  The quark-meson coupling model for nuclear matter, which describes nuclear
matter as non-overlapping MIT bags bound by the self-consistent exchange of
scalar and vector mesons, is modified by introducing medium modification of the
bag constant. We model the density dependence of the bag constant in two
different ways: one invokes a direct coupling of the bag constant to the scalar
meson field, and the other relates the bag constant to the in-medium nucleon
mass. Both models feature a decreasing bag constant with increasing density. We
find that when the bag constant is significantly reduced in nuclear medium with
respect to its free-space value, large canceling isoscalar Lorentz scalar and
vector potentials for the nucleon in nuclear matter emerge naturally. Such
potentials are comparable to those suggested by relativistic nuclear
phenomenology and finite-density QCD sum rules. This suggests that the
reduction of bag constant in nuclear medium may play an important role in low-
and medium-energy nuclear physics.
