Level statistical properties of the spherical mean-field plus standard pairing model

The effect of pairing correlations on the spectral statistical behavior of the spherical mean-field plus standard pairing model is investigated based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. It is found that varying the pairing interaction strength G in the model alters the statistical properties of the spectrum of the model. The spectrum is regular when G is nonzero and either well below or well beyond the critical region of normal (localized) to superconducting (pair condensate) phase transition of the model, through which it is likely to display features of chaotic behavior. It is verified that the level statistics governed by the interplay between the single-particle energies and the pairing interaction for Ca48-53 calculated from the model with single-particle energies and a pairing strength extracted from experimental data indeed exhibits, for two of the Ca isotopes, spectral behaviors that deviate from the Poisson statistics within the phase transitional region, while most isotopes display regular spectra.