Extensive systematizations of theoretical and experimental nuclear densities and of optical potential strengths extracted from heavy-ion elastic scattering data analyses at low and intermediate energies are presented. The energy dependence of the nuclear potential is accounted for within a model based on the nonlocal nature of the interaction. The systematics indicates that the heavy-ion nuclear potential can be described in a simple global way through a double-folding shape, which basically depends only on the density of nucleons of the partners in the collision. The possibility of extracting information about the nucleon-nucleon interaction from the heavy-ion potential is investigated.

In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime). The rate is determined by Coulomb barrier penetration in dense environments and by the astrophysical S-factor at low energies. We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases. The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate. The results are illustrated for the example of the ^{12}C+^{12}C fusion reaction. This reaction is very important for the understanding of nuclear burning in evolved stars, in exploding white dwarfs producing type Ia supernovae, and in accreting neutron stars. The S-factor at stellar energies depends on a reliable fit and extrapolation of the experimental data. We calculate the energy dependence of the S-factor using a recently developed parameter-free model for the nuclear interaction, taking into account the effects of the Pauli nonlocality. For illustration, we analyze the efficiency of carbon burning in a wide range of densities and temperatures of stellar matter with the emphasis on carbon ignition at densities rho > 10^9 g/cc.Comment: 22 pages, 6 figures, accepted for publication in PR

We analyze thermonuclear and pycnonuclear fusion reactions in dense matter containing atomic nuclei of different types. We extend a phenomenological expression for the reaction rate, proposed recently by Gasques et al. (2005) for the one-component plasma of nuclei, to the multi-component plasma. The expression contains several fit parameters which we adjust to reproduce the best microscopic calculations available in the literature. Furthermore, we show that pycnonuclear burning is drastically affected by an (unknown) structure of the multi-component matter (a regular lattice, a uniform mix, etc.). We apply the results to study nuclear burning in a carbon_12-oxygen_16 mixture. In this context we present new calculations of the astrophysical S-factors for carbon-oxygen and oxygen-oxygen fusion reactions. We show that the presence of a CO lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities > 3e9 g cm^{-3} and temperatures T<1e8 K.Comment: 16 pages, 5 figures, to appear in Phys. Rev.