The Transition from Isolated Resonances
to the Continuum
Carl R. Brune
1 Introduction
Many nuclear reactions of astrophysical importance are modeled by HauserFeshbach (HF) calculations, the well-established approach for computing average
cross sections when many resonant levels are involved. For this approach to be
successful it is necessary that the parameters of the model (optical potentials, level
densities, etc.) be reasonably well understood and that number of resonant states
involved be sufficiently large. The latter point is one of the questions we would like
to address. A rule of thumb of at least 10 levels in the energy window of interest
has been given but many caveats apply [1]. In principle a HF reaction rate should
have a temperature-dependent theoretical statistical uncertainty associated with the
finite number of contributing levels. A quantitative understanding of this statistical
uncertainty can in turn be used to quantify the applicability of the model and to
asses the uncertainty in the derived reaction rate. These considerations also have
important implication for the planning and interpretation of experiments. Because
measurements are performed with a finite energy resolution due to target thickness
and other factors, energy average is also present in experimental data.
C. R. Brune ()
Edwards Accelerator Laboratory, Department of Physics and Astronomy, Ohio University,
Athens, OH, USA
e-mail: brune@ohio.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_5
45
to the Continuum
Carl R. Brune
1 Introduction
Many nuclear reactions of astrophysical importance are modeled by HauserFeshbach (HF) calculations, the well-established approach for computing average
cross sections when many resonant levels are involved. For this approach to be
successful it is necessary that the parameters of the model (optical potentials, level
densities, etc.) be reasonably well understood and that number of resonant states
involved be sufficiently large. The latter point is one of the questions we would like
to address. A rule of thumb of at least 10 levels in the energy window of interest
has been given but many caveats apply [1]. In principle a HF reaction rate should
have a temperature-dependent theoretical statistical uncertainty associated with the
finite number of contributing levels. A quantitative understanding of this statistical
uncertainty can in turn be used to quantify the applicability of the model and to
asses the uncertainty in the derived reaction rate. These considerations also have
important implication for the planning and interpretation of experiments. Because
measurements are performed with a finite energy resolution due to target thickness
and other factors, energy average is also present in experimental data.
C. R. Brune ()
Edwards Accelerator Laboratory, Department of Physics and Astronomy, Ohio University,
Athens, OH, USA
e-mail: brune@ohio.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_5
45