What question did this study set out to answer?

The study aims to explore the effects of controlled anisotropic deformation on ECSM electron-like bound shells and their structural properties.

May 28, 2026Open Access

Controlled Anisotropic Fine-Structure-Like Splitting of ECSM Electron-Like Bound Shells

Key Points

The study aims to explore the effects of controlled anisotropic deformation on ECSM electron-like bound shells and their structural properties.
Introduced a controlled anisotropic deformation to the V12 ECSM shell hierarchy.
Compared isotropic and anisotropic shell structures under various criteria.
Validated findings using a detailed notebook with 24 final criteria.
Achieved fine-structure-like sublevel splitting for nonzero anisotropy while maintaining shell capacity.
All structural stability criteria were satisfied, leading to a final label of PASS.
Reconstructed the V12 isotropic shell structure at zero anisotropy successfully.

Abstract

This paper reports the V13 ECSM electron-like packet test, extending the V12 response-well bound-state shell hierarchy by introducing a controlled anisotropic deformation. The construction recovers the V12 isotropic shell structure at zero anisotropy, then shows fine-structure-like sublevel splitting for nonzero anisotropy while preserving shell capacity, determinant filling, duplicate exclusion, closure filling, and chi-deformed structural stability. The notebook passes all 24 final criteria, with final label: PASS: controlled anisotropic fine-structure-like splitting of ECSM bound shells.

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