Neutron pairing with medium polarization beyond the Landau approximation

Abstract

We revisit the long-standing problem of the superfluid transition temperature Tc in dilute neutron matter. It is well known that Tc is strongly affected by medium polarization effects (screening) which modify the pairing interaction in the medium. We study these effects within the random-phase approximation (RPA). It turns out that the widely used Landau approximation is sufficient only at densities below about 0.002 fm −3 . At higher densities, the full RPA leads to stronger screening than the Landau approximation.

Pairing in pure neutron matter

“…In these diagrams, the interaction Ṽ shown by the dotted lines is meant to be antisymmetrized, 12| Ṽ |34 = 12|V |34 − 12|V |43 , i.e., it includes also the exchange graphs which are not drawn. [34] and of our own work [36], respectively. The turquoise triangles, purple points, and green squares are QMC results of Gandolfi et al [37], Abe and Seki [38], and Gezerlis and Carlson [39], respectively.…”

“…It is seen that the two screening calculations [34,36] do still not quite agree with each other. We will come back to a more detailed discussion of these calculations below.…”

“…There have been many attempts to calculate the induced interactions in the literature [30][31][32][33][34][35][36]. Especially the earlier calculations [30,31] found an extremely strong suppression of the gap.…”

Low-Density Neutron Matter and the Unitary Limit

“…It is known from a general argument (see e.g., references [44][45][46]), which applies to any dilute fermionic system, that the pair correlations of fermions interacting with a large scattering length differ from what is considered in the conventional BCS theory. Corrections due to pair correlations in the normal phase of neutron matter have been considered by several authors [47][48][49][50][51][52] using the Nozières-Schmitt-Rink approach [46], which is the simplest one that interpolates correctly between the BCS and BCE limits. BCS-BEC crossover effects and the existence, above the critical temperature T c for the transition to the superfluid state, of a pseudo-gap in neutron matter have been also recently studied within the in-medium T-matrix formalism by Durel and Urban in reference [53].…”

Low-density neutron matter and the unitary limit

“…[42][43][44]), which applies to any dilute fermionic system, that the pair correlations of fermions interacting with a large scattering length differ from what is considered in the conventional BCS theory. Corrections due to pair correlations in the normal phase of neutron matter have been considered by several authors [45][46][47][48][49][50] using the Nozières-Schmitt-Rink approach [44], which is the simplest one that interpolates correclty between the BCS and BCE limits. BCS-BEC crossover effects and the existence, above the critical temperature T c for the transition to the superfluid state, of a pseudo-gap in neutron matter have been also recently studied within the in-medium Tmatrix formalism by Durel and Urban in Ref.…”