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

A parameter-free nonlocal double-folding-inspired interaction is proposed for the nucleus-nucleus systems. Excellent reproductions of elastic scattering differential cross section data were obtained for several systems over a wide range of bombarding energies. Our results should be of value in the description of the scattering of other many-body systems. [S0031-9007(97)05269-1] PACS numbers: 21.30. Fe, 25.70.Bc The mean field interaction between complex quantum many-body systems (nucleus-nucleus, cluster-cluster, etc.) is still an open question in current physics research. The study of this matter is a fundamental step in the understanding of many-body dynamics. In the nucleus-nucleus case, significant progress has been achieved concerning this question during the last decade [1], as a consequence of the measurement of accurate and extensive elastic scattering data at intermediate energies. Nuclear rainbow scattering, first observed in a systems [2][3][4] and later in light heavy ions [5][6][7], probes the nucleus-nucleus potential not only at the surface region but also at smaller distances, and ambiguities in the real part of the potentials have been removed. The resulting phenomenological interactions have significant dependence upon the bombarding energies. Some theoretical models have been developed to account for this energy dependence through realistic mean field potentials. Nowadays, the most successful models seem to be those based on the DDM3Y interaction [8][9][10] which is an improvement of the originally energyindependent double-folding potential [11]. But, in order to fit the data, the density-and energy-dependent DDM3Y potential needs a renormalization factor which besides being system dependent [1,12] is still slightly energy dependent [1].In this Letter we show, by an extensive description of elastic scattering data using an optical integro-differential equation, that the dependence on the bombarding energy of the real bare potential is mostly due to the intrinsically nonlocal nature of the effective one-body interaction. The real bare potential (by bare we mean the average, mean field, interaction with no coupled channels effects) is constructed using the folding model. It contains no adjustable parameters and is energy independent. The absorptive part is taken to be a three parameters WoodsSaxon interaction. We also supply a simple approach to obtain the local-equivalent energy-dependent potential.Before we set the stage for the analysis of elastic scattering data, we first describe our theoretical model.When dealing with nonlocal interactions, one is required to solve the integro-differential equationwhere, on physical grounds [13], the kernel function is taken to be symmetric: U͑ R, R 0 ͒ U͑ R 0 , R͒. We take for U͑ R, R 0 ͒ the following form motivated by the physics problem at handIn our analysis, the Coulomb interaction, V C ͑R͒, was obtained using an expression for the double sharp cutoff folded potential [14] and the local energy-dependent imaginary potential, W ͑R, E͒, was taken t...

A new technique to analyze fusion data is developed. From experimental cross sections and results of coupled-channel calculations a dimensionless function is constructed. In collisions of strongly bound nuclei this quantity is very close to a universal function of a variable related to the collision energy, whereas for weakly bound projectiles the effects of breakup coupling are measured by the deviations with respect to this universal function. This technique is applied to collisions of stable and unstable weakly bound isotopes.

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