Extended Skyrme Equation of State in asymmetric nuclear matter

We present a new equation of state for infinite systems (symmetric, asymmetric and neutron matter) based on an extended Skyrme functional constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces with very good accuracy the main features of microscopic calculations and it is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest

Linear response in infinite nuclear matter as a tool to reveal finite size instabilities

Nuclear effective interactions are often modelled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd-even or rotating nuclei. In this article, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.Comment: Based on talk presented at 18th Nuclear Physics Workshop "Maria and Pierre Curie", 2011, Kazimierz, Polan

Spurious finite-size instabilities in nuclear energy density functionals: spin channel

It has been recently shown, that some Skyrme functionals can lead to non-converging results in the calculation of some properties of atomic nuclei. A previous study has pointed out a possible link between these convergence problems and the appearance of finite-size instabilities in symmetric nuclear matter (SNM) around saturation density. We show that the finite-size instabilities not only affect the ground state properties of atomic nuclei, but they can also influence the calculations of vibrational excited states in finite nuclei. We perform systematic fully-self consistent Random Phase Approximation (RPA) calculations in spherical doubly-magic nuclei. We employ several Skyrme functionals and vary the isoscalar and isovector coupling constants of the time-odd term $\mathbf{s}\cdot \Delta \mathbf{s}$ . We determine critical values of these coupling constants beyond which the RPA calculations do not converge because RPA the stability matrix becomes non-positive.By comparing the RPA calculations of atomic nuclei with those performed for SNM we establish a correspondence between the critical densities in the infinite system and the critical coupling constants for which the RPA calculations do not converge. We find a quantitative stability criterion to detect finite-size instabilities related to the spin $\mathbf{s}\cdot \Delta \mathbf{s}$ term of a functional. This criterion could be easily implemented into the standard fitting protocols to fix the coupling constants of the Skyrme functional

Fitting Skyrme functionals using linear response theory

Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.Comment: Proceeding of 19th Nuclear Physics Workshop "Marie & Pierre Curie" Kazimierz 201

Partial wave decomposition of the N3LO equation of state

By means of a partial wave decomposition, we separate their contributions to the equation of state (EoS) of symmetric nuclear matter for the N3LO pseudo-potential. In particular, we show that although both the tensor and the spin-orbit terms do not contribute to the EoS, they give a non-vanishing contribution to the separate (JLS) channels

Tools for incorporating a D-wave contribution in Skyrme energy density functionals

The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional

Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation

The formalism of the linear response for the Skyrme energy density functional including tensor terms derived in articles [1,2] for nuclear matter is applied here to the case of pure neutron matter. As in article [2] we present analytical results for the response function in all channels, the Landau parameters and the odd-power sum rules. Special emphasis is given to the inverse energy weighted sum rule because it can be used to detect non physical instabilities. Typical examples are discussed and numerical results shown. Moreover, as a direct application, neutrino propagation in neutron matter is investigated through its neutrino mean free path at zero temperature. This quantity turns out to be very sensitive to the tensor terms of the Skyrme energy density functional

Fitting (NLO)-L-3 pseudo-potentials through central plus tensor Landau parameters

Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of next-to-next-to-next-to-leading order ((NLO)-L-3) pseudo-potentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at (NLO)-L-3 is given

Power law in a gauge-invariant cut-off regularisation

We study one-loop quantum corrections of a compactified Abelian 5d gauge field theory. We use a cut-off regularisation procedure which respects the symmetries of the model, i.e. gauge invariance, exhibits the expected power-like divergences and therefore allows the derivation of power-law behavior of the effective 4d gauge coupling in a coherent manner.Comment: 5 pages, 1 figure, 5 graphs, few references added, to appear in Phys.Rev. Rapid Communication

Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities

The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, $M_{-1}$, as a tool to detect instabilities in Skyrme functionals.Comment: Submitted to Phys. Rev.