An introductory guide to effective operators in nuclei

Abstract

In this tutorial-style article we discuss the time-independent perturbation formalism of Brandow for effective interactions and operators in a nonrigorous, intuitive way. The simple example of a 2\ifmmode\times\else\texttimes\fi{}2 matrix is used to introduce the basic concepts, for instance the notion of folded diagrams. The same example is used subsequently in a discussion of the branch points arising from "level crossings" and the associated convergence difficulties with the perturbation series. Numerical calculations of the effective interaction and the effective charge are then reviewed, focussing, for the most part, on the ($1s0d$) shell. Whenever possible, simple physical models are used to illustrate the results. A fairly comprehensive summary of the calculations to date is given, and we attempt to synthesize and draw conclusions.