The shell model - Dead or alive?
The shell model is the most robust microscopic theory for addressing nuclear structure questions. Unfortunately, it is only as good as the input Hamiltonian and the appropriateness of the selected model space, and both of these elements usually prove to be a significant challenge. There are three basic types of theories: 1) algebraic models, boson and fermion, which focus on symmetries, exact and approximate, of a Hamiltonian and usually use model spaces that are severely truncated; 2) numerically oriented schemes that accommodate larger spaces but rely on special techniques and algorithms for producing convergent results; and 3) models that employ statistical concepts, like statistical spectroscopy of the 70s and 80s and Monte Carlo methods of the 90s, schemes that are not limited by the usual dimensionality considerations. These three approaches, with their pluses and minuses, are reviewed. A new scheme is then suggested that incorporates the best characteristics of these three approaches to yield a symmetry driven theory that is not limited to simplified spaces and Hamiltonians while remaining tractable for large-scale calculations of the type required for testing a theory against experimental data and for predicting new physical phenomena. Special attention is focused on unifying concepts linking the shell model with the much simpler and very successful mean-field and collective-model theories. As an example of a modern shell-model theory, some recent results for M1 (scissors) transitions in deformed nuclei are presented.