Statistical analysis of quadrupole transitions in shape-coexisting nuclei: Bridging theory and experiment

Abstract

This work presents a combined statistical and algebraic analysis of electric quadrupole transition probabilities B(E2) in nuclei exhibiting shape coexistence (SC). Experimental B(E2) values for selected intra-band and inter-band transitions are examined using random matrix theory (RMT), where the unfolding procedure and the Porter–Thomas distribution are employed to quantify the degree of correlation among transition strengths. The extracted correlation parameter and the variance of the unfolded B(E2) distributions are interpreted in connection with configuration mixing, providing statistical signatures of coexisting spherical, γ-soft, and deformed structures. To complement the experimental analysis, theoretical B(E2) values are calculated within the Interacting Boson Model (IBM-1). A detailed derivation of the reduced matrix elements of the quadrupole operator in the U(5), O(6), and SU(3) dynamical symmetry limits is provided, including the explicit angular-momentum dependence of B(E2; J_i → J_f). The symmetry character of each nucleus and the structure of the excited bands (ground, γ, and β bands) are specified, and the IBM parameters are determined through a least-squares fit to low-lying energy levels. A comparison between experimental and theoretical B(E2) distributions reveals that nuclei located in known SC regions—particularly the Cd isotopic chain—exhibit a systematic reduction in the variance of ground-band transition strengths, consistent with enhanced configuration mixing. These results demonstrate that statistical properties of B(E2) values, when combined with IBM symmetry analysis, provide a sensitive complementary tool for identifying and characterizing shape coexistence in atomic nuclei.