In this paper, we tried to get a new signature of regular nuclei based on their quadrupole transition rates. We have analyzed the experimental electric quadrupole transition probabilities of well-known "regular nuclei". The results indicate finding specific repetition patterns for E2 transition rates, similar to what has been reported for the energy levels of these nuclei. We also tested the existence of this observed repetition scheme for all known isotopes whose experimental transition rates are available and introduced several new candidates as regular nuclei. Then, the energy spectra (Experimental) of these new suggested "regular nuclei" are investigated in the framework of the Interacting Boson Model, in which the parameters of Hamiltonian confirm the placement of these nuclei in the "Alhassid-Whelan arc of regularity" region. In order to further study the statistical distribution of experimental energy levels related to the electromagnetic transitions we are considering, we studied using the random matrix theory. The results confirmed their regularity.
In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the [Formula: see text]Cd, [Formula: see text]Cd and [Formula: see text]Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of different energy levels indicates that there is a close relationship between ground and excited-state quantum phase transitions (ESQPTs).
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