Towards an Improved Level Density Description for Unstable Nuclei

Astrophysical investigations of the nucleosynthesis in stars (r-process, rp-process) and in the early Universe require the knowledge of thermonuclear rates involving exotic nuclei which currently are not accessible experimentally. In most cases the statistical model approach (Hauser-Feshbach, HF) is used for cross section and reaction rate calculations. (Only when the level density of a nucleus becomes too low (<10 MeV ?1), the direct reaction mechanism may dominate 1,2]. This is the case for nuclei close to magic numbers). Essential for the quality of the HF-calculations is the employed level density description 2]. It is also important to have a reliable criterion enabling one to decide which reaction model to apply. The level density predictions are the weakest point in the present procedures for HF cross section calculations 2]. The nuclear level density (U) usually is described with the backshifted Fermi gas expression 2,3]. Then (U) is dependent only on two quantities: the level density parameter a and the backshift , which determines the energy of the rst excited state. In order to get a reasonably good t to experimental level densities it was necessary to divide the nuclei into three classes 2] (nu-clei close to magic numbers, other spherical nuclei, and deformed nuclei), thus increasing the number of parameters by a factor of three. The deviations were still up to a factor of 4{5. Employing a diierent treatment of the density parameter a which includes thermal damping of shell eeects 4], it was possible to improve the t to the experimental values. All nuclei can now be described with a single parameter set consisting of just three parameters. In our attempts to further improve the results, we combined this approach with a more consistent evaluation of the pairing gap n;p which is directly related to the backshift 2,3]. We calculated the neutron pairing gap n via the even-odd mass diierence 1 4 E (Z; N) is the mass for the nucleus (Z; N) 5]. The same procedure can be applied for the proton energy gap p. Thus, better structural eeects can be incorporated in a consistent way, regardless of the mass formula used. We tted experimentally known values of 278 nuclei using diierent mass formulae 6,7] and the standard, smooth treatment of the pairing gap (/ 12= p A) 2,4] as well as the method described above. As a preliminary result we found the best t using the MM oller …