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The Invariant-Mass-Based Equation for Bound States of the Hydrogen and the Helium Atoms
Version 1
: Received: 14 August 2023 / Approved: 14 August 2023 / Online: 15 August 2023 (03:36:50 CEST)
How to cite: Agafonov, A. The Invariant-Mass-Based Equation for Bound States of the Hydrogen and the Helium Atoms. Preprints 2023, 2023081031. https://doi.org/10.20944/preprints202308.1031.v1 Agafonov, A. The Invariant-Mass-Based Equation for Bound States of the Hydrogen and the Helium Atoms. Preprints 2023, 2023081031. https://doi.org/10.20944/preprints202308.1031.v1
Abstract
The invariant mass of free particles is used to derive a bound-state equation for several particle atomic systems at rest. This relativistic-kinematic bound-state equation is applied to the hydrogen and helium atoms. The derived equation has the well-known solutions for the single-electron bound states of the hydrogen atom, and the two-electron states of the helium atom. For the hydrogen atom, existence of the two-particle bound states, for which the electron and the proton kinetic energies are of the same order of magnitude, is predicted. The three-particle bound states with the same feature of the kinetic energies can exist in the helium atom. Radiative operators for processes involving the hydrogen two-particle bound states, are obtained. It is discussed that these new two- and three-particle bound states should be optically inactive.
Keywords
bound-state equation; one-electron atom; two-electron atom, radiative transitions
Subject
Physical Sciences, Atomic and Molecular Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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