  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.
