Universal predictions for statistical nuclear correlations

We explore statistical correlations of collective nuclear excitations under a multiparameter deformation of the Hamiltonian, in the framework of the interacting boson model. The distribution of Hamiltonian matrix elements is found to behave as P(|Hij|)∝1/√|Hij|exp(-|Hij|/V), with a parametric correlation of the type ln left-angle H(x)H(y)right-angle ∝-|x-y|. The studies are done in both the regular and chaotic regimes of the Hamiltonian. Model-independent predictions for a wide variety of correlation functions and distributions, which depend on wave functions and energies, are made from parametric random matrix theory and found to agree with the IBM results. Being a multiparameter theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. Specifically, Berry close-quote s phase can modify short distance correlations, breaking certain universal predictions. copyright 1996 The American Physical Society