Three-State Mixing as a Phenomenological Framework for Multiple Shape Coexistence
Abstract
Shape coexistence represents one of the most striking manifestations of competing collective and single-particle degrees of freedom in atomic nuclei. While the coexistence and mixing of two configurations can be described within the well-established Two-State Mixing framework, the observation of three or more competing structures requires a more general treatment. In this work, we introduce a Three-State Mixing (3SM) model in which three intrinsic configurations are related to the physical states through an SO(3) rotation. The framework establishes a direct connection between experimental observables, configuration-mixing amplitudes, and intrinsic properties, while the experimentally known excitation energies allow the corresponding effective Hamiltonian and interaction strengths to be reconstructed. The model is applied to the low-lying structure of 116Sn using electromagnetic matrix elements recently determined through a comprehensive Coulomb-excitation measurement. The analysis identifies three intrinsic configurations characterized by spherical, weakly oblate, and strongly deformed triaxial shapes, together with substantial configuration mixing among the physical 0+ states. The present formulation provides a general phenomenological framework for investigating systems in which multiple configurations coexist and strongly interact.
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BibTeX
@misc{siciliano2026threestate,
title = {{Three-State Mixing as a Phenomenological Framework for Multiple Shape Coexistence}},
author = {Marco Siciliano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19300},
eprint = {2609.19300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19300},
}
RIS
TY - UNPB
TI - Three-State Mixing as a Phenomenological Framework for Multiple Shape Coexistence
AU - Marco Siciliano
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19300
UR - https://arxiv.org/abs/2609.19300
AB - Shape coexistence represents one of the most striking manifestations of competing collective and single-particle degrees of freedom in atomic nuclei. While the coexistence and mixing of two configurations can be described within the well-established Two-State Mixing framework, the observation of three or more competing structures requires a more general treatment. In this work, we introduce a Three-State Mixing (3SM) model in which three intrinsic configurations are related to the physical states through an SO(3) rotation. The framework establishes a direct connection between experimental observables, configuration-mixing amplitudes, and intrinsic properties, while the experimentally known excitation energies allow the corresponding effective Hamiltonian and interaction strengths to be reconstructed. The model is applied to the low-lying structure of ^116Sn using electromagnetic matrix elements recently determined through a comprehensive Coulomb-excitation measurement. The analysis identifies three intrinsic configurations characterized by spherical, weakly oblate, and strongly deformed triaxial shapes, together with substantial configuration mixing among the physical 0^+ states. The present formulation provides a general phenomenological framework for investigating systems in which multiple configurations coexist and strongly interact.
ER -