  Typical nuclear equations of state and a quark bag model, surprisingly, allow
compact stars with alternate layers of neutrons and quarks. One can determine
on the basis of the Gibbs free energy which phase, nuclear or quark, is
energetically favorable. Using the nuclear equation of state of Wiringa, and a
quark equation of state given by Freedman and McLerran, the allowed quark
parameter space for such layer stars is searched. This paper differs from past
work in that configurations are found in which quark matter is located exterior
and interior to shells of nuclear matter, i.e., dependent on quark parameters,
a star may contain several alternating layers of quark and nuclear matter.
Given the uncertainty in the quark parameter space, one can estimate the
probability for finding pure neutron stars, pure quark stars (strange stars),
stars with a quark core and a nucleon exterior, or layer stars. Several layer
models are presented. The physical characteristics, stability, and results of a
thorough search of the quark parameter space are presented.
