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We investigate effects of thermal and quantum fluctuations of the superfluidorder parameter in $^1S_{0}$ superfluids in neutron stars. We construct aseparable potential to reproduce the $^1S_{0}$ phase shift reconstructed byusing the partial wave analysis from nucleon scattering data. We includesuperfluid fluctuations within a strong-coupling approximation developed byNozi\`eres and Schmitt-Rink and determine self-consistently the superfluidorder parameter as well as the chemical potential. We show that the quantumdepletion, which gives a fraction of noncondensed neutrons at zero temperaturedue to quantum pairing fluctuations, plays an important role not only near thecritical temperature from superfluid states to normal states but also at zerotemperature. We derive the dispersion relation of Anderson-Bogoliubov modesassociated with phase fluctuations, and show also that there is a nonzerofraction of noncondensed components in the neutron number as a result of thestrong-coupling effect. Our results indicate that superfluid fluctuations areimportant for thermodynamic properties in neutron stars.

Strong-coupling effects of pairing fluctuations, and Anderson-Bogoliubov mode in neutron $^1$S$_0$ superfluids in neutron stars