Order and disorder in the nuclear shell model

Abstract

We discuss how the large-basis shell-model wave functions can be used to understand the transition from order in the low-lying nuclear levels to disorder at high excitation energy. The level spacing at high excitation energy shows the usual Wigner (GOE) distribution. But other properties at both low and high excitation show deviations from the GOE. The strength distribution of basis states amplitudes in the eigenfunctions is not uniform but evolves from a Breit-Wigner shape at weak off-diagonal interaction strengths to a Gaussian shape for the normal off-diagonal interaction strength. We define an information entropy in the shell-model basis for each eigenstate which shows a smooth increase at low excitation energy to a value near the GOE limit at high excitation energy. This information entropy has a temperature associated with it which is nearly identical to the temperature obtained from the level density and from the Fermi distribution function for the single-particle occupancies. The interrelation between quantum chaos, Fermi liquid theory and thermalization is discussed.