Classical nuclear models such as the shell model, the liquid-drop model, and the “magic number” concept have historically been used to describe nuclear stability [1]-[4].

While these approaches successfully explain many isotopic behaviors, they fail to account for transitional regions, particularly in heavy nuclei such as Mercury (Hg) [3][5]-[7].

The Alikhan Symmetry Model proposes a complementary framework in which the nucleus is interpreted as a layered proton-neutron structure [5].

In this model, stability emerges from the spatial symmetry between polar and equatorial regions, even-odd neutron parity, and the balance between nuclear attraction and Coulomb repulsion [5].

It should be noted at the outset that the present model is qualitative in nature and is intended to reveal systematic structural correlations rather than provide exact quantitative predictions.

The primary objective of this study is to test the explanatory power of the Alikhan Symmetry Model against experimental half-life data of Hg isotopes across a wide mass range.

The neutron framework is constructed using symmetrical layers distributed around the equator.

Each layer follows a numeric sequence (1 + 3 + 6 + 9 + 12 + …), representing spatial shells [5], arising from the progressive filling of concentric equatorial layers with increasing circumference, reflecting a simplified geometric growth of nuclear cross-sections.

When the equatorial balance (“Ekvator balansı”) equals zero, the nucleus is perfectly symmetric, ensuring stability [5][8][9].

In this framework, a value of 0 corresponds to an equal number of neutrons on both sides of the equatorial plane, whereas deviations of ±1 arise when one additional neutron occupies either the upper or lower equatorial-adjacent layer, producing mechanical and energetic asymmetry.

This geometric interpretation does not replace quantum mechanical descriptions but provides a complementary macroscopic symmetry criterion.

A deviation of ±1 introduces mechanical and energetic imbalance, leading to reduced stability [9].

The “stability interval” refers to the range of isotopic compositions where nuclear attraction and Coulomb repulsion reach equilibrium [6].

In practical terms, this interval corresponds to a limited N-Z range in which the equatorial balance remains equal to 0 or fluctuates minimally (±1) without destroying global symmetry.

Deficit (“def”) and surplus (“artıq”) zones in the N-Z balance define regions of instability [6][10].

These results suggest that spatial symmetry considerations can serve as a unifying framework linking empirical decay data with structural nuclear models.

A clear correlation between spatial symmetry, neutron parity, and experimental half-lives is established [6][9][10].

The Alikhan Symmetry Model complements the magic number concept (N = 82, 126) by interpreting magic closures as the completion of symmetric structural layers [1][2][5]. In particular, the neutron magic number N = 126 corresponds in the model to the completion of a fully symmetric neutron framework layer, after which additional neutrons necessarily occupy asymmetric positions, leading to instability.

Hg (Z = 80), being close to the magic proton number 82, exhibits quasi-magic behavior aligned with harmonic shell closure in the model [1][8].

Stability is thus understood not only as quantum shell filling but also as a dynamic equilibrium between symmetry and force interactions [5][9].

The Alikhan symmetry-based framework provides a coherent explanation for the stability of Mercury isotopes consistent with experimental observations [6].

By uniting structural symmetry, proton-neutron parity, and nuclear-Coulomb balance, the model refines the understanding of isotopic stability [5][9].

Although qualitative, the approach uncovers systematic relationships that align with established nuclear principles, demonstrating that spatial symmetry considerations can enhance modern nuclear theories [1]-[4]. Future studies may extend this approach to other heavy nuclei to further evaluate its general applicability.