Collective modes of the order parameter in a triplet superfluid neutron liquid

TL;DR

This paper analyzes the spectrum of collective excitations in triplet superfluid neutron matter, identifying one Goldstone mode and two internal vibration modes, with implications for understanding neutron star superfluidity.

Contribution

It provides a detailed derivation and solution of dispersion equations for collective modes in anisotropic triplet superfluid neutron matter, including both unitary and nonunitary excitations.

Findings

Only one Goldstone mode associated with gauge symmetry breaking.

No additional Goldstone modes for rotational symmetry breaking.

Identification of two internal vibration modes at specific frequencies.

Abstract

The complete spectrum of collective modes of the triplet order parameter in the superfluid neutron matter is examined in the BCS approximation below the pair-breaking threshold. The dispersion equations both for the unitary and nonunitary excitations are derived and solved in the limit of $q\rightarrow0$ by taking into account the anisotropy of the energy gap for the case of $P$-wave pairing. By our analysis, there is only one Goldstone mode which is associated with the broken gauge symmetry. We found no additional Goldstone modes associated with the broken rotational symmetry but found that the oscillations of the total angular momentum are qualitatively similar to the "normal-flapping" mode in the A-phase of superfluid Helium. There are also two collective modes associated with internal vibrations of the structure of the order parameter oscillating with $\omega(T=0) =1.20\Delta_{0}$ and $\omega(T=0) =0.61\Delta_{0}$.