4,005 research outputs found

### 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

### 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

### 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 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

### 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

### 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

### Correlations in Nuclear Matter

We analyze the nuclear matter correlation properties in terms of the pair
correlation function. To this aim we systematically compare the results for the
variational method in the Lowest Order Constrained Variational (LOCV)
approximation and for the Bruekner-Hartree-Fock (BHF) scheme. A formal link
between the Jastrow correlation factor of LOCV and the Defect Function (DF) of
BHF is established and it is shown under which conditions and approximations
the two approaches are equivalent. From the numerical comparison it turns out
that the two correlation functions are quite close, which indicates in
particular that the DF is approximately local and momentum independent. The
Equations of State (EOS) of Nuclear Matter in the two approaches are also
compared. It is found that once the three-body forces (TBF) are introduced the
two EOS are fairly close, while the agreement between the correlation functions
holds with or without TBF.Comment: 11 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

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