Random Matrix Theory

Abstract

Before about 1956, there was no systematic statistical theory of nuclear energy level structure. There was a shortage of close spacings in experimentally obtained energy levels which was generally dismissed as being due to instrumental resolution failings. Wigner was the first to give an explanation of this observed shortage of close spacings using statistical arguments. Wigner [Wigner 1967] himself refers to the following excerpt by Dyson to summarize the motivation behind the use of statistical methods [Dyson 1962a]: “Recent theoretical analyses have had impressive success in interpreting the detailed structure of the low-lying excited states of complex nuclei. Still, there must come a point beyond which such analyses of individual levels cannot usefully go. For example, observations of levels of heavy nuclei in the neutron-capture region give precise information concerning a stretch of levels from number N to number (N+n) , where N is an integer of the order of 10⁶. It is improbable that level assignments based on shell structure and collective or individual-particle quantum numbers can ever be pushed as far as the millionth level.