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(\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 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's phase can modify short distance correlations, breaking certain universal predictions.