Prediction of nuclear reaction rates for astrophysics

The investigation of explosive nuclear burning in astrophysical environments is a challenge for both theoretical and experimental nuclear physicists. Highly unstable nuclei are produced in such processes which again can be targets for subsequent reactions. The majority of reactions can be described in the framework of the statistical model (compound nucleus mechanism, Hauser–Feshbach approach), provided that the level density of the compound nucleus is sufficiently large in the contributing energy window [1]. Among the nuclear properties needed in this treatment are masses, optical potentials, level densities, resonance energies and widths of the GDR. All these necessary ingredients have to be provided in as reliable a way as possible, also for nuclei where no such information is available experimentally. A recent experiment [2] has underlined that the low-energy extrapolation of the widely used optical α+nucleus potentials may still have to be improved. Currently, there are only few global parametrizations for optical α+nucleus potentials at astrophysical energies. Most global potentials are of the Saxon–Woods form, parametrized at energies above about 70 MeV, e.g. [3]. The high Coloumb barrier makes a direct experimental approach very difficult at low energies. More recently, there were attempts to extend those parametrizations to energies below 70 MeV [4]. Early astrophysical statistical model calculations [5, 6] made use of simplified equivalent square well potentials and the black nucleus approximation. Improved calculations [7] employed a phenomenological Woods–Saxon potential [8], based on extensive data [9]. However, it was not clear how well all these potentials would work for heavy targets with A > 60 or in the thermonuclear energy range. Most recent experimental investigations [10, 11] found a systematic mass– and energy– dependence of the optical potentials and were very successful in describing experimental scattering data, as well as bound and quasi–bound states and B(E2) values, with folding potentials. Based on that work, a global parametrization of the volume integrals can be found [12]. In this description, the real part of the nuclear potential is given by a folding potential V f (r, E). The imaginary part W (r, E) is of Woods–Saxon shape with a strongly energy–dependent depth. Nuclear structure and deformation information determines the shape of the energy–dependence by including level density dependent terms [12]. It is easy to show that the final transmission coefficients are not only sensitive to the strength of the potential but also to its geometry. Experimental data seemed to indicate that the geometry …