  The Nambu--Jona-Lasinio (NJL) model has been extensively studied by many
researchers. In previous work we have generalized the NJL model to include a
covariant model of confinement. In the present work we consider further
modification of the model so as to reproduce the type of Euclidean-space
momentum- dependent quark mass values obtained in lattice simulations of QCD.
This may be done by introducing a nonlocal interaction, while preserving the
chiral symmetry of the Lagrangian. In other work on nonlocal models, by other
researchers, the momentum dependence of the quark self-energy is directly
related to the regularization scheme. In contrast, in our work, the
regularization is independent of the nonlocality we introduce. It is of
interest to note that the value of the condensate ratio,
$<\bar{s}s>/<\bar{u}d>$, is about 1.7 when evaluated using chiral perturbation
theory and is only about 1.1 in standard applications of the NJL model. We find
that our nonlocal model can reproduce the larger value of the condensate ratio
when reasonable values are used for the strength of the 't Hooft interaction.
(In an earlier study of the $\eta$(547) and $\eta$'(958) mesons, we found that
use of the larger value of the condensate ratio led to a very good fit to the
mixing angles and decay constants of these mesons.) We also study the density
dependence of both the quark condensate and the momentum-dependent quark mass
values. Without the addition of new parameters, we reproduce the density
dependence of the condensate given by a well-known model- independent
expression valid for small baryon density.
