  We explore the effects of a microscopic nuclear three-body force on the
threshold baryon density for kaon condensation in chemical equilibrium neutron
star matter and on the composition of the kaon condensed phase in the framework
of the Brueckner-Hartree-Fock approach. Our results show that the nuclear
three-body force affects strongly the high-density behavior of nuclear symmetry
energy and consequently reduces considerably the critical density for kaon
condensation provided that the proton strangeness content is not very large.
The dependence of the threshold density on the symmetry energy becomes weaker
as the proton strangeness content increases. The kaon condensed phase of
neutron star matter turns out to be proton-rich instead of neutron-rich. The
three-body force has an important influence on the composition of the kaon
condensed phase. Inclusion of the three-body force contribution in the nuclear
symmetry energy results in a significant reduction of the proton and kaon
fractions in the kaon condensed phase which is more proton-rich in the case of
no three-body force. Our results are compared to other theoretical predictions
by adopting different models for the nuclear symmetry energy. The possible
implications of our results for the neutron star structure are also briefly
discussed.

Nuclear Theory