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Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

In this paper, we report on a study of the spectral features associated with dipole resonances in medium-mass nuclei ( E ≤ 12 MeV ) , as revealed in the framework of the spd-interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe ansatz equation. In general, calculated spectra around the critical point of the vibrational to γ -soft transitions appear to approach those of a Gaussian orthogonal ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength c p in the transition region; that is, when c p is zero, or when the system approaches one of its dynamical symmetry limits, the spectra display regular features, while for stronger c p values, or when near to the critical phase transition region, the spectral features show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector boson modes of the theory. As part of this work we also found out that chaoticity occurred when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive- and negative-parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for A ≈ 32 – 138 nuclei.