Mathematical Physics


Advance on Electron Deep Orbits of the Hydrogen Atom

Authors: J.L.Paillet, A.Meulenberg

In previous works, we discussed arguments for and against the deep orbits, as exemplified in published solutions. So we considered the works of Maly and Va’vra on the topic, the most complete solution available and one showing an infinite family of EDO solutions. In particular, we deeply analyzed their 2nd of these papers, where they consider a finite nucleus and look for solutions with a Coulomb potential modified inside the nucleus. In the present paper, we quickly recall our analysis, verification, and extension of their results. Moreover, we answer to a recent criticism that the EDOs would represent negative energy states and therefore would not qualify as an answer to the questions posed by Cold Fusion results. We can prove, by means of a simple algebraic argument based on the solution process, that, while at the transition region, the energy of the EDOs are positive. Next, we deepen the essential role of Special Relativity as source of the EDOs, which we discussed in previous papers. But the central topic of our present study is an initial analysis of the magnetic interactions near the nucleus, with the aim of solving important physical questions: do the EDOs satisfy the Heisenberg Uncertainty relation (HUR)? Are the orbits stable? So, we examine some works related to the Vigier-Barut Model, with potentials including magnetic coupling. We also carried out approximate computations to evaluate the strength of these interactions and the possibilities of their answering some of our questions. As a first result, we can expect the HUR to be respected by EDOs, due to the high energies of the magnetic interactions near the nucleus. Present computations for stability do not yet give a plain result; we need further studies and tools based on QED to face the complexity of the near-nuclear region. For the creation of EDOs, we outline a possibility based on magnetic coupling.

Comments: 12 Pages.

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[v1] 2017-01-28 10:44:20

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