Nuclear level density and the determination of thermonuclear rates for astrophysics

Abstract

The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. In recent calculations the nuclear level density -as an important ingredient to the statistical model (Hauser-Feshbach) -has shown the highest uncertainties. We present a global parametrization of nuclear level densities within the back-shifted Fermi-gas formalism. Employment of an energy-dependent level density parameter a, based on microscopic corrections from a recent FRDM mass formula, and a backshift δ, based on pairing and shell corrections, leads to a highly improved fit of level densities at the neutron-separation energy in the mass range 20 ≤ A ≤ 245. The importance of using proper microscopic corrections from mass formulae is emphasized. The resulting level description is well suited for astrophysical applications.The level density can also provide clues to the applicability of the statistical model which is only correct for a high density of excited states. Using the above description, one can derive a "map" for the applicability of the model to reactions of stable and unstable nuclei with neutral and charged particles.

Proton‐induced Thermonuclear Reaction Rates for A = 20–40 Nuclei

“…Therefore, for each reaction considered, Rauscher & Thielemann (2000) present a lower temperature limit for the validity of their Hauser-Feshbach reaction T low HF rates. However, these estimates are based on level-density arguments alone (see Rauscher, Thielemann, & Kratz 1997), rather than on a rigorous comparison with experimental data. It is evident from the above discussion that the experimental reaction rates compiled in the present work can be used to test the reliability of theoretical Hauser-Feshbach reaction rates in the mass A \ 20È40 region.…”

The equation of state and composition of hot, dense matter in core-collapse supernovae

“…However, the question deserves further investigation, especially considering the new data from Rauscher et al (1997); Rauscher & Thielemann (2000); Rauscher (2003). The expression used in Liu et al (2007) is related to an energy-dependent level density parameter with microscopic correction to a nuclear mass model (Rauscher et al 1997;Rauscher & Thielemann 2000;Rauscher 2003). Our code can incorporate various options for the partition functions.…”

Exploration of direct neutron capture with covariant density functional theory inputs

“…[14], in which HFB theory is used along with the Bruyères-le-Châtel renormalization of the JeukenneLejeune-Mahaux (JLMB) optical potential. The direct comparison of our predicted σ DC with the experimentally measured cross section σ γ for 16 O is validated by the inapplicability of the statistical model for such low Z nuclei (see, e.g., [8]). …”

“…Statistical models are often used for these estimates, wherein an average over the contribution of individual resonances is made [6,7]. To justify this averaging, there must be a sufficiently high (∼ 10 levels / MeV) level density in the compound nucleus at energies populated by the incident neutron [8]. Rather than requiring information on the location and properties of individual levels for each nuclear species, statistical model calculations utilize parameterized level density formulae.…”

“…levels and one-neutron separation energies for calculations of neutron capture cross sections [8,15]. Two features missing in these studies were consideration of pairing correlations and the coupling of bound levels to resonant levels in the continuum.…”