BCS approximation to the effective vector vertex of superfluid fermions

Abstract

We examine the effective interaction of nonrelativistic fermions with an external vector field in superfluid systems. In contrast to the complicated vertex equation, usually used in this case, we apply the approach which does not employ an explicit form of the pairing interaction. This allows to obtain a simple analytic expression for the vertex function only in terms of the order parameter and other macroscopic parameters of the system.We use this effective vertex to analyze the linear response function of the superfluid medium at finite temperatures. At the time-like momentum transfer, the imaginary part of the response function is found to be proportional to V 4 F , i.e. the energy losses through vector currents are strongly suppressed. As an application, we calculate the neutrino energy losses through neutral weak currents caused by the pair recombination in the superfluid neutron matter at temperatures lower than the critical one for the 1 S 0 pairing. This approach confirms a strong suppression of the neutrino energy losses as predicted in Ref. [2].

Elementary excitations in homogeneous neutron star matter

“…Of course, the static-electron approximation cannot be kept for the whole energy range and in general one has to consider the exact strength function: the full response function given by the matrix (4) has to be calculated in its complete form. This is what we will do in the rest of the article and is in line with previous studies on neutrino interactions in neutron-star matter [2][3][4][5][6][7][8][9][10]. Our discussion on the static approximation was intended only to assess its validity and limitation.…”

Superfluid response and the neutrino emissivity of baryon matter: Fermi-liquid effects

“…This process was suggested [1] many years ago as an efficient mechanism for cooling of neutron stars in some ranges of temperature and/or matter density. The interest in this process has been recently revived [2][3][4][5][6] in connection with the fact that the existing theory of thermal neutrino radiation from superfluid neutron matter leads to a rapid cooling of the neutron star crust, which is in dramatic discrepancy with the observed data of superbursts [7,8]. It was realized that a better understanding of an efficiency of the neutrino emission in the pair recombination is necessary to explain modern observations.…”

Neutrino emissivity of anisotropic neutron superfluids

“…According to modern investigations [4][5][6][7][8], the neutrino radiation caused by the pairing of baryons into singlet state is strongly suppressed, and the dominant neutrino emission, at the long-cooling epoch, occurs from the triplet-correlated condensate of superfluid neutrons which, as expected, exists in the superdense core of the star. Neutrino energy losses owing to the triplet PBF processes have been initially derived in Ref.…”