UNIVERSAL PREDICTIONS FOR STATISTICAL NUCLEAR CORRELATIONS

We explore statistical correlations of collective nuclear excitations under a multiparameter deformation of the Hamiltonian, in the framewor k of the interacting boson model. The distribution of Hamiltonian matr ix elements is found to behave as P(\H-ij\)proportional to 1/root\H-ij \exp(-\H-ij\/V), with a parametric correlation of the type ln[H(x)H(y) ]proportional to-\x-y\. The studies are done in both the regular and c haotic 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 matri x theory and found to agree with the IBM results. Being a multiparamet er theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. S pecifically, Berry's phase can modify short distance correlations, bre aking certain universal predictions.