${}^1{S}_0$ pairing for neutrons in dense neutron matter induced by a soft pion

Abstract

The possibility of neutron pairing in the ${}^1{S}_0$ channel is studied for dense neutron matter in a vicinity of the ${\pi }^0$ condensation point. The ${}^1{S}_0$ 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 $V_{\pi }(p,p^{\prime })$ are positive. The solution of the gap equation reveals strong momentum dependence.

Comments: v1: 6 pages, 6 figures, 1 table; v2: 7 pages, 6 figures, 2 tables, frameworks of the work are formulated more clearly, several references are added