11,935 research outputs found
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
A simple model for the microscopic effective pairing interaction
The microscopic effective pairing interaction in the -channel is
investigated for two different values of the chemical potential 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 .Comment: LaTeX, 8 pages, 6 ps-figure
Surface behaviour of the pairing gap in semi-infinite nuclear matter
The -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 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
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
Dispersive effects in neutron matter superfluidity
The explicit energy dependence of the single particle self-energy (dispersive
effects), due to short range correlations, is included in the treatment of
neutron matter superfluidity. The method can be applied in general to strong
interacting fermion systems, and it is expected to be valid whenever the
pairing gap is substantially smaller than the Fermi kinetic energy. The results
for neutron matter show that dispersive effects are strong in the density
region near the gap closure.Comment: 9 pages, 4 ps figure
Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential
The gap equation in the -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 turned out to be
very sensitive to the cutoff in the momentum space in the equation
for the effective interaction. It is necessary to take to guarantee 1% accuracy for . The gap equation itself is
solved directly, without any additional approximations. The solution reveals
the surface enhancement of the gap 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
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 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 between 0.4 and
0.8 fm. It is found that the Equation of State is determined by the
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
fm does not indicate any pathological behavior of the
neutron Equation of State.Comment: 17 pages, 7 figures. To be published in Phys. Rev.
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