Microscopic approaches to nuclear structure: Configuration interaction

Abstract

The configuration interaction (CI) approach to solving the nuclear many-body problem, also known as the interacting shell model, has proven to be powerful tool in understanding the structure of nuclei. The principal criticism of past applications of the shell model is the reliance on empirical tuning to interaction matrix elements. If an accurate description of nuclei far from the valley of stability, where little or no data is available, a more fundamental approach is needed. This starts with recent ab initio approaches with effective interactions in the no-core shell model (NCSM). Using effective-field theory for guidance, fully ab initio descriptions of nuclei up to 16O with QCD based NN, NNN, and NNNN interactions will be possible within the next five years. An important task is then to determine how to use these NCSM results to develop effective interactions to describe heavier nuclei without the need to resort to an empirical retuning with every model space. Thus, it is likely that more traditional CI applications utilizing direct diagonalization and more fundamental interactions will be applicable to nuclei with perhaps up to one hundred constituents. But, these direct diagonalization CI applications will always be computationally limited due to the rapid increase in the number of configurations with particle number. Very recently, the shifted-contour method has been applied to the Auxiliary-field Monte Carlo approach to the Shell Model (AFMCSM), and preliminary applications exhibit a remarkable taming of the notorious sign problem. If the mitigation of the sign problem holds true, the AFMCSM will offer a method to compute quantum correlations to mean-field applications for just about all nuclei; giving exact results for CI model spaces that can approach 1020-25. In these lectures, I will discuss modern applications of CI to the nuclear many-body problem that have the potential to guide nuclear structure theory into the next decade.