# Dynamical Derivation of the Momentum Space Shell Structure for Quarkyonic Matter

## TL;DR

This paper develops a quasi-particle model of Quarkyonic Matter, revealing a shell structure in momentum space that emerges at high densities, with implications for neutron star physics.

## Contribution

It introduces a novel quasi-particle model incorporating hard core nucleon interactions to describe the shell structure in Quarkyonic Matter.

## Key findings

- Nucleonic shell forms above a critical density
- Shell becomes thinner at higher densities
- Model exhibits behavior relevant to neutron star structure

## Abstract

The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + \Delta. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard core size, and for large densities becomes a thin shell. We explore the basic features of such a model, and argue this model has the semi-quantitative behaviour needed to describe neutron stars.