Medium polarization effects on neutron matter superfluidity

Abstract

We solve the 'So gap equation for neutron matter using an effective interaction based on the Argonne VM potential that includes effects of the polarization (RPA) graphs. We find a substantial reduction of the gap, and a slight extension of the domain of superfluidity to larger densities. We demonstrate the inadequacy of using the weak coupling approximation. The superfluid properties of neutron matter are an important issue for the understanding of neutron star physics [ 11. This problem is usually studied in the BCS theory [2] or using the Green functions techniques [ 3-51. Both yield the same gap equation for the modified quasi-particle spectrum, but the latter has the advantage of providing a more or less systematic way of building the pairing interaction in a series of the bare interaction. The first term is the bare potential itself [4,6]. At this level, some agreement exists between the various results in the literature, provided the gap equation is solved exactly and a realistic nucleonnucleon interaction is used [ 7-91. The necessity of going beyond this approximation is rather clear, as the next approximations involve the polarisability (with respect to density and spin-density fluctuations), which is expected, as for nuclear matter, to play an important role. Yet there was initially no clear guideline to select the most important higher order graphs, until the Babu-Brown theory [ lo] for the effective interaction appeared. These authors showed that the exchange of the WA particle-hole series between two particles is not a good description of the effective interaction, as it produces a too strong polarizability, if not an instability, of nuclear matter. They proposed to include into the particle-hole channel, the so-called induced interaction, which guarantees antisymmetry and Landau sum rules, and which makes the nuclear matter Landau parameter Fe less negative.As for the 'SO pairing in neutron matter, the first calculations along these lines were rather confusing, as they predicted an enhancement [ 11,12 ]

3P2−3F2Baldo1, Elgarøy2, Engvik3 et al. 1998Phys. Rev. CSelf Cite15481971View full textAdd to dashboardCite

“…The results of different groups are in close agreement on the 1 S 0 pairing gap values and on its density dependence, which shows a peak value of about 3 MeV at a Fermi momentum close to k F ≈ 0.8 fm −1 [2][3][4][5]. All these calculations adopt the bare NN interaction as the pairing force, and it has been pointed out that the screening by the medium of the interaction could strongly reduce the pairing strength in this channel [5][6][7]. However, the issue of the many-body calculation of the pairing effective interaction is a complex one and still far from a satisfactory solution.…”

Superfluid properties of the inner crust of neutron stars

“…Recently, ab initio quantum Monte Carlo calculations have been carried out for low-density infinite neutron matter (k F,n 0.5 fm −1 ) [48], with an effort to understand the differences with other Monte Carlo results [49][50][51]. A quenching of the mean-field pairing gap is predicted, resulting in a larger pairing gap than what previous calculations found [52][53][54][55][56].…”

Screening effects on1S0pairing in neutron matter

“…In that work the momentum dependence is mostly neglected that amounts to overestimate the suppression. Closer to the present approach is the polarization potential [4,13] calculated from the induced interaction theory [14], which gives substantially the same gap when treated within the Landau parameter approximation [15]. Finally,we should mention a parallel study on finite nuclei [16], where the polarization potential is given by the coupling to surface vibrations.…”

“…However, it is planned to parallel this work for nuclear matter in the near future. In the past we have mainly been concentrating on the influence of either dynamic self-energy corrections [2] (see also [3]) or vertex corrections to the neutron matter pairing problem [4]. All investigations in this direction invariably led to the conclusion that dynamic self-energy corrections yield a quite strong reduction of 1 S 0 pairing in neutron matter.…”