Neutrino mean free path and in-medium nuclear interaction

Neutrinos produced during the collapse of a massive star are trapped in a nuclear medium (the proto-neutron star). Typically, neutrino energies (10-100 MeV) are of the order of nuclear giant resonances energies. Hence, neutrino propagation is modified by the possibility of coherent scattering on nucleons. We have compared the predictions of different nuclear interaction models. It turns out that their main discrepancies are related to the density dependence of the k-effective mass as well as to the onset of instabilities as density increases. This last point had led us to a systematic study of instabilities of infinite matter with effective Skyrme-type interactions. We have shown that for such interactions there is always a critical density, above which the system becomes unstable.Comment: 4 pages, 4 figures, Proceedings of the 17th Divisional Conference on Nuclear Physics in Astrophysics (NPDC17), 30th September - 4th October 2002, ATOMKI, Debrecen, Hungary, to appear in Nuclear Physics

Extended Skyrme interaction (II): ground state of nuclei and of nuclear matter

We study the effect of time-odd components of the Skyrme energy density functionals on the ground state of finite nuclei and in nuclear matter. The spin-density dependent terms, which have been recently proposed as an extension of the standard Skyrme interaction, are shown to change the total binding energy of odd-nuclei by only few tenths of keV, while the time-odd components of standard Skyrme interactions give an effect that is larger by one order of magnitude. The HFB-17 mass formula based on a Skyrme parametrization is adjusted including the new spin-density dependent terms. A comprehensive study of binding energies in the whole mass table of 2149 nuclei gives a root mean square (rms) deviation of 0.575 MeV between experimental data and the calculated results, which is slightly better than the original HFB-17 mass formula. From the analysis of the spin instabilities of nuclear matter, restrictions on the parameters governing the spin-density dependent terms are evaluated. We conclude that with the extended Skyrme interaction, the Landau parameters $G_0$ and $G_0^\prime$ could be tuned with a large flexibility without changing the ground-state properties in nuclei and in nuclear matter.Comment: 18 pages, 4 tables, 6 figure

Extended Skyrme interaction (I): spin fluctuations in dense matter

Most of the Skyrme interactions are known to predict spin or isospin instabilities beyond the saturation density of nuclear matter which contradict predictions based on realistic interactions. A modification of the standard Skyrme interaction is proposed so that the ferromagnetic instability is removed. The new terms are density dependent and modify only the spin p-h interaction in the case of spin-saturated system. Consequences for the nuclear response function and neutrino mean free path are shown. The overall effect of the RPA correlations makes dense matter more transparent for neutrino propagation by a factor of 2 to 10 depending of the density.Comment: 6 pages, 5 Figs., 2 Tab

Analytical mass formula and nuclear surface properties in the ETF approximation

The problem of the determination of the nuclear surface and surface symmetry energy is addressed in the framework of the Extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. For the case of symmetric nuclei, the resulting ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed, which cannot be simply deduced from the local part of the functional. In the case of asymmetric nuclei, we propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves over previous models and leads to a precision better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.Comment: 27 pages, 18 figures, submitted to PR

Neutrino propagation in Neutron Matter and the Nuclear Equation of State

We study the propagation of neutrinos inside dense matter under the conditions prevailing in a proto-neutron star. Equations of state obtained with different nuclear effective interactions (Skyrme type and Gogny type) are first discussed. It is found that for many interactions, spin and/or isospin instabilities occur at densities larger than the saturation density of nuclear matter. From this study we select two representative interactions, SLy230b and D1P. We calculate the response functions in pure neutron matter where nuclear correlations are described at the Hartree-Fock plus RPA level. These response functions allow us to evaluate neutrino mean free paths corresponding to neutral current processes.Comment: 8 pages, 7 figures, to appear in "The Nuclear Many-Body Problem 2001", NATO Science Series II (Kluwer Academic Publishers

Can realistic interaction be useful for nuclear mean-field approaches?

Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that realistic interaction, which is derived from the base $2N$ and $3N$ interaction, furnish a new theoretical instrument for advancing nuclear mean-field approaches.Comment: 9 pages including 6 figures, published in EPJA 52, 185 (2016

The neutron star inner crust and symmetry energy

The cell structure of clusters in the inner crust of a cold \beta-equilibrium neutron star is studied within a Thomas Fermi approach and compared with other approaches which include shell effects. Relativistic nuclear models are considered. We conclude that the symmetry energy slope L may have quite dramatic effects on the cell structure if it is very large or small. Rod-like and slab-like pasta clusters have been obtained in all models except one with a large slope L.Comment: 16 pages, 5 figure

Densities and energies of nuclei in dilute matter

We explore the ground-state properties of nuclear clusters embedded in a gas of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations. Two alternative representations of clusters are introduced, namely coordinate-space and energy-space clusters. We parameterize their density profiles in spherical symmetry in terms of basic properties of the energy density functionals used and propose an analytical, Woods-Saxon density profile whose parameters depend, not only on the composition of the cluster, but also of the nucleon gas. We study the clusters' energies with the help of the local-density approximation, validated through our microscopic results. We find that the volume energies of coordinate-space clusters are determined by the saturation properties of matter, while the surface energies are strongly affected by the presence of the gas. We conclude that both the density profiles and the cluster energies are strongly affected by the gas and discuss implications for the nuclear EoS and related perspectives. Our study provides a simple, but microscopically motivated modeling of the energetics of clusterized matter at subsaturation densities, for direct use in consequential applications of astrophysical interest.Comment: 20 pages, incl. 12 figure

Spin-isospin Response in Finite Nuclei from an Extended Skyrme Interaction

The magnetic dipole (M1) and the Gamow-Teller (GT) excitations of finite nuclei have been studied in a fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) approach by using a Skyrme energy density functional with spin and spin-isospin densities. To this end, we adopt the extended SLy5st interaction which includes spin-density dependent terms and stabilize nuclear matter with respect to spin instabilities. The effect of the spin-density dependent terms is examined in both the mean field and the spin-flip excited state calculations. The numerical results show that those terms give appreciable repulsive contributions to the M1 and GT response functions of finite nuclei.Comment: 6 pages, 2 figure