  For a dense stellar matter, which is electrically neutral and in beta
equilibrium, the electron chemical potential, mu_e, will depend nontrivially on
baryonic matter density. It is generally expected that as density increases,
the electron chemical potential will increase and new degrees of freedom will
emerge as mu_e becomes comparable to their energy scales. Assuming the
electrical neutrality and beta equilibrium for the stellar matter, we have
studied how the density dependence of lepton chemical potentials varies for
different models of nuclear interactions that are constrained by experiments up
to nuclear matter density, n_0, but extrapolate differently(unconstrained)
beyond n_0 and calculated the relative abundances of nucleons(neutron and
proton) and leptons(electron and muon) and their density dependencies. We find
that the density dependence of the electron chemical potential is strongly
dependent on the structure of the nuclear symmetry energy relevant to
softness/stfness of the nuclear matter EOS that measures the energy relevant to
the neutron-proton asymmetry. As a consequence, the relative abundances of
neutrons, protons, electrons, and muons as well as the kaon condensation are
strongly dependent on the nuclear symmetry energy. An intriguing result in our
finding is that contrary to the accepted lore, kaon condensation in neutron
star matter, which is considered to be the first phase transitions beyond n_0
and plays a crucial role in certain scenarios of compact-star formation, is not
directly tied to the softness or stiffness of the EOS beyond n_0. This point is
illustrated with a "super-soft" EOS that is fit to the pi^-/pi^+ ratio data of
GSI which excludes kaon condensation at any density.

High Energy Astrophysical Phenomena;Nuclear Theory