Collective Modes in a Superfluid Neutron Gas within the Quasiparticle Random-Phase Approximation

TL;DR

This paper investigates collective excitations in a superfluid neutron gas at zero temperature using the quasiparticle random phase approximation, revealing an ungapped mode consistent with the Goldstone theorem and its impact on neutron star crust thermodynamics.

Contribution

It introduces a realistic density-dependent pairing interaction within the QRPA framework to study collective modes in superfluid neutron matter.

Findings

Identifies an ungapped collective mode consistent with Goldstone's theorem.

Shows the mode's linear dispersion at low momentum matching the hydrodynamic speed of sound.

Calculates the mode's contribution to the specific heat of neutron star crusts.

Abstract

We study collective excitations in a superfluid neutron gas at zero temperature within the quasiparticle random phase approximation. The particle-hole residual interaction is obtained from a Skyrme functional, while a separable interaction is used in the pairing channel which gives a realistic density dependence of the pairing gap. In accordance with the Goldstone theorem, we find an ungapped collective mode (analogous to the Bogoliubov-Anderson mode). At low momentum, its dispersion relation is approximately linear and its slope coincides with the hydrodynamic speed of sound calculated with the Skyrme equation of state. The response functions are compared with those obtained within the Landau approximation. We also compute the contribution of the collective mode to the specific heat of the neutron gas, which is relevant for the thermodynamic properties of the inner crust of neutron stars.