  In dense stellar environments, nuclei may become unstable against electron
captures and/or neutron emissions. These processes are of particular importance
for determining the internal constitution of white-dwarf cores and neutron-star
crusts. In this paper, the role of electron exchange and polarization effects
is studied. In particular, the instability condition for the onset of electron
captures and neutron emissions is extended so as to account for electron
exchange and polarization. Moreover, general analytical expressions for the
corresponding density and pressure are derived. The corrections to the
electron-capture threshold in white-dwarf cores are found to be very small.
Likewise, the neutron-drip density and pressure in the crusts of accreting and
nonaccreting neutron stars are only slightly shifted. Depending on the nuclear
mass model employed, electron polarization may change the composition of the
crust of nonaccreting neutron stars. On the other hand, the current
uncertainties in the masses of neutron-rich Kr and Sr isotopes are found to be
more important than electron exchange and polarization effects.
