Hidden Angular Momentum in Atomic Systems (HAMAS)

Jincheng Zhang

Published Aug 19, 2026• 0 citations

Abstract

The conventional description of angular momentum in atomic physics divides the total angular momentum of an electron into an orbital part, L, and a spin part, S. In this work we propose the existence of an additional, hidden component of angular momentum, L_h, that is not directly observable through standard measurements of L or S but contributes to the full algebraic structure of the atomic system. We construct a formalism in which the total angular momentum operator J is expressed as J = L + S + L_h, and we show that L_h satisfies a set of commutation relations with the Hamiltonian that guarantee its conservation in isolated atoms. The hidden component is shown to arise naturally from the coupling of the electron's intrinsic spin to the electromagnetic field in a gauge-invariant manner. We discuss the theoretical implications of L_h for the spectrum of hydrogenic atoms and for multi-electron systems, and we propose that high-precision spectroscopic techniques, such as optical lattice clocks and quantum logic spectroscopy, can detect the influence of L_h through subtle shifts in energy levels and selection rules. The presence of hidden angular momentum suggests that the set of quantum numbers needed to fully characterize atomic states should be expanded, potentially leading to new insights into atomic structure and to the identification of previously unobserved spectral lines.

DOI: 10.5281/zenodo.22005294

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