Nuclear Shell Model and Level Density
Vladimir Zelevinsky and Sofia Karampagia
1 Introduction
The knowledge of the nuclear level density as a function of excitation energy and
nuclear spin is necessary for many practical problems of nuclear physics and its
applications. There are several approaches to this task. Frequently the empirical
expressions are used based on the traditional Fermi-gas picture, with or without
the backshift parameter reflecting the existence of the pairing gap, and with the
adjusted main parameter. [1–3]. The combinations of the mean-field combinatorics,
pairing and some collective effects were used in the most broad attempts for
the general description of the level density [4, 5]. The shell-model Monte Carlo
method accounts for more parts of the interparticle interactions [6–8]. The general
introduction to the problem and some historical comments can be found in the recent
review article [9].
It seems natural to use the full solution of the nuclear shell model without making
approximations in the choice of the parts of the interaction taken into account.
Certainly, there are obvious deficiencies in using the shell model for the extraction of
the level density. The shell-model interactions are presented typically by the matrix
elements of the two-body processes. The dozens and hundreds matrix elements
should be carefully selected based on the original nucleon-nucleon interaction,
theoretical arguments, and detailed fit of well-known experimental quantities. This
selection has to be done before applications to the level density and checked by the
V. Zelevinsky ()
Department of Physics and Astronomy and NSCL/FRIB, Michigan State University, East
Lansing, MI, USA
e-mail: zelevins@frib.msu.edu
S. Karampagia
Department of Physics, Grand Valley State University, Allendale, MI, USA
© 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_14
123
Vladimir Zelevinsky and Sofia Karampagia
1 Introduction
The knowledge of the nuclear level density as a function of excitation energy and
nuclear spin is necessary for many practical problems of nuclear physics and its
applications. There are several approaches to this task. Frequently the empirical
expressions are used based on the traditional Fermi-gas picture, with or without
the backshift parameter reflecting the existence of the pairing gap, and with the
adjusted main parameter. [1–3]. The combinations of the mean-field combinatorics,
pairing and some collective effects were used in the most broad attempts for
the general description of the level density [4, 5]. The shell-model Monte Carlo
method accounts for more parts of the interparticle interactions [6–8]. The general
introduction to the problem and some historical comments can be found in the recent
review article [9].
It seems natural to use the full solution of the nuclear shell model without making
approximations in the choice of the parts of the interaction taken into account.
Certainly, there are obvious deficiencies in using the shell model for the extraction of
the level density. The shell-model interactions are presented typically by the matrix
elements of the two-body processes. The dozens and hundreds matrix elements
should be carefully selected based on the original nucleon-nucleon interaction,
theoretical arguments, and detailed fit of well-known experimental quantities. This
selection has to be done before applications to the level density and checked by the
V. Zelevinsky ()
Department of Physics and Astronomy and NSCL/FRIB, Michigan State University, East
Lansing, MI, USA
e-mail: zelevins@frib.msu.edu
S. Karampagia
Department of Physics, Grand Valley State University, Allendale, MI, USA
© 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_14
123