Strong-coupling effects of pairing fluctuations, and Anderson-Bogoliubov and Higgs modes in neutron 1S0 superfluids in neutron stars

We investigate effects of thermal and quantum fluctuations of the superfluid order parameter in 1S0 superfluids in neutron stars. We construct a separable potential to reproduce the 1S0 phase shift reconstructed by using the partial wave analysis from nucleon scattering data. We include superfluid fluctuations within a strong-coupling approximation developed by Nozières and Schmitt-Rink and determine self-consistently the superfluid order parameter as well as the chemical potential. We show that the quantum depletion, which gives a fraction of non-condensed neutrons at zero temperature due to quantum pairing fluctuations, plays an important role not only near the critical temperature from superfluid states to normal states but also at zero temperature. We derive the dispersion relation of Anderson-Bogoliubov and Higgs modes associated with phase and amplitude fluctuations, respectively, and show also that there is a nonzero fraction of non-condensed components in the neutron number as a result of the strong-coupling effect. Our results indicate that superfluid fluctuations are important for thermodynamic properties in neutron stars.