The last decade has witnessed both quantitative and qualitative progresses in Shell Model 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 we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate 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 of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

The shell model as a unified view of nuclear structure

Energy levels of light nuclei A=8,9,10

The experimental and theoretical evidence for intrinsic reflection-asymmetric shapes in nuclei is reviewed. The theoretical methods discussed cover a wide spectrum, from mean-field theory and its extensions to algebraic and cluster approaches. The experimental data for nuclear ground states and at low and high spin, cited as evidence for reflection asymmetry, are collected and categorized. The extensive data on electric dipole transition moments and their theoretical interpretation are surveyed, along with available data on electric octupole moments. The evidence for reflection-asymmetric molecular states in light nuclei is summarized. The application of reflection-asymmetric theories to descriptions of the fission barrier, bimodal fission, superdeformation, and hyperdeformations is reviewed, and some other perspectives in the wider context of nuclear physics are also given. [S0034-6861(96)00102-X]

Intrinsic reflection asymmetry in atomic nuclei

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.

https://iopscience.iop.org/article/10.1088/1361-6633/aa5bc5/pdf

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review.

A comprehensive analysis is made of the experimental information on Gamow-Teller beta decay for the light (A\ensuremath{\le}18) nuclei. Experimental data on half-lives, Q values, and branching ratios are tabulated. Experimental logft values and beta-decay matrix elements are deduced from these data. The one-body-transition densities necessary to predict the beta-decay matrix elements are then calculated using a recently constructed shell-model Hamiltonian operating in the first four major shells. Using these parameters, effective Gamow-Teller operators are deduced for the 0p shell from a least-squares fit to 16 experimental matrix elements. The effective operators are used to calculate 83 decay matrix elements. Some specific decays are discussed.

Gamow-Teller beta-decay rates for A <= 18 nuclei.

The enigma of 114Cd. A classical case of ambiguities in quantum mechanical state mixing

Low spin identical bands are found in sets of widely dispersed nuclei, spanning as much as 24 mass units. Moreover, they occur in regions of rapid structural and shape changes. A correlation ansatz to identify such nuclei, based on the concepts of {ital N}{sub {ital p}N{ital n}} and {ital F} spin, is discussed.

Identical bands in widely dispersed nuclei.

It is shown that identical rotational energy spacings in pairs of even-even nuclei do not set these nuclei qualitatively apart from others. Rather, they represent the terminus or limiting case of a continuous range of spacings whose behavior is controlled by the balance between residual {ital p}-{ital n} pairing interactions and whose phenomenology can be simply described.

Identical bands and the varieties of rotational behavior.

It is shown that the simple correlation of {ital E}(2{sub 1}{sup +}) and {ital E}(4{sub 1}{sup +}) energies can be a sensitive indicator of underlying shell structure and, in particular, that recent suggestions of radically different structure near the neutron drip line may be most easily signaled by this observable.

W.-T. Chou

Papers

Gamow-Teller beta-decay rates for A <= 18 nuclei.

The enigma of 114Cd. A classical case of ambiguities in quantum mechanical state mixing

Identical bands in widely dispersed nuclei.

Identical bands and the varieties of rotational behavior.

Possible signatures of shell structure near the drip lines.