Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model

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 quasiparticle model of quarkyonic matter based on the constituent quark model, where the quark and nucleon masses are related by in 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 quasiparticle 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 semiquantitative behavior needed to describe neutron stars.