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.

In-medium enhancement of the modified Urca neutrino reaction rates

We calculate modified Urca neutrino emission rates in the dense nuclear matter in neutron star cores. We find that these rates are strongly enhanced in the beta-stable matter in regions of the core close to the direct Urca process threshold. This enhancement can be tracked to the use of the in-medium nucleon spectrum in the virtual nucleon propagator. We describe the in-medium nucleon scattering in the non-relativistic Bruckner-Hartree-Fock framework taking into account two-body as well as the effective three-body forces, although the proposed enhancement does not rely on a particular way of the nucleon interaction treatment. Finally we suggest a simple approximate expression for the emissivity of the n-branch of the modified Urca process that can be used in the neutron stars cooling simulations with any nucleon equation of state of dense matter.Comment: 8 pages, 3 figures; accepted for publication in PLB. In v.2 misprint in eq.(9) corrected and discussion of cooling curves expande

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

Surface properties of nuclear pairing with the Gogny force in a simplified model

Surface properties of neutron-neutron (T=1) pairing in semi-infinite nuclear matter in a hard wall potential are investigated in BCS approximation using the Gogny force. Surface enhancement of the gap function, pairing tensor and correlation energy density is put into evidence.Comment: 16 pages; 4 figures ; submitted to Phys. Lett.

In medium T-matrix for nuclear matter with three-body forces - binding energy and single particle properties

We present spectral calculations of nuclear matter properties including three-body forces. Within the in-medium T-matrix approach, implemented with the CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we compute the energy per particle in symmetric and neutron matter. The three-body forces are included via an effective density dependent two-body force in the in-medium T-matrix equations. After fine tuning the parameters of the three-body force to reproduce the phenomenological saturation point in symmetric nuclear matter, we calculate the incompressibility and the energy per particle in neutron matter. We find a soft equation of state in symmetric nuclear matter but a relatively large value of the symmetry energy. We study the the influence of the three-body forces on the single-particle properties. For symmetric matter the spectral function is broadened at all momenta and all densities, while an opposite effect is found for the case of neutrons only. Noticeable modification of the spectral functions are realized only for densities above the saturation density. The modifications of the self-energy and the effective mass are not very large and appear to be strongly suppressed above the Fermi momentum.Comment: 20 pages, 11 figure

Octupole deformation properties of the Barcelona-Catania-Paris energy density functionals

We discuss the octupole deformation properties of the recently proposed Barcelona-Catania-Paris (BCP) energy density functionals for two sets of isotopes, those of radium and barium, where it is believed that octupole deformation plays a role in the description of the ground state. The analysis is carried out in the mean field framework (Hartree- Fock- Bogoliubov approximation) by using the axially symmetric octupole moment as a constraint. The main ingredients entering the octupole collective Hamiltonian are evaluated and the lowest lying octupole eigenstates are obtained. In this way we restore, in an approximate way, the parity symmetry spontaneously broken by the mean field and also incorporate octupole fluctuations around the ground state solution. For each isotope the energy of the lowest lying $1^{-}$state and the $B(E1)$ and $B(E3)$ transition probabilities have been computed and compared to both the experimental data and the results obtained in the same framework with the Gogny D1S interaction, which are used here as a well established benchmark. Finally, the octupolarity of the configurations involved in the way down to fission of $^{240}$Pu, which is strongly connected to the asymmetric fragment mass distribution, is studied. We confirm with this thorough study the suitability of the BCP functionals to describe octupole related phenomena.Comment: 13 pages, 13 figure

Accurate nuclear masses from a three parameter Kohn-Sham DFT approach (BCPM)

Given the promising features of the recently proposed Barcelona-Catania-Paris (BCP) functional \cite{Baldo.08}, it is the purpose of this paper to still improve on it. It is, for instance, shown that the number of open parameters can be reduced from 4-5 to 2-3, i.e. by practically a factor of two. One parameter is tightly fixed by a fine-tuning of the bulk, a second by the surface energy. The third is the strength of the spin-orbit potential on which the final result does not depend within the scatter of the values used in Skyrme and Gogny like functionals. An energy rms value of 1.58 MeV is obtained from a fit of these three parameters to the 579 measured masses reported in the Audi and Waspra 2003 compilation. This rms value compares favorably with the one obtained using other successful mean field theories. Charge radii are also well reproduced when compared with experiment. The energies of some excited states, mostly the isoscalar giant monopole resonances, are studied within this model as well.Comment: 23 pages, 12 figure

Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals

I discuss the inadequacy of the "projected density" prescription to be used in density dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that at least for the restoration of spatial symmetries like rotations, translations or parity the above prescription yields catastrophic results for the energy that drive the intrinsic wave function to configurations with infinite deformation, preventing thereby its use both in projection after and before variation.Comment: To be published as a contribution to J. Phys G, Special Issue, Focus Section: Open Problems in Nuclear Structur