Light clusters in nuclear matter and the “pasta” phase

Abstract

The effects of including light clusters in nuclear matter at low densities are investigated within four different parametrizations of relativistic models at finite temperature. Both homogeneous and inhomogeneous matter (pasta phase) are described for neutral nuclear matter with fixed proton fractions. We discuss the effect of the density dependence of the symmetry energy, the temperature and the proton fraction on the non-homogeneous matter forming the inner crust of proto-neutron stars. It is shown that the number of nucleons in the clusters, the cluster proton fraction and the sizes of the Wigner Seitz cell and of the cluster are very sensitive to the density dependence of the symmetry energy. PACS number(s):21.65.+f, 24.10.Jv, 26.60.+c, 95.30.Tg

Light clusters, pasta phases, and phase transitions in core-collapse supernova matter

“…The electronic pressure P e is given by Eq. (17). Within the CP and CLD approaches, the electron contribution coincides with the homogeneous matter contribution.…”

“…When clusters are present, there are equilibrium conditions for them, too [17]. The total free-energy density and the total proton density of the system are given by…”

“…For the coupling constants, we consider g vj = A j g v and g ρj = |Z j − N j |g ρ , where A j is the mass number, and Z j ,N j are the proton and neutron numbers, respectively [17]. The chemical potential of a cluster j is defined as μ j = N j μ n + Z j μ p .…”

“…The interface between these regions is sharp. Finite-size effects are taken into account by surface and Coulomb terms in the energy density [17].…”

“…Besides TF, we use the coexisting-phases (CP) method, which is numerically much faster than the TF method, and where the Gibbs equilibrium conditions are used to get the lowest free-energy state, and the surface and Coulomb terms are added "by hand" (see, e.g., Ref. [17]). Within this method, we also include the effect of light clusters.…”