# Coupling between superfluid neutrons and superfluid protons in the elementary excitations of neutron star matter

## TL;DR

This paper investigates how superfluid neutrons and protons interact in neutron star matter, revealing coupled collective excitations and damping effects that influence stellar phenomena like neutrino emission and cooling.

## Contribution

It introduces a generalized Random Phase Approximation framework to analyze neutron-proton coupling effects in superfluid neutron star matter, ensuring consistency with Ward's identities.

## Key findings

- Coupled neutron-proton collective modes are identified.
- Neutron-proton coupling causes significant damping of excitations.
- High-density conditions lead to more independent neutron and proton excitations.

## Abstract

Several phenomena occurring in neutron stars are affected by the elementary excitations that characterize the stellar matter. In particular, low-energy excitations can play a major role in the emission and propagation of neutrinos, neutron star cooling and transport processes. In this paper, we consider the elementary modes in the star region where both proton and neutron components are superfluid. We study the overall spectral functions of protons, neutrons and electrons on the basis of the Coulomb and nuclear interactions. This study is performed in the framework of the Random Phase Approximation, generalized to superfluid systems. The formalism we use ensures that the Generalized Ward's Identities are satisfied. We focus on the coupling between neutrons and protons. On one hand this coupling results in collective modes that involve simultaneously neutrons and protons, on the other hand it produces a damping of the excitations. Both effects are especially visible in the spectral functions of the different components of the matter. At high density while the neutrons and protons tend to develop independent excitations, as indicated by the spectral functions, the neutron-proton coupling still produces a strong damping of the modes.