Investigating the spectral statistics of \(3_1^ - \) levels using random matrix theory in the odd–odd nuclei

In this paper, the spectral statistics of all the observed \(3_1^ - \) levels in the odd–odd nuclei have been analysed in the framework of random matrix theory. Also, the possible effects of the shell model configurations, mass regions, theoretical quadrupole deformation, experimental half-lives and major decay modes on the statistical situations related to negative parity states have been studied. In order to prepare different sequences, we have used the latest available empirical data on the \(10 \le A \le 250\) mass region for 216 nuclei. Using the maximum likelihood estimation technique, the parameter of the Berry–Robnik distribution function in different sequences has been extracted and the statistical situation of these sequences in comparison with regular and chaotic limits is described. Our results show the maximum chaoticity for these odd–odd nuclei in \(100< A < 150\) mass region, short-lived nuclei. These odd–odd nuclei have the maximum theoretical quadrupole deformations. Also, there are some suggestions on the effect of shell model configuration and decay modes on the statistical situation of these negative parity states in odd–odd nuclei.