Jean-luc Paillet
andrew meulenberg
Jean-Luc Paillet
580 California St., Suite 400
San Francisco, CA, 94104
Basis for Electron Deep Orbits of the Hydrogen Atom
Sign up for access to the world's latest research
Abstract
In this paper, we look into the difficult question of electron deep levels (EDLs) in the hydrogen atom. Acceptance of these levels and, in particular, experimental evidence of their existence would have major implications for the basis for cold fusion and would open up new fields of femto-physics and-chemistry. An introduction shows some general considerations on these orbits as " anomalous " (and usually rejected) solutions of relativistic quantum equations. The first part of our study is devoted to a discussion of the arguments against the deep orbits and for them, as exemplified in published solutions. We examine each of the principal negative arguments found in the literature and show how it is possible to resolve the questions raised. In fact, most of the problems are related to the singularity of the Coulomb potential when considering the nucleus as a point charge, and so they can be easily resolved when considering a more realistic potential with finite value inside the nucleus. In a second part, we consider specific works on deep orbits, named Dirac Deep Levels (DDLs), as solutions of the relativistic Schrödinger and of the Dirac equations. The latter presents the most complete solution and development for spin ½ particles, and includes an infinite family of DDL solutions. We examine particularities of these DDL solutions and more generally of the anomalous solutions. Next we analyze the methods for, and the properties of, the solutions that include a corrected potential inside the nucleus, and we examine the questions raised by this new element. Finally we indicate, in the conclusion, open questions such as the physical meaning of the relation between quantum numbers determining the deep levels and the fact that the angular momentum seems two orders-of-magnitude lower than the values associated with the Planck constant. Introduction For many decades, the question of the existence of electron deep levels (EDLs) for the hydrogen atom led to numerous works and debates. Why once more a study on this subject? For several reasons: • the arguments in favor of the deep orbits have become progressively more mature by the use of relativistic quantum tools for a full three-dimensional description of the system; • by accepting the reality of a non-singular central potential within a nuclear region, many mathematical arguments against anomalous solutions of the relativistic equations no longer pertain; • numerical evaluation of the relativistic equations are now detailed and available for interpretation of the models, their implications, and their predictions; • hydrogen atoms, including deuterium, with electron deep orbits (femto-atoms) can contribute to the understanding of: processes of cold fusion inside condensed matter, the avoidance of nuclear fragmentation in D-D => 4 He fusion reactions, and a means of increasing the rate of energy transfer between an excited nucleus and the surrounding lattice; • and, above all, recognition of these levels opens up a whole new realm of atomic, nuclear, and subatomic-particle physics as well as nuclear chemistry. There are various theoretical ways to define a state of the hydrogen atom with electron deep level (EDL) or deep Dirac level (DDL) orbits. In the following, we denote H # as any state of hydrogen atom with EDL orbits. Some authors use the term hydrino for denoting the H # states owing to the work of [1] on the hypothetical existence of H atoms with orbit levels under the Bohr ground level and where the values of orbit radii are fractional values of the Bohr radius. Here we do not use this term, a physical concept specifically attached to the cited work, because it is not deduced from (standard) quantum equations, while we essentially consider the states H # obtained by the methods of relativistic quantum physics. With the quantum equations habitually used in the literature for computing the bound states of the H atom, we can note that there is in general a crossroad with a choice of value or a choice of sign for a square root in a parameter. According to which path is chosen, the resolution process leads either to the usual solution or to an unusual one called an "anomalous" solution; one that is rejected in the Quantum Mechanics Textbooks.
References (24)
- R.L.Mills. The Grand Unified Theory of Classical Physics, 2011, ed. Black Light Power. Vydrino
- J. Maly and J. Va'vra, Electron Transitions on Deep Dirac Levels II, Fusion Technology, Vol. 27, January 1995
- Jan Naudts. On the hydrino state of the relativistic hydrogen atom, http://arXiv:physics/0507193v2
- David Tong: Lectures on Quantum Field Theory. University of Cambridge, UK. http://www.damtp.cam.ac.uk/user/tong/qft.html
- H.Kleinert. Particles and Quantum Field. Lectures at the Freie Universität Berlin. http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf
- L.I. Schiff. Quantum Mechanics. 3e Edition. McGraw Publishing Company, 1968.
- S.Weinberg. The Quantum Theory of Field. Vol.1., Foundations, Cambridge University Press,1995.
- Antonio S.de Castro. Orthogonality criterion for banishing Hydrino states from standard quantum mechanics. Physics Letters A 369 (2007) 380-383.
- J-L. Paillet, A.Meulenberg, Arguments for the Anomalous Solutions of the Dirac equations, http://viXra.org/abs/1506.0177.
- T. Nadareishvili and A. Khelashvili. Some Problems of Self-Adjoint Extension in the Schrodinger equation. http://arxiv.org/pdf/0903.0234.pdf
- Guy Bonneau, Jacques Faraut, Galliano Valent. Self-adjoint extensions of operators and the teaching of quantum mechanics. http://arXiv:quant-ph/0103153v1
- Norman Dombey.The hydrino and other unlikely states. http://arxiv.org/pdf/physics/0608095.pdf
- E.T.Whittaker , G.N.Watson,Modern Analysis. 4th ed. chapter XVI.Cambridge Univ. Press., 1940.
- J.A.Maly, J.Va'vra, Electron Transitions on Deep Dirac Levels I, Fusion Technol., 24, p.307 (1993)
- Bern Thaller, The Dirac Operator, in Relativistic Electronic Structure Theory: Part 1. Theory (Theoretical and Computational Chemistry # 11), Chap. 2, Ed. P. Schwerdtfeger, 2002.
- A.Meulenberg, J-L.Paillet, "Nature of the deep-Dirac levels," this proceedings
- Bern Thaller. The Dirac Equation, Springer-Verlag, 1992.
- S.Fluegge, Practical Quantum Mechanics, Vol.2, Springer V. Berlin,1974.
- R T Deck, Jacques G Amar and Gustave Fralick. Nuclear size corrections to the energy levels of single-electron and -muon atoms. J. Phys. B: At. Mol. Opt. Phys. 38 (2005) 2173-2186
- J.J.Sakurai, Jim Napolitano. Modern Quantum Mechanics, 2d Ed. Addison-Wesley.
- D.Andrae. Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules, Physics Reports 336, pp.413-525, 2000.
- G.Arfken, Mathematical Methods for Physicists 3 rd ed n (New York: Academic) p 756. 1965
- M. Abramowitz, I. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 9th Ed., 1970.
- John W. Pearson. Computation of Hypergeometric Functions. School of Mathematics, The University of Edinburgh, 2009/9/4. Link= ox.ac.uk