Investigation of the effect of the displacement of energy levels on spectral statistics of deformed nuclei

In this paper, the spectral statistics of prolatedeformed nuclei are investigated by using random matrix theory. To this aim, we used both available experimental data and also the energy levels of ground, beta, and gamma bands of 51 deformed even-even nuclei, which are determined via partial SU(3) dynamical symmetry limit of interacting boson model. The results verified the ability of the considered models in the restoration of experimental data and also the displacement of beta and gamma energy bands. Also, the dependence of the statistical situation of energy levels is considered to the mass of nuclei, spins, half-lives of the ground state, bands of energy, and different configurations of excited bands of energies. The results suggested obvious differences in the spectral situation of the levels in different rotational bands and also different mass regions. Also, the displacement of levels and the lower energy of  state in comparison with level reduce the correlation of levels in spectral statistics.