Universal Predictions for Statistical Nuclear Correlations

Details Universal Predictions for Statistical Nuclear Correlations Universal Predictions for Statistical Nuclear Correlations

1995-10-03

arxiv.org/abs/nucl-th/9510002v1

Phys.Rev.C54:147-158,1996

Physics

Nuclear Physics

Nuclear Theory

Latex file + 12 postscript figures

Scientific paper

10.1103/PhysRevC.54.147

We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp(-|H_{ij}|/V)$, with a parametric correlation of the type $\log \langle H(x)H(y)\rangle\propto -|x-y|$. 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 wavefunctions and energies are found from parametric random matrix theory and are compared to the nuclear excitations. We find that our universal predictions are observed in the nuclear states. Being a multi-parameter 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.

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