Effects of vibration and rigidity modes of motion on the spectral statistics of spherical nuclei

Abstract

In this paper, we investigated the effects of \b{eta}-vibration and \b{eta}-rigidity on the energy levels from the viewpoint of statistical fluctuations of nuclear systems. To this aim, a parameter-free collective solution of the Bohr Hamiltonian in the five-dimensional harmonic oscillator potential with a linear energy dependence and an asymptotic limit of the slope are used to determine all of the observed normal states in even-even nuclei with ~ 2.00 - 2.15 ratio in the A ~ 90 -140 mass region. Different sequences are prepared of the energy levels, both experimental values and theoretical predictions, which are categorized as their spin-parity, \b{eta} oscillator quanta, and seniority numbers and analyzed in the framework of random matrix theory to show their statistical situation in comparison with regular and correlated limits. Also, up to 2226 levels with the same 2+ spin-parity assignment are determined for different systems in which the stiffness parameter for them changed between a = 0 and a =1 limits and then analyzed in the same process. The results showed a transition between correlated behavior and regularity when the rigidity increased in considered systems. Also, there are apparent relations between the chaocity degrees of considered sequences and the considered criteria for classifications.