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

Abstract

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 appears to approach that 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, cp, in the transition region; that is, when cp is zero, or when the system approaches one of its dynamical symmetries limits the spectrum display regular features, while for stronger cp values, or when near to the critical phase transition region, the spectral feature 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 bosons modes of the theory. As part of this work we also found out that chaoticity occurs 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.

Description of 2_3^+, 0_3^+Intruder States in 130Xe Nucleus by Mixing of Transitional Hamiltonian and O(6) Casimir Operator

“…We have extracted the best set of Hamiltonian's parameters, i.e.  and  , via the available experimental data [25][26][27][28][29] for excitation energies of selected states,…”

“…. The parameters of IBM-2 Hamiltonian for 130 Xe isotope which are extracted by least square method from experimental data were taken from[25][26][27][28][29] Ϭ is regarded as the quality for extraction processes (N=5 the Boson number)…”

Random Matrix Theory in Cd isotopes

“…, for the chaotic system, and as well an unfolding procedure to calculate the spectral statistics [18][19][20]. In Cd isotopes, the lengths of J π sequences are short, and therefore a much better measure is to use the ratio of consecutive spacings of adjacent energy levels, and recognize that there will be uncertainties associated with the unfolding.…”

Nuclear supersymmetry and dual algebraic structures

“…The quantum shape phase transition (QSPT) of even and odd nuclei based on q-deformed ( ) su 1, 1 algebraic model was studied in [40]. An extension of the original IBM to the multilevel case including negative parity f-and p-bosons was made and the affine ( ) su 1, 1 algebraic approach was applied to solve the multi-level pairing problem numerically via the dual algebraic structure, [41].…”