https://doi.org/10.1140/epja/s10050-023-01225-y
Regular Article - Theoretical Physics
Cluster pictures of three dimensional harmonic oscillators with frequencies in rational ratios
Chiba Institute of Technology, 275-0023, Narashino, Chiba, Japan
a
masahiko.sugawara@it-chiba.ac.jp
Received:
14
March
2023
Accepted:
13
December
2023
Published online:
28
December
2023
Degeneracies of axially deformed harmonic oscillators with frequencies in rational ratios are decomposed into the sequences of 2, 6, 12, 20, 30, 42... that are the ones appearing in the spherical three dimensional harmonic oscillator. This property had been already discussed some time ago in relation to clustering phenomena for prolate cases, based on a multiple-SU(3) group structure. Recently this interpretation was extended to oblate cases using Harvey description applied to the fusion process of multiple-centered harmonic oscillators. Actually, it is known that degeneracies of three dimensional harmonic oscillators with frequencies in rational ratios are always decomposed into these numbers from the classification scheme of their eigen-states. Therefore cluster pictures adopted in the analysis of axially deformed harmonic oscillators can be generalized to include triaxially deformed cases. In this report, cluster pictures of three dimensional harmonic oscillators with frequencies in rational ratios are classified based on the dimensionality of their geometries and it is noted that the classification scheme is consistent with Harvey’s description. Moreover it is suggested that although not so simple as the oblate case, a similar pattern of cluster structures may appear in the traxially deformed case. Finally the configurations at the next higher shell closures than 
Mg are considered based on the present classification scheme and their implications are discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
