Fusion of neutron rich oxygen isotopes in the crust of accreting neutron stars

Fusion reactions in the crust of an accreting neutron star are an important source of heat, and the depth at which these reactions occur is important for determining the temperature profile of the star. Fusion reactions depend strongly on the nuclear charge $Z$. Nuclei with $Z\le 6$ can fuse at low densities in a liquid ocean. However, nuclei with Z=8 or 10 may not burn until higher densities where the crust is solid and electron capture has made the nuclei neutron rich. We calculate the $S$ factor for fusion reactions of neutron rich nuclei including $^{24}$O + $^{24}$O and $^{28}$Ne + $^{28}$Ne. We use a simple barrier penetration model. The $S$ factor could be further enhanced by dynamical effects involving the neutron rich skin. This possible enhancement in $S$ should be studied in the laboratory with neutron rich radioactive beams. We model the structure of the crust with molecular dynamics simulations. We find that the crust of accreting neutron stars may contain micro-crystals or regions of phase separation. Nevertheless, the screening factors that we determine for the enhancement of the rate of thermonuclear reactions are insensitive to these features. Finally, we calculate the rate of thermonuclear $^{24}$O + $^{24}$O fusion and find that $^{24}$O should burn at densities near $10^{11}$ g/cm$^3$. The energy released from this and similar reactions may be important for the temperature profile of the star.Comment: 7 pages, 4 figs, minor changes, to be published in Phys. Rev.

Hydrogen-Helium Mixtures in the Interiors of Giant Planets

Equilibrium properties of hydrogen-helium mixtures under conditions similar to the interior of giant gas planets are studied by means of first principle density functional molecular dynamics simulations. We investigate the molecular and atomic fluid phase of hydrogen with and without the presence of helium for densities between $\rho=0.19$ g$$cm$^{-3}$ and $\rho=0.66$ g$$cm$^{-3}$ and temperatures from $T=500$K to $T=8000 {K}$. Helium has a crucial influence on the ionic and electronic structure of the liquid. Hydrogen molecule bonds are shortened as well as strengthened which leads to more stable hydrogen molecules compared to pure hydrogen for the same thermodynamic conditions. The {\it ab initio} treatment of the mixture enables us to investigate the validity of the widely used linear mixing approximation. We find deviations of up to 8% in energy and volume from linear mixing at constant pressure in the region of molecular dissociation.Comment: 13 pages, 18 figures, submitted to PR

Coulomb tunneling for fusion reactions in dense matter: Path integral Monte Carlo versus mean field

We compare Path Integral Monte Carlo calculations by Militzer and Pollock (Phys. Rev. B 71, 134303, 2005) of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find a very good agreement of two approaches at temperatures higher than ~1/5 of the ion plasma temperature. We obtain a simple parameterization of the mean field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertainties of nuclear reaction rates taking carbon burning in dense stellar matter as an example.Comment: 13 pages, 7 figures, to appear in Phys. Rev.

Effective Screened Potentials of Strongly Coupled Semiclassical Plasma

The pseudopotentials of particle interaction of astrongly coupled semiclassical plasma, taking into account bothquantum-mechanical effects of diffraction at short distances andalso screening field effects at large distances are obtained. Thelimiting cases of potentials are considered.Comment: 15 pages, TeX, 7 figure

Classical Nucleation Theory of the One-Component Plasma

We investigate the crystallization rate of a one-component plasma (OCP) in the context of classical nucleation theory. From our derivation of the free energy of an arbitrary distribution of solid clusters embedded in a liquid phase, we derive the steady-state nucleation rate of an OCP as a function of the Coulomb coupling parameter. Our result for the rate is in accord with recent molecular dynamics simulations, but it is greater than that of previous analytical estimates by many orders of magnitude. Further molecular dynamics simulations of the nucleation rate of a supercooled liquid OCP for several values of the coupling parameter would clarify the physics of this process.Comment: 6 pages, 1 figure, accepted by PR

Noncommutative Complex Scalar Field and Casimir Effect

A noncommutative complex scalar field, satisfying the deformed canonical commutation relations proposed by Carmona et al. [27]-[31], is constructed. Using these noncommutative deformed canonical commutation relations, a model describing the dynamics of the noncommutative complex scalar field is proposed. The noncommutative field equations are solved, and the vacuum energy is calculated to the second order in the parameter of noncommutativity. As an application to this model, the Casimir effect, due to the zero point fluctuations of the noncommutative complex scalar field, is considered. It turns out that in spite of its smallness, the noncommutativity gives rise to a repulsive force at the microscopic level, leading to a modifed Casimr potential with a minimum at the point amin= racine(5/84){\pi}{\theta}.Comment: Revtex style, 28 page

Conformal Symmetry of Supergravities in AdS spaces

We show that the background field method applied to supergravity in adS space-time provides the path integral for the theory in the bulk with conformal symmetry associated with the isometry of the adS space. This in turn allows to establish the rigid conformal invariance of the generating functional for the supergravity correlators on the boundary.Comment: 14 pages, Late

Nuclear Reaction Rates in a Plasma

The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. We derive a result that expresses the complete effects of Coulomb barrier penetration and of the influence of the surrounding plasma in terms of matrix elements of well defined operators. We find that possible "dynamical screening" effects that have been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of the correlation functions in a classical Coulomb gas, followed by construction of an effective two body potential and a quantum barrier penetration calculation, will miss physics that is as important as the physics that it includes.Comment: 66 pages, revtex, Errors Fixed, Explanation Adde

Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes

We study general S2xS1 Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity $J$ is not zero. We derive an explicit expression for the metric form on the future Cauchy horizon in terms of the initial data on the past horizon and conclude the universal relation A\p A\f=(8\pi J)^2 where A\p and A\f are the areas of past and future Cauchy horizon respectively.Comment: 17 pages, 1 figur