The shell model as a unified view of nuclear structure
Abstract
The last decade has witnessed both quantitative and qualitative progress in shellmodel studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^{9} using the Lanczos tridiagonal construction, whose formal and numerical aspects are analyzed in this review. In addition, many new approximation methods have been developed in order to overcome the dimensionality limitations. New effective nucleonnucleon interactions have been constructed that contain both two and threebody contributions. The former are derived from realistic potentials (i.e., potentials consistent with twonucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shellformation properties of the realistic twobody forces. This combination appears to solve a number of hitherto puzzling problems. The present review concentrates on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the shell model to describe simultaneously all the manifestations of the nuclear dynamics, either singleparticle or collective in nature. The review also treats in some detail the problems associated with rotational motion, the origin of quenching of the GamowTeller transitions, double β decays, the effect of isospin nonconserving nuclear forces, and the specificities of neutronrich nuclei. Many other calculations—which appear to have “merely” spectroscopic interest—are touched upon briefly, although the authors are fully aware that much of the credibility of the shell model rests on them.
 Publication:

Reviews of Modern Physics
 Pub Date:
 April 2005
 DOI:
 10.1103/RevModPhys.77.427
 arXiv:
 arXiv:nuclth/0402046
 Bibcode:
 2005RvMP...77..427C
 Keywords:

 21.60.Cs;
 01.30.Rr;
 21.30.x;
 21.10.Pc;
 21.10.Re;
 23.40.s;
 21.10.Hw;
 Shell model;
 Surveys and tutorial papers;
 resource letters;
 Nuclear forces;
 Singleparticle levels and strength functions;
 Collective levels;
 Beta decay;
 double beta decay;
 electron and muon capture;
 Spin parity and isobaric spin;
 Nuclear Theory
 EPrint:
 64 pages, 60 figures