  It has recently been argued that long range forces due to the exchange of
massless neutrinos give rise to a very large self-energy in a dense,
finite-ranged, weakly-charged medium. Such an effect, if real, would
destabilize a neutron star. To address this issue we have studied the related
problem of a massless neutrino field in the presence of an external, static
electroweak potential of finite range. To be precise, we have computed to one
loop the exact vacuum energy for the case of a spherical square well potential
of depth alpha and radius R. For small wells, the vacuum energy is reliably
determined by a perturbative expansion in the external potential. For large
wells, however, the perturbative expansion breaks down. A manifestation of this
breakdown is that the vacuum carries a non-zero neutrino charge. The energy and
neutrino charge of the ground state are, to a good approximation for large
wells, those of a neutrino condensate with chemical potential mu=alpha. Our
results demonstrate explicitly that long-range forces due to the exchange of
massless neutrinos do not threaten the stability of neutron stars.
