  The neutron-proton effective mass splitting in neutron-rich nucleonic matter
reflects the space-time nonlocality of the isovector nuclear interaction. It
affects the neutron/proton ratio during the earlier evolution of the Universe,
cooling of protoneutron stars, structure of rare isotopes and dynamics of
heavy-ion collisions. While there is still no consensus on whether the
neutron-proton effective mass splitting is negative, zero or positive and how
it depends on the density as well as the isospin-asymmetry of the medium,
significant progress has been made in recent yeas in addressing these issues.
We first recall the connections among the neutron-proton effective mass
splitting, the momentum dependence of the isovector potential and the density
dependence of the symmetry energy. We then make a few observations about the
progress in calculating the neutron-proton effective mass splitting using
various nuclear many-body theories and its effects on the isospin-dependence of
in-medium nucleon-nucleon cross sections. Perhaps, our most reliable knowledge
so far about the neutron-proton effective mass splitting at saturation density
of nuclear matter comes from optical model analyses of huge sets of
nucleon-nucleus scattering data accumulated over the last five decades. The
momentum dependence of the symmetry potential from these analyses provide a
useful boundary condition at saturation density for calibrating nuclear
many-body calculations. Several observables in heavy-ion collisions have been
identified as sensitive probes of the neutron-proton effective mass splitting
in dense neutron-rich matter based on transport model simulations. We review
these observables and comment on the latest experimental findings.
