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Symmetries of the oblate deformed harmonic oscillator

Martin Freer,Thomas Marsh,James Souter

JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS（2022）

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Abstract
A study of oblate shell closures of the deformed harmonic oscillator (HO) shows that the associated magic numbers are linked to a universal sequence of the triangular numbers (1, 3, 6, 10, 15, 21 horizontal ellipsis ) which describe equally prolate, spherical and oblate structures. This provides a new basis for the understanding of the deformed HO. The consequences for oblate nuclei are discussed, in particular C-12 and Si-28.
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Key words
nuclear clustering, deformed harmonic oscillator, structure of light nuclei
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