Effects of the liquid-gas phase transition and cluster formation on the symmetry energy

Various definitions of the symmetry energy are introduced for nuclei, dilute nuclear matter below saturation density and stellar matter, which is found in compact stars or core-collapse supernovae. The resulting differences are exemplified by calculations in a theoretical approach based on a generalized relativistic density functional for dense matter. It contains nucleonic clusters as explicit degrees of freedom with medium dependent properties that are derived for light clusters from a quantum statistical approach. With such a model the dissolution of clusters at high densities can be described. The effects of the liquid-gas phase transition in nuclear matter and of cluster formation in stellar matter on the density dependence of the symmetry energy are studied for different temperatures. It is observed that correlations and the formation of inhomogeneous matter at low densities and temperatures causes an increase of the symmetry energy as compared to calculations assuming a uniform uncorrelated spatial distribution of constituent baryons and leptons.Comment: 20 pages, 19 figures, version accepted for publication in EPJA special volume on Nuclear Symmetry Energ

Composition and thermodynamics of nuclear matter with light clusters

We investigate nuclear matter at finite temperature and density, including the formation of light clusters up to the alpha particle The novel feature of this work is to include the formation of clusters as well as their dissolution due to medium effects in a systematic way using two many-body theories: a microscopic quantum statistical (QS) approach and a generalized relativistic mean field (RMF) model. Nucleons and clusters are modified by medium effects. Both approaches reproduce the limiting cases of nuclear statistical equilibrium (NSE) at low densities and cluster-free nuclear matter at high densities. The treatment of the cluster dissociation is based on the Mott effect due to Pauli blocking, implemented in slightly different ways in the QS and the generalized RMF approaches. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures T <= 20 MeV and baryon number densities from zero to a few times saturation density. The effect of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy is studied. Comparison is made with other theoretical approaches, in particular those, which are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.Comment: 32 pages, 15 figures, minor corrections, accepted for publication in Physical Review

On Unconstrained SU(2) Gluodynamics with Theta Angle

The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing theta angle. It is shown that for any theta angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained nonlocal theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different theta angles are canonically equivalent as on the original constrained level.Comment: 13 pages Revtex, no figures; several misprints corrected; version to appear in Eur. Phys. J.

Alpha-particle condensation in nuclei

A round up of the present status of the conjecture that n alpha nuclei form an alpha-particle condensate in excited states close to the n alpha threshold is given. Experiments which could demonstrate the condensate character are proposed. Possible lines of further theoretical developments are discussed.Comment: 6 page

Analysis of previous microscopic calculations for second 0+0^+ state in 12^{12}C in terms of 3-alpha particle Bose-condensed state

The wave function of the second $0^+$ state of $^{12}$C which was obtained long time ago by solving the microscopic 3$\alpha$ problem is shown to be almost completely equivalent to the wave function of the 3$\alpha$ condensed state which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second $0^+$ state of $^{12}$C which is the key state for the synthesis of $^{12}$C in stars ('Hoyle' state), and which is one of the typical mysterious $0^+$ states in light nuclei, as a gas-like structure of three $\alpha$ particles, Bose-condensed into an identical s-wave function.Comment: revtex, 5 pages, 2 figures, submitted to Phys. Rev.