The nuclear shell model

Abstract

In this series of lectures we discuss the basic notions of the spherical shell model. Starting from a regularized nucleon-nucleon interaction, we define the model as an approximation to the exact solution of the full secular problem. We introduce the notions of valence space, effective interaction and effective operator. We analyse the structure of the realistic effective interactions, identifying their monopole part with the spherical mean field. The multipole hamiltonian is shown to have a simple and universal form that includes pairing (isovector and isoscalar), quadrupole, octupole, hexadecapole and (σ · τ) (σ · τ). We describe the methods of resolution of the secular problem, in particular the Lanczos method. Finally, we present some results on two different open problems in nuclear structure; the quenching of the strength of the spin operators in the nuclear medium and the spherical shell model description of deformation and superdeformation.KeywordsShell ModelStrength FunctionSlater DeterminantShell Model CalculationLanczos MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.