Symmetry energy coefficients for asymmetric nuclear matter

Abstract

Symmetry energy coefficients of asymmetric nuclear matter generalized are investigated as the inverse of nuclear matter polarizabilities with two different approaches. Firstly a general calculation shows they may depend on the neutron-proton asymmetry itself. The choice of particular prescriptions for the density fluctuations lead to certain isospin (n-p asymmetry) dependences of the polarizabilities. Secondly, with Skyrme type interactions, the static limit of the dynamical polarizability is investigated corresponding to the inverse symmetry energy coefficient which assumes different values at different asymmetries (and densities and temperatures). The symmetry energy coefficient (in the isovector channel) is found to increase as n-p asymmetries increase. The spin symmetry energy coefficient is also briefly investigated. I IntroductionThe (n-p) symmetry energy coefficient and its dependence on the nuclear density has been extensively studied and this is of relevance, for example, for the description of macroscopic nuclear properties as well as for proto-neutron and neutron stars. It represents the tendency of nuclear forces to have greater binding energies (E/A) for symmetric systems -equal number of protons and neutrons. It contributes as a coefficient for the squared neutron-proton asymmetry in usual macroscopic mass formula,, where H 0 does not depend on the asymmetry, Z, N and A are the proton, neutron and mass numbers respectively. Other powers of the asymmetry (proportional to (N − Z) n for n = 2 [1]) are usually expected to be less relevant for the equation of state (EOS) of nuclear matter based on such parameterizations [2,3]. The same kind of parameterization is considered for nuclear matter where instead of nucleon numbers one has to deal with densities. a τ is also the parameter which measures the response of the system to a perturbation which tends to separate protons from neutrons. It is given by the static polarizability of the system which also may depend on the asymmetry of the medium. This point has been developped and emphasized recently [4,5]. The spin symmetry energy coefficient of nuclear matter may also be defined, a σ , representing the cost in energy to make the system spin-asymmetric (and eventually polarized nuclear matter). The spin channel is relevant for the study of the neutrino interaction with matter because it couples with axial vector current together with the scalar channel [6,7,8]. A suppression of the spin susceptibility (in this work we will be dealing rather with its inverse) leads to the suppression of Gamow Teller transitions which are of interest for the supernovae mechanism [8] and eventually to instabilities associated to ferromagnetic polarized states [9,8]. In this work we articulate and extend the ideas developped previously for the dependence of symmetry energy coefficients on neutron-proton asymmetry. For this we use a calculation for the static polarizabilities -proportional to the inverse of the symmetry coefficients in asymmetric matterwhich was done using Sky...

Octet baryon masses and magnetic moments in hot and dense isospin asymmetric nuclear matter

“…The thermodynamical properties of asymmetric nuclear matter such as Equation of State (EoS) and the symmetry energy have been widely studied [10][11][12][13][14][15][16][17] (also see references their in). Beside the study of thermodynamical properties of asymmetric nuclear matter, the dependence of structural properties of baryons on isospin asymmetry of the nuclear medium plays a major role in baryonic studies.…”