  According to the generally accepted phase diagram of QCD, at low temperature
and high baryon number density the chiral phase transition of QCD is of first
order and the co-existence of the Nambu-Goldstone phase and the Wigner phase
should appear. This is in conflict with the usual claim that the quark gap
equation has no Wigner solution in the case of nonzero current quark mass. In
this paper we analyze the reason why the Wigner solution does not exist in the
usual treatment and try to propose a new approach to discuss this question. As
a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the
Wigner solution at finite current quark mass. We then generalize this approach
to the case of finite chemical potential and discuss partial restoration of
chiral symmetry at finite chemical potential and compare our results with those
in the normal NJL model.
