The Shell-Model - Introduction

DUSM-Novosleky-Vallières

## Introduction - The Shell-Model

The atomic nucleus presents one of the most challenging
many-body problems. Recent experiments have been probing nuclei under
extreme conditions of high spin, large deformations, high excitation
energies (finite temperature), and neutron-to-proton ratios at their limit of
stability. A wealth of experimental data on such nuclei is expected in the near
future from new radioactive beam facilities. The understanding of nuclear
structure is important in various astrophysical
applications and in tests of fundamental symmetries.
A major program in computational physics is to calculate nuclear properties
from underlying realistic nuclear forces.
The shell model is among the most fundamental models
of nuclear structure; some of the effective interactions used
in this approach
can be traced back to the nucleon-nucleon G-matrix.
In this model, valence nucleons (outside closed shells) move in a
mean-field potential and interact via a residual nuclear force.
The model (in its simplest non-interacting version) was introduced
almost 50 years ago by Mayer [mayer,49] and by
Haxel, Jensen and Suess [Haxel,49]. It has
proven very successful in describing the
properties of nuclei with few valence nucleons [Talmi,93],
including energy levels, magnetic and quadrupole moments, electromagnetic
transition probabilities, beta-decay rates and reaction cross-sections.
It has also been used as the theoretical basis for several
algebraic nuclear models.
The shell model became the standard model for describing the systematics
observed in the spectra and transition intensities of
p- [Cohen,65], sd- [Wildenthal,88]-[Brown,88]
and lower fp-shell [French,69]-[Martinez-Pinedo,97] nuclei.
Since the size of the model space increases rapidly with the
number of valence nucleons and/or orbits,
full major shell calculations were limited to nuclei with
A < 49 [Caurier,94]-[Martinez-Pinedo,97].
The Drexel University Parallel Shell Model
(DUPSM) method
is an approach recently developed to enable calculations
of nuclear properties in large model spaces.
We are developing this model and applying it
at the forefront of nuclear
structure physics.

#### References

- [Mayer,49] M. G. Mayer, Phys. Rev.
**75**, 1969 (1949).
- [Haxel,49] O. Haxel, J. H. D. Jensen and H. E. Suess, Phys. Rev.
**75**, 1766 (1949).
- [Talmi,93] I. Talmi, Simple Models of Complex Nuclei,
(Harwood academic, Switzerland, 1993).
- [Cohen,65] S. Cohen and D. Kurath, Nucl. Phys.
** 73**, 1 (1965).
- [Wildenthal,88] B. H. Wildenthal, Prog. Part. Nucl. Phys.
** 11**, 5 (1984);
Wildenthal, Ann. Phys. ** 182**, 191 (1988).
- [Brown,88] B.A. Brown and B.H. Wildenthal, Ann. Rev. Nucl. Part. Sci.
** 38**, 29 (1988).
- [French,69] J. B. French, E. C. Halbert, J. B. McGrory and
S. S. M. Wong, Adv. Nucl. Phys.
** 3**, 193 (1969).
- [Richter,91] W. A. Richter, M.G. Vandermerwe, R.E. Julies,
and B.A. Brown, Nucl. Phys.
** A523**, 325 (1991).
- [Caurier,94] E. Caurier, A. P. Zuker, A. Poves and G. Martinez-Pinedo,
Phys. Rev.
** C 50**, 225 (1994).
- [Martinez-Pinedo,97] G. Martinez-Pinedo, A. P. Zuker, A. Poves and E. Caurier,
Phys. Rev.
** C 55**, 187 (1997).