Magic numbers of cylindrical symmetry
Andriana Martinou, Dennis Bonatsos

TL;DR
This paper proposes a new perspective on nuclear magic numbers based on symmetry and selection rules, explaining phenomena that challenge traditional definitions and predicting two distinct sets of magic numbers from harmonic oscillator symmetries.
Contribution
It introduces a symmetry-based framework using quadrupole interaction selection rules to define two sets of magic numbers, addressing limitations of the traditional energy gap approach.
Findings
Identifies two sets of magic numbers from harmonic oscillator symmetries.
Explains phenomena like the island of inversion and shape coexistence.
Predicts new magic numbers based on cylindrical symmetry.
Abstract
In nuclear physics a magic number is defined as the nucleon number, which is separated by a significantly large single-particle energy gap from the next nucleon. Magic numbers define the nuclear shells, which are considered to be active, only if they are partially occupied by nucleons. As a consequence the single particle interactions of the valence nucleons lead to the description of the collective properties of the whole nucleus in the shell model theory. But phenomena as the island of inversion, the shape coexistence and the break down of the N=20 magic number reveal that the above definition of a magic number is deficient. A complementary definition should rely on the selection rules of the single particle interactions. Specifically the selection rules of the quadrupole-quadrupole interaction lead to two sets of magic numbers, namely the harmonic oscillator magic numbers 2, 8 20,…
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Taxonomy
TopicsNuclear physics research studies · Scientific Research and Discoveries · Earth Systems and Cosmic Evolution
