Heavy and intermediate weight nuclei have energy-level spectra which are quite complex. It is therefore natural to use statistical methods in describing their energy-level structure. The statistical properties of interest here are the level spacing distributions. Detailed studies of these distributions were instigated in 1956 when Wigner surmised that many different nuclei give rise to the same distribu¬tion of nearest neighbor spacings relative to the mean spa¬cing. Strictly speaking, the surmise applied to groupings of highly excited states of the same spin and parity. It was later found by Rosenzweig and Porter that not only var¬ious nuclei, but many complex atoms also give rise to this same distribution. Recently, the distribution of next-nearest neighbor spacings relative to the mean nearest neighbor spacing has been investigated for nuclear spectra. Indications are that this distribution is universal for many systems. Higher order distributions will undoubtedly be examined in the future. Theoretical work has been pur¬sued using statistical theories involving matrix ensem¬bles: Wigner proposed ensembles of Hamiltonian matrices. Dyson has preferred to work with ensembles of unitary matrices. Both approaches have successfully predicted the nearest neighbor, distribution and Dyson's work has also yielded the next-nearest neighbor distribution.
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