Papers by Jean-luc Paillet
viXra, 2016
This work continues our previous works on electron deep orbits of the hydrogen atom. An introduct... more This work continues our previous works on electron deep orbits of the hydrogen atom. An introduction shows the importance of the deep orbits of hydrogen (H or D) for research in the LENR domain, and gives some general considerations on the Electron Deep Orbits (EDOs). In a first part we quickly recall the known criticism against the EDO and how we face it. In particular, a solution to fix all problems is to consider a modified Coulomb potential with finite value inside the nucleus. For this reason, we deeply analyzed the specific work of Maly and Va’vra on deep orbits as solutions of the Dirac equation, with such a modified Coulomb potential without singular point. Then, by using a more complete ansatz, we made numerous computations on the wavefunctions of these EDOs, allowing to confirm the approximate size of the mean radii of orbits and to find further properties. Moreover, we observed that the essential element for obtaining deep orbits solutions is special relativity. At a firs...
Journal of Condensed Matter Nuclear Science, #29, 2019
We address a number of questions relating to the progress of our study on the relativistic-electr... more We address a number of questions relating to the progress of our study on the relativistic-electron deep orbits (EDOs): (1) How to combine different EM potentials having two possible versions (attractive and repulsive), while rejecting unrealistic energies? (2) What about the angular momentum of the deep electrons? How is the Heisenberg Uncertainty Relation satisfied in these EDOs? (3) From where is extracted the high kinetic energy (of order 100 MeV) of the deep-orbit electrons? (4) What is the behavior of the effective potential V eff as a function of distance to the nucleus? (5) What is the order of magnitude of the radiative corrections for the EDO's? (6) What is the relation between EDO solutions of the Dirac equation and the high energy resonances (with high binding energies) corresponding to a semi-classical local minimum of energy?
Maly and Va’vra (M&V) in 1993 and 1995 presented a computational evaluation of the Dirac equation... more Maly and Va’vra (M&V) in 1993 and 1995 presented a computational evaluation of the Dirac equations that included the ‘anomalous’ solution. The regular solutions of these equations are the basis for modern quantum mechanical predictions for comparison with the experimental values of atomic-electron orbital energies. The other solution, discussed in the literature for over 55 years, is relativistic and considered anomalous because its predicted levels are very deep (up to 511 keV) and have never been observed. Nevertheless, the existence of these deep levels provides a ready explanation of the mechanism for penetration of the Coulomb barrier and the means of D–D fusion below the He fragmentation levels. Since these levels also provide the basis for all of the other cold fusion observations (both PdD and NiH systems), it is important that arguments for and against the Dirac model be examined. The theoretical support for this anomalous solution is provided in a companion paper in this c...
mail: [email protected] ABSTRACT In this paper, we present an original discrete eve... more mail: [email protected] ABSTRACT In this paper, we present an original discrete event formalism for the specification of control systems at a high level of abstraction. The concept of event being more natural than the concept of state, the proposed formalism is centered on this concept of event. It allows the expression of an asynchronous behaviour using this concept. In addition, this formalism offers an explicit representation of time that allows to use temporal simulations for the validation of the formal specifications, after translation into DEVS models.
DECM is a formalism allowing users to describe specifications of discrete event control systems, ... more DECM is a formalism allowing users to describe specifications of discrete event control systems, in a natural way, by means of clauses. When a precondition is satisfied, a control event is emitted towards the controlled device, and we can consider that the effect of this command is realized after some delay. Previously, we considered precise delays that represent in fact mean delays. In order to have a finer representation of real situations, we introduce here imprecise delays, in the form of "Min-Max" delays. Then, a delay is represented through an interval, and any value in the interval is a possible value for the actual delay. In these conditions, if the delays are too imprecise, then the model indicates that a correct running cannot be ensured.
Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1978
In this paper, we look into the difficult question of electron deep levels in the hydrogen atom. ... more In this paper, we look into the difficult question of electron deep levels in the hydrogen atom. 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 the second part, we consider specific works on deep orbits as solutions of the relativistic Schrödinger and of the Dirac equations, named Dirac Deep Levels (DDLs). The latter presents the most complete solution and development for spin 1 / 2 particles, and includes an infinite family of DDL solutions. We examine particularities of these DDL solutions and more generally of the anomalous solutions. We next 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. As a prerequisite to a deep comprehension of the resolution methods, we recall in the appendices some essential elements of the Dirac theory.
In this paper, we present DECM (Discrete Event Calculus Model), an original discrete event mathem... more In this paper, we present DECM (Discrete Event Calculus Model), an original discrete event mathematical model for the specification of control systems at a high level of abstraction. Because the concept of event is more natural for nonspecialists than the concept of state, the proposed model is centered on the latter concept. This in turn permits the expression of asynchronous
In this paper, we look into the difficult question of electron deep levels (EDLs) in the hydrogen... more 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.
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Papers by Jean-luc Paillet