Finiteness of Multi-body Neutrino Exchange Potential Energy in Neutron Stars

The multi-body neutrino potential energy is analytically estimated for a spherical neutron star with a vector potential model for neutrinos. We show that the self-energy and the neutrino number of the neutron star coincide with the semi-classical values in the large volume limit, and confirm that there is no catastrophe in neutron stars with massless neutrinos.