V_{\pi}(p,p')$ are positive. The solution of the gap equation reveals strong momentum dependence.