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

Super-Symmetry transformation for excitation processes

Quantum Mechanics SUper-SYmmetry (QM-SUSY) provides a general framework for studies using phenomenological potentials for nucleons (or clusters) interacting with a core. The SUSY potentials result from the transformation of the mean field potential in order to account for the Pauli blocking of the core orbitals. In this article, we discuss how other potentials (like external probes or residual interactions between the valence nucleons) are affected by the SUSY transformation. We illustrate how the SUSY transformations induce off-diagonal terms in coordinate space that play the essential role on the induced transition probabilities on two examples: the electric operators and Gaussian external fields. We show that excitation operators, doorway states, strength and sum rules are modified.Comment: 14 pages, 13 figure

On the maximum mass of hyperonic neutron stars

Chiral Lagrangian and quark-meson coupling models of hyperon matter are used to estimate the maximum mass of neutron stars. Our relativistic calculations include, for the first time, both Hartree and Fock contributions in a consistent manner. Being related to the underlying quark structure of baryons, these models are considered to be good candidates for describing the dense core of neutron stars. Taking account of the known experimental constraints at saturation density, the equations of state deduced from these relativistic approaches cannot sustain a neutron star with a mass larger than 1.6-1.66 $M_\odot$

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

Neutrino propagation in dense hadronic matter

Neutrino propagation in protoneutron stars requires the knowledge of the composition as well as the dynamical response function of dense hadronic matter. Matter at very high densities is probably composed of other particles than nucleons and little is known on the Fermi liquid properties of hadronic multicomponent systems. We will discuss the effects that the presence of $\Lambda$ hyperons might have on the response and, in particular, on its influence on the thermodynamical stability of the system and the mean free path of neutrinos in dense matter.Comment: Proceedings of the XX Max Born Symposium ''Nuclear effects in neutrino interactions'', Wroclaw (Poland), December 7-10, 200

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