Strong-coupling effects of pairing fluctuations, and Anderson-Bogoliubov mode in neutron $^1$S$_0$ superfluids in neutron stars

TL;DR

This paper studies the impact of strong-coupling pairing fluctuations on neutron superfluids in neutron stars, revealing significant quantum depletion and collective mode effects that influence thermodynamics.

Contribution

It develops a strong-coupling theoretical framework for neutron superfluids, incorporating fluctuations and deriving their effects on superfluid properties and collective excitations.

Findings

Quantum depletion is significant even at zero temperature.

Superfluid fluctuations affect thermodynamic properties in neutron stars.

Derived dispersion relation for Anderson-Bogoliubov modes.

Abstract

We investigate effects of thermal and quantum fluctuations of the superfluid order parameter in $^1S_{0}$ superfluids in neutron stars. We construct a separable potential to reproduce the $^1S_{0}$ phase shift reconstructed by using the partial wave analysis from nucleon scattering data. We include superfluid fluctuations within a strong-coupling approximation developed by Nozi\`eres and Schmitt-Rink and determine self-consistently the superfluid order parameter as well as the chemical potential. We show that the quantum depletion, which gives a fraction of noncondensed neutrons at zero temperature due to quantum pairing fluctuations, plays an important role not only near the critical temperature from superfluid states to normal states but also at zero temperature. We derive the dispersion relation of Anderson-Bogoliubov modes associated with phase fluctuations, and show also that there is a nonzero fraction of noncondensed components in the neutron number as a result of the strong-coupling effect. Our results indicate that superfluid fluctuations are important for thermodynamic properties in neutron stars.