The role of the boundary conditions in the Wigner-Seitz approximation applied to the neutron star inner crust

The influence of the boundary conditions used in the Wigner-Seitz approximation applied to the neutron star inner crust is examined. The generalized energy functional method which includes neutron and proton pairing correlations is used. Predictions of two versions of the boundary conditions are compared with each other. The uncertainties in the equilibrium configuration (Z,R_c) of the crust, where Z is the proton charge and R_c the radius of the Wigner-Seitz cell, correspond to variation of Z by 2 -- 6 units and of R_c, by 1 -- 2 fm. The effect of the boundary conditions is enhanced at increasing density. These uncertainties are smaller than the variation of Z and R_c coming from the inclusion of pairing. The value of the pairing gap itself, especially at high density, can depend on the boundary condition used.Comment: LaTeX, 11 pages, 3 figures, to be published in Phys. Lett.

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

Nuclear matter hole spectral function in the Bethe-Brueckner-Goldstone approach

The hole spectral function is calculated in nuclear matter to assess the relevance of nucleon-nucleon short range correlations. The calculation is carried out within the Brueckner scheme of many-body theory by using several nucleon-nucleon realistic interactions. Results are compared with other approaches based on variational methods and transport theory. Discrepancies appear in the high energy region, which is sensitive to short range correlations, and are due to the different many-body treatment more than to the specific N-N interaction used. Another conclusion is that the momentum dependence of the G-matrix should be taken into account in any self consistent approach.Comment: 7 pages, 5 figure

Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential

The gap equation in the $^1S_0$-channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap $\Delta$ turned out to be very sensitive to the cutoff $K_{max}$ in the momentum space in the equation for the effective interaction. It is necessary to take $K_{max}=160-180 fm^{-1}$ to guarantee 1% accuracy for $\Delta$. The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap $\Delta$ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of $\Delta$ turned out to be rather close to the empirical values for heavy atomic nuclei.Comment: 17 pages, 12 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

Neutron matter at low density and the unitary limit

Neutron matter at low density is studied within the hole-line expansion. Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and 0.8 fm$^{-1}$. It is found that the Equation of State is determined by the $^1S_0$ channel only, the three-body forces contribution is quite small, the effect of the single particle potential is negligible and the three hole-line contribution is below 5% of the total energy and indeed vanishing small at the lowest densities. Despite the unitary limit is actually never reached, the total energy stays very close to one half of the free gas value throughout the considered density range. A rank one separable representation of the bare NN interaction, which reproduces the physical scattering length and effective range, gives results almost indistinguishable from the full Brueckner G-matrix calculations with a realistic force. The extension of the calculations below $k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the neutron Equation of State.Comment: 17 pages, 7 figures. To be published in Phys. Rev.

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

The maximum and minimum mass of protoneutron stars in the Brueckner theory

We study the structure of protoneutron stars within the finite-temperature Brueckner-Bethe-Goldstone theoretical approach, paying particular attention to how it is joined to a low-density nuclear equation of state (EOS). We find a slight sensitivity of the minimum value of the protoneutron star mass on the low-density equation of state, whereas the maximum mass is hardly affected.Comment: 8 pages, 8 figure

Building scars for integrable systems

It is shown, by means of a simple specific example, that for integrable systems it is possible to build up approximate eigenfunctions, called {\it asymptotic eigenfunctions}, which are concentrated as much as one wants to a classical trajectory and have a lifetime as long as one wants. These states are directly related to the presence of shell structures in the quantal spectrum of the system. It is argued that the result can be extended to classically chaotic system, at least in the asymptotic regime