Geometric Derivation of Effective Nuclear Charge from the Ω-Model: A First-Principles Approach

This paper presents a first-principles approach to deriving the effective nuclear charge Zeff in atomic systems using the Ω-Model, a unified geometric framework forgravity and electromagnetism. Unlike traditional methods that rely on empirical shielding constants, this method calculates Zeff directly from the electron’s orbital and energy frequencies, modified by the geometric shielding effects of inner electron shells. The approach is applied to hydrogen-like atoms, multi-electron systems, andextended to the case of argon (Ar) to show its applicability. In particular, the paper explores the use of the reduced-mass Bohr radius, demonstrating that this providesmore accurate results compared to the standard Bohr radius.