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PACS 13.75.Ev -Hyperon-nucleon interactions PACS 26.60.Kp -Equations of state of neutron-star matter PACS 26.60.-c -Nuclear matter aspects of neutron stars PACS 97.60.Jd -Neutron stars

The effects of the α particles in nuclear matter at low densities are investigated within three 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 and stellar matter subject to β-equilibrium and trapped neutrinos. In homogeneous matter, α particles are only present at densities below 0.02 fm −3 and their presence decreases with the increase of the temperature and, for a fixed temperature, the α particle fraction decreases for smaller proton fractions. A repulsive interaction is important to mimic the dissolution of the clusters in homogeneous matter. The effects of the α particles on the pasta structure is very small except close to the critical temperatures and / or proton fractions when it may still predict a pasta phase while no pasta phase would occur in the absence of light clusters. It is shown that for densities above 0.01 fm 3 the α particle fraction in the pasta phase is much larger than the α particle fraction in homogeneous matter. PACS number(s):21.65.+f, 24.10.Jv, 26.60.+c, 95.30.Tg

The effect of strong magnetic fields on the equation of state (EoS) for compact stars described with density dependent relativistic hadronic models is studied. A comparison with other mean-field relativistic models is done. It is shown that the largest differences between models occur for low densities and that the magnetic field affects the crust properties of star, namely its extension. PACS numbers: 26.60.-c 26.60.Kp 97.60.Jd 24.10.Jv I. INTRODUCTIONThe study of very asymmetric nuclear matter is presently an important issue due to the radioactive beams which will be operating in the near future and which will allow the investigation of a region of the nuclear matter phase space unaccessible till recently. Asymmetric nuclear matter is of particular interest for the description of stellar matter of compact stars.Compact star properties depend a lot on the model used to describe the hadronic equation of state (EoS). In particular relativistic nuclear mean-field models [1,2] are very popular to describe stellar matter because causality will always be satisfied. The imposition of constraints, both coming from measured star properties or from relativistic heavy ion collisions in the laboratory, is essential to test the different models [3].Magnetars are neutron stars which may have surface magnetic fields larger that 10 15 G [4-6] and which were discovered at the x-ray and γ-ray energies (for a review refer [7]). They are identified with the anomalous x-ray pulsars (AXP) and soft γ-ray repeaters. Taking as reference the critical

A consistent theory of the ground state energy and its splitting due to the process of tunneling for the Lipkin model is presented. For the functional integral in terms of the spin coherent states for the partition function of the model we accurately calculate the trivial and the instanton saddle point contributions.We show that such calculation has to be perfomed very accurately taking into account the discrete nature of the functional integral. Such accurate consideration leads to finite corrections to a naive continous consideration.We present comparison with numerical calculation of the ground state energy and the tunneling splitting and with the results obtained by the quasiclassical method and get excellent agreement. 03.65.Db,75.10.Jm, 75.30.Gw Typeset using REVT E X

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(3 . 6) Except for the above replacement, there is no modification in this paper.