  Recent years have seen extensive applications of the Nambu--Jona-Lasinio
(NJL) model in the study of matter at high density. There is a good deal of
interest in the predictions of diquark condensation and color
superconductivity, with suggested applications to the study the properties of
neutron stars. As the researchers in this field note, the NJL model does not
describe confinement, so that one is limited to the study of the deconfined
phase, which may set in at several times nuclear matter density. Recently, we
have extended the NJL model to include a covariant confinement model. In the
present work our goal is to include a phenomenological model of deconfinement
at finite matter density, using some analogy to what is known concerning
"string breaking" and deconfinement at finite temperature. Various models may
be used, but for this work we choose a specific model for the density
dependence of the parameters of our confining interaction. We perform
relativistic random-phase-approximation (RPA) calculations of the properties of
the $\pi(138), K(495), f_0(980), a_0(980)$ and $K_0^*(1430)$ mesons and their
radial excitations. In the model chosen for this work, there are no mesonic
states beyond about $2\rho_{NM}$, where $\rho_{NM}$ is the density of nuclear
matter. This inability of the model to support hadronic excitations at large
values of the density is taken as a signal of deconfinement. In addition to the
density dependence of the confining interaction, we use the density-dependent
quark mass values obtained in either the SU(2) or SU(3)-flavor versions of the
NJL model.
