Ratio of consecutive level spacings as a signature of chaos in nuclear many-body models

Abstract

Statistical properties of nuclear energy levels and nuclear transitions have long been juxtaposed to the limit of random matrix theory. A novel practical measure of chaos onset, the ratio of consecutive energy spacings, that does not require the unfolding of energy levels, was previously introduced for all three canonical random matrix ensembles, along with the expressions for the regular and chaotic limits. In this study, an expression for this ratio interpolating between the regular and chaotic limits is introduced and applied to the energy levels calculated in the realistic nuclear shell model and in the interacting boson model. The results are consistent with those extracted from the traditional statistics of nearest-neighbor spacings with unfolding; we find the relation between the ways of convergence to the chaotic limit.