A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R_c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.Comment: 24 pages, 14 figures; LaTeX, submitted to EPJ

A simple model for the microscopic effective pairing interaction

The microscopic effective pairing interaction in the $^1S_0$-channel is investigated for two different values of the chemical potential $\mu$ starting from the separable form of the Paris NN-potential. It is shown that, within a high accuracy, this effective interaction can be approximated by the off-shell free T-matrix taken at the negative energy $E=2\mu$.Comment: LaTeX, 8 pages, 6 ps-figure

Surface behaviour of the pairing gap in semi-infinite nuclear matter

The $^1S_0$-pairing gap in semi-infinite nuclear matter is evaluated microscopically using the effective pairing interaction recently found explicitly in the coordinate representation starting from the separable form of the Paris NN-potential. Instead of direct iterative solution of the gap equation, a new method proposed by V.A.Khodel, V.V.Khodel and J.W.Clark was used which simplifies the procedure significantly. The gap $\Delta$ obtained in our calculations exibits a strong variation in the surface region with a pronounced maximum near the surface.Comment: 9 pages, 2 ps figure

Surface behaviour of the pairing gap in a slab of nuclear matter

The surface behaviour of the pairing gap previously studied for semi-infinite nuclear matter is analyzed in the slab geometry. The gap-shape function is calculated in two cases: (a) pairing with the Gogny force in a hard-wall potential and (b) pairing with the separable Paris interaction in a Saxon-Woods mean-field potential. It is shown that the surface features are preserved in the case of slab geometry, being almost independent of the width of the slab. It is also demonstrated that the surface enhancement is strengthened as the absolute value of chemical potential $|\mu|$ decreases which simulates the approach to the nucleon drip line.Comment: 12 pages, 2 figure

Microscopic origin of pairing

A brief review of recent progress in the ab intio theory of nuclear pairing is given. Nowdays several successful solutions of the ab intio BCS theory gap equation were published which show that it is a promising first step in the problem. However, the role of many-body correlations that go beyond the BCS scheme remains uncertain and requires further investigations. As an alternative, the semi-microscopic model is discussed in which the effective pairing interaction calculated from the first principles is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei.Comment: Contribution to the Volume 50 years of Nuclear BCS edited by World Scientifi

Non-locality in the nucleon-nucleon interaction and nuclear matter saturation

We study the possible relationship between the saturation properties of nuclear matter and the inclusion of non-locality in the nucleon-nucleon interaction. To this purpose we compute the saturation curve of nuclear matter within the Bethe-Brueckner-Goldstone theory using a recently proposed realistic non-local potential, and compare it with the corresponding curves obtained with a purely local realistic interaction (Argonne v$_{18}$) and the most recent version of the one-boson exchange potential (CD Bonn). We find that the inclusion of non-locality in the two-nucleon bare interaction strongly affects saturation, but it is unable to provide a consistent description of few-body nuclear systems and nuclear matter.Comment: 9 pages, 8 figures; v2: introduction extended, references added, discussion of fig.8 reformulated; to be published in Phys. Rev.

Hybrid protoneutron stars with the MIT bag model

We study the hadron-quark phase transition in the interior of protoneutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the finite-temperature Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ the MIT bag model both with a constant and a density-dependent bag parameter. We calculate the structure of protostars with the equation of state comprising both phases and find maximum masses below 1.6 solar masses. Metastable heavy hybrid protostars are not found.Comment: 12 pages, 9 figures submitted to Phys. Rev.

Protoneutron stars within the Brueckner-Bethe-Goldstone theory

We study the structure of newly born neutron stars (protoneutron stars) within the finite temperature Brueckner-Bethe-Goldstone theoretical approach including also hyperons. We find that for purely nucleonic stars both finite temperature and neutrino trapping reduce the value of the maximum mass. For hyperonic stars the effect is reversed, because neutrino trapping shifts the appearance of hyperons to larger baryon density and stiffens considerably the equation of state.Comment: 11 pages, 7 figures, submitted to Astronomy & Astrophysic