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Solution of the Dirac equation with Coulomb and magnetic moment interactions
Abstract
The Dirac equation for a charged spin 1/2 particle with an anomalous magnetic moment in the Coulomb field is solved. A new phenomenon of formation of very narrow resonances of very high mass at small distances is demonstrated.
... Magnetic forces between spin 1/2 particles lead to the effective radial potentials of this type [1][2][3], with one or more deep narrow wells. Magnetic interactions are studied for various problems ranging from macroscopic to microscopic scales [4][5][6][7][8][9][10]. ...
... Let us consider, for example, a relativistic charged spinless particle m in a field of a fixed (quantum ) magnetic moment ⃗ [11], or alterentivly , a charged spin 1/2 particle of mass m and magntic moment ⃗ , in the field of a fixed charge [12,13]. In both cases the radial equation has the form [− 2 2 + − 2 ] ( ) = 0 (1) Where the effective potential is given, apart from the Coulomb potential , by ( ) = 2 + 3 + 4 (2) Clearly, if one solves the same problem with a Dirac equation and give also an anomalous magnetic moment ⃗ to the particle, then additional terms are added to equation (2). Further models may also treat the magnetic moment of both particles. ...
... Let us consider, for example, a relativistic charged spinless particle m in a field of a fixed (quantum ) magnetic moment ⃗ [11], or alterentivly , a charged spin 1/2 particle of mass m and magntic moment ⃗ , in the field of a fixed charge [12,13]. In both cases the radial equation has the form [− 2 2 + − 2 ] ( ) = 0 (1) Where the effective potential is given, apart from the Coulomb potential , by ( ) = 2 + 3 + 4 (2) Clearly, if one solves the same problem with a Dirac equation and give also an anomalous magnetic moment ⃗ to the particle, then additional terms are added to equation (2). Further models may also treat the magnetic moment of both particles. ...
In the present work, we present different two body potentials which have oscillatory shapes. The eigenvalues and eigenfunctions are obtained for those problems by solving Schrodinger equation using Nikiforov Uvarov method.
... For critical binding of high-Z nuclei we compare in sect. 5.4 the analytic solutions of the KGP equation to the numerical solutions of DP presented by Thaller [15], and review another analysis done by Barut and Kraus [16,17]. Our findings are summarized in sect. ...
... The DP equation also allows for the so-called superpositronium states as described by Barut and Kraus [16,17]. Such states represent resonances due to the magnetic interaction that reside incredibly close to the center of the atom i.e. r 2 ≈aα /mc, but this feature is absent from the KGP formation of the Coulomb problem as all KGP-Coulomb wave functions which can be normalized can be successfully matched to their Dirac (g = 2) companions. ...
We investigate relativistic quantum mechanics (RQM) for particles with arbitrary magnetic moment. We compare two well known RQM models: a) Dirac equation supplemented with an incremental Pauli term (DP); b) Klein-Gordon equations with full Pauli EM dipole moment term (KGP). We compare exact solutions to the external field cases in the limit of weak and strong (critical) fields for: i) homogeneous magnetic field, and ii) the Coulomb \( 1/r\)-potential. For i) we consider the Landau energies and the Landau states as a function of the gyromagnetic factor (g-factor). For ii) we investigate contribution to the Lamb shift and the fine structure splitting. For both we address the limit of strong binding and show that these two formulations grossly disagree. We discuss possible experiments capable of distinguishing between KGP and DP models in laboratory. We describe the impact of our considerations in the astrophysical context (magnetars). We introduce novel RQM models of magnetic moments which can be further explored.
... Section 5.2 suggests an improved version of the KGP equation, which produces better strong field behavior. For critical binding of high-Z nuclei we compare in section 5.3 the analytic solutions of the KGP equation to the numerical solutions of DP presented by Thaller [13], and review another analysis done by Barut and Kraus [14,15]. Our findings are summarized in section 6 where we also discuss future research directions. ...
... The DP equation also allows for the so-called superpositronium states as described by Barut and Kraus [14,15]. Such states represent resonances due to the magnetic interaction that reside incredibly close to the center of the atom i.e r 2 ≈ aα /mc, but this feature is absent from the KGP formation of the Coulomb problem as all KGP-Coulomb wave functions which can be normalized can be successfully matched to their Dirac (g = 2) companions. ...
We investigate relativistic quantum mechanics (RQM) for particles with arbitrary magnetic moment. We compare two well known RQM models: a) Dirac equation supplemented with an incremental Pauli term (DP); b) Klein-Gordon equations with full Pauli EM dipole moment term (KGP). We compare exact solutions to the external field cases in the limit of weak and strong (critical) fields for: i) homogeneous magnetic field, and ii) the Coulomb 1=r-potential. For i) we consider the Landau energies and the Landau states as a function of the gyromagnetic factor (g-factor). For ii) we investigate contribution to the Lamb shift and the fine structure splitting. For both we address the limit of strong binding and show that these two formulations grossly disagree. We discuss possible experiments capable of distinguishing between KGP and DP models in laboratory and note that novel RQM models of magnetic moments can be explored.
... We assume that the a k can be so defined. This system is a generalization of one used in [1] to model a relativistic electron in a Coulomb field with anomalous magnetic moment; in [1] the weights were set to unity. For (3.8) we see that ...
... We assume that the a k can be so defined. This system is a generalization of one used in [1] to model a relativistic electron in a Coulomb field with anomalous magnetic moment; in [1] the weights were set to unity. For (3.8) we see that ...
In this paper we consider the one dimensional Dirac system
1.1
where α k (x) < 0, λ is a complex spectral parameter, and the remaining coefficients are suitably smooth and real valued. We regard (1.1) as regular at x = a but singular at x = b ; in Section 4 we extend our result to problems having two singular endpoints.
Equation (1.1) arises from the three dimensional Dirac equation with spherically symmetric potential, following a separation of variables. For the choices p(x) = k/x , α k (x) = 1, p 2 ( x ) = (z/x) + c , p 1 ( x ) = (z/x) – c , and appropriate values of the constants, (1.1) is the radial wave equation in relativistic quantum mechanics for a particle in a field of potential V = z/x [ 17 ]. Such an equation was studied by Kalf [ 11 ] in the context of limit point-limit circle criteria, which is one of the matters we consider here.
... The existence of bound states of neutrino (latent) with protons, deuterons, and other nuclei follows from the well-known estimations of anomalous neutrino magnetic moment 1 and the Dirac's equation. 2,3 The concept of relic neutrino leads to the possibility of the neutrino component of the matter. If we assume the existence of the neutrino component of the matter, the question arises as to whether these neutrinos are capable of initiating nuclear transmutations. ...
... 6 The assumption on the occurrence of reactions (1)-(3) appeared as a result of the study of the background gamma spectra formation in germanium gamma spectrometers, used in astrophysical research. 4 Given below is experimental evidence on the existence of reactions (1)- (3). The data proving the existence of the above reactions are also provided ...
Anomalous elemental changes have been observed on the Pd complexes after D2 gas permeation. This effect--effect Y. Iwamura--belongs to a new category of nuclear reactions. The effect of Y. Iwamura can stimulate development of physics of electromagnetic interaction neutrino including physics of relic neutrino and physics of the dineutrons. It is possible to suggest that low-energy neutrino and even relic neutrino can initiate effect of transmutation in special cases. The suggested hypothesis application about new class nu- nuclear reaction existence can be useful for the problems: alternative energetic, radioactive isotopes reducing and rare isotopes production.
... where q, p i , r ij ∈ C ([a, b]) (i, j = 1, 2) are complex-valued functions, and E ∈ C is in general a complex parameter. Apart from few cases in which the Dirac equation possesses exact solutions given in a closed-form (see, e.g., [15][16][17][18]), numerical methods are available for calculating approximate solutions and estimating parts of the spectra [19][20][21][22][23][24]. Nonetheless, the recent paper [25] provides exact solutions to system (14a)-(14b) in the form spectral parameter power series (SPPS). ...
In this work we consider the one-dimensional Dirac equation including an electrostatic potential with compact support, and focus on the regime of bound states. We obtain exact expressions for both the characteristic function and the eigenfunctions in L ² (ℝ, ℂ ² ), given in the form of power series of the energy parameter. This approach is meant for arbitrary bounded potentials, so that a square potential is a special case of the theory here presented. We derive an efficient numerical method for the calculation of approximate eigen-energies of the bound states. Finally, we investigate the physical sense of the eigen-energies that are forbidden in the non-relativistic regime in terms of the Klein tunneling.
... The Vigier-Barut (V-B) model and the works related to this model derived from works of Barut, e.g., Refs. [35,36], which were carried in a relativistic context, with a more complete Dirac equation. However, the above-named V-B model and the related works were made in a nonrelativistic framework. ...
We look into the difficult question of electron deep orbits (EDOs) in the hydrogen atom. Introductory chapters show these orbits as “anomalous” (usually rejected) solutions of relativistic quantum equations; their interest for LENR; the principal negative arguments found in the literature; how it is possible to resolve the questions raised; and some specific works on EDOs. We analyze the EDO works of Maly and Va’vra and define a more complete ansatz for the “inside” solutions. We demonstrate that the essential element for obtaining EDOs is Special Relativity. To extend the model, we analyze 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? Finally, we demonstrate how to satisfy the HUR for electrons confined near the nucleus (relativistic effects on the nuclear potentials), and why we expect high-energy resonances near the nucleus.
... (c) E-mail: pinaki.roy@tdtu.edu.vn (corresponding author) the relativistic Coulomb problem in a higher-dimensional curved space of constant positive [12,13] as well as negative curvature [14] have been found. In view of the observations made earlier, we feel it is important to study the Dirac Coulomb problem in (2 + 1)-dimensional curved spaces of constant positive and negative curvatures. ...
In this paper, we study generalizations of the two-dimensional relativistic Coulomb problem in curved geometries with constant positive and negative curvature. It is shown that in both cases the effective Schrödinger-like equations exhibit features of broken supersymmetry and the spectrum is obtained using the SWKB method. Some features of the spectra and restoration of supersymmetry in the zero curvature limit have also been analyzed.
... First, we analyzed several works on this subject from Barut [10][11][12][13] as well as the subsequent works on the socalled "Barut-Vigier model" [14][15][16][17][18] on the hydrogen atom. These latter papers were developed in a non-relativistic context, unlike those of Barut himself. ...
In previous works, we analyzed and countered arguments against the deep orbits, as discussed in published solutions. Moreover, we revealed the essential role of Special Relativity as source of electron deep orbits (EDOs). We also showed, from a well-known analytic method of solution of the Dirac equation, that the obtained EDOs have a positive energy. When including the magnetic interactions near the nucleus, we observed a breakthrough in how to satisfy the Heisenberg Uncertainty Relation (HUR) for electrons confined near the nucleus, in a radial zone of only a few fm. Here we chose a different method, by directly facing the HUR for such confined electrons, from which we deduce the coefficient γ of these highly relativistic electrons. Then we show the effective Coulomb potential due to a relativistic correction, can maintain the electrons in containment. Next we resume and deepen our study of the effects of EM interactions near the nucleus. We first obtain computation results: though approximate, we can effectively expect high-energy resonances near the nucleus. These results should be confirmed by using QFT-based methods.
... The possible structure of the nuclear molecules that was observed in this experiment can be explained with the magnetic beads model. This model is in agreement with model where nuclear molecules are formed fro m Vigier ato ms [5][6] coupled by magnetic mo ments in a linear thread-like structures. It is assumed that in nuclear molecu le some nucleon transfers are possible. ...
Several self-consistent observations have led to the conclusion that long-lived multi-core systems (nuclear molecules) exist. This conclusion is based on next results:
1. Some even and no add Bi isotopes were observed in the experiment;
2. The large-scale generation of elements in the clusters spontaneously emitted from the bismuth salt samples was found. There was no bismuth in these clusters, but only possible bismuth decay products (carbon, potassium)
3. Bismuth isotopes generation and clusters emission appeared with more that one year delay;
4 Bismuth isotopes generation and clusters emission might be initiated by flash light or alpha irradiation;
5. Emitted clusters had magnet properties;
6. The traces of the long linear structures (nuclear molecules) movement on the Si detector surface were found.
The phenomenological model of the nuclear molecules was suggested.
... The Vigier-Barut model and the works related to this model, derive from works of Barut, e.g. [23,24]. In these articles, the author looks for an analytic solution of the Dirac equation for a charged lepton with anomalous magnetic momentum (AMM) in Coulomb potential. ...
In the 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 second 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.
... • To study the stability of EDOs, we still have to work more deeply on the properties of magnetic interactions and other possible effects near the nucleus, in order to evaluate the possible combinations of potential energies. In particular, the ones involved in the works of Vigier [32], Barut et al. [33] and Samsonenko et al. [34], and the correction to the Dirac operator due to the anomalous magnetic moment of the electron [35] might pertain. ...
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 ⟨r⟩ of orbits and to find further properties. Moreover, we observed that the essential element for obtaining deep orbits solutions is special relativity. At a first glance, this fact results from an obvious algebraic property of the expression of energy levels obtained by the relativistic equations. Now, a comparative analysis of the relativistic and of the non-relativistic Schrödinger equation allows us to affirm that Special Relativity leads to the existence of EDOs because of the non-linear form of the relativistic expression for the total energy, which implies a relativistic non-linear correction to the Coulomb potential.
... Both electron and positron have large magnetic moments which contribute to the second potential well in effective potential, at distances much smaller then Bohr radius. Barut and his coworkers predicted that this second potential well can support resonances [3,4]. ...
... Critchtield (1976) has generalised the Dirac equation in a central field to include the scalar potential proportional to r and r -1. Barut and Kraus (1976) have solved the Dirac equation with the Coulomb potential plus the additional interaction due to the anomalous magnetic moment of the electron in the Coulomb field. The aim of this paper is to present the exact solutions for the electromagnetic potentials which assume particular functional dependance on the space co-ordinate. ...
In this paper Dirac equation for two electromagnetic potentials viz vector potential and scalar potential have been solved.
These solutions of the Dirac equation are written in terms of known solutions of the Schrödinger equation. The presentation
is within the two-component relativistic description. Mainly the bound state solutions have been obtained.
There are many publications out there dealing with the problem of magnetic interaction between elementary particles with intrinsic dipole moments. Basically, the magnetic interaction becomes significant at sufficiently small distances; therefore, the problem is complicated by the need to take into account relativistic effects. The derived equations with the composite potential of the Coulomb and magnetic dipole-dipole interactions generally do not have a clear and simple analytical solution. In this paper, we propose an approach to study a particular case of electron-electron interaction by numerically solving the M2 equation [7] [9].
Electrochemical reactions are usually thermally-activated and submitted to mass-transfer effects. Although classically, enhanced kinetics of an electrochemical reaction is obtained by heating the cell and feeding the reactant by forced convection, other means can be used to improve mass- and charge-transfer. This paper shortly reviews the effects of magnetic fields in electrochemistry. Using a static or an alternating magnetic field enables to enhance electrodeposition and electrocatalysis, via improved gas and species convection, electrochemical kinetics and whole reaction efficiency. Such enhancement can mainly be related to Lorentz and Kelvin forces, magneto-hydrodynamics (MHD), chiral-induced spin selectivity (CISS) and hyperthermia, these effects being described herein.
The interaction ΔUAMM of the Dirac particle anomalous magnetic moment (AMM) with the Coulomb field of a nucleus and its effect on the low-lying atomic levels are studied for Zα > 1 using both perturbative and essentially nonperturbative approaches. The Zα dependence of particle wavefunctions (WFs) is fully taken into account from the beginning. In deriving the ΔUAMM contribution, the nucleus is viewed either as a uniformly charged extended Coulomb source or as a distributed system formed by pointlike u and d quarks. When estimated nonperturbatively, the ΔUAMM-induced effects in the Dirac equation framework prove to be identical for these two cases. At the same time, the ΔUAMM-induced effect is specific in that its perturbative and nonperturbative estimates are very different for Δg ≃ const and practically identical as soon as the dynamical screening of AMM at short distances is taken into account in the Dirac equation.
The effects induced by the interaction ΔUAMM of the anomalous component of the electron magnetic moment with the Coulomb field of a nucleus at Zα > 1 are examined for the lower levels of a hydrogen-like atom within purely perturbative and essentially nonperturbative in α/π approaches. Owing to the specific features of the ΔUAMM operator for a point-like Coulomb source, the distribution of the charge over the volume of the nucleus is set in the nonperturbative case at the quark structure level using valence (constituent) u and d quarks. It is demonstrated that such nonperturbative analysis turns out to be nontrivial as well as the manner in which its results are altered in the transition from the central problem with spherical symmetry to the inclusion of the peripheral contribution. It is also demonstrated that these methods yield matching (with an accuracy no worse than 0.1%) results for the shift of levels 1s1/2 and 2p1/2 due to ΔUAMM at all values of Z through to critical ones. Thus, it is confirmed that the perturbation theory in α/π provides correct results for superheavy atoms if the complete dependence of the wave function on Zα is taken into account from the beginning.
The quantum mechanical charge-dipole and dipole-dipole interactions between elementary particles are considered. The incorrectness and difficulties of the standard perturbative treatment is shown. The nonperturbative treatment not only resolves these difficulties, but shows the existence of new type of resonance states which have far-reaching applications in nuclear and particle physics.
“Can high-energy physics be too easy?” asked a recent editorial in “Nature.”1) At present, the picture mostly used in high-energy phenomenology is becoming admittedly very complicated. Besides leptons (which we see), one introduces families of “quarks,” each with different colours, then the so-called “gluons,” which are the gauge vector mesons binding the quarks, then there are the so-called “Higgs particles,” which give masses to some of the vector mesons (all of which are not seen in the laboratory). One is already beginning to talk about a second generation of more fundamental and simpler objects for these quarks and gluons etc., even though these first generations of “basic” objects have not been seen. This type of framework seems to create more problems than it solves.2)
It is demonstrated that δ-functionlike singularities of the relativistic interaction Hamiltonian of two spin particles with electromagnetic interactions have an effect on the muon-proton overlap in the ground state of pµ-atoms of the order of 1–2% that may be important for the interpretation of high-accuracy measurements of the rate of muon capture by protons in hydrogen.
There is growing evidence that the electromagnetic interactions of fundamental particles have a much richer and deeper structure than that given by the perturbation series of quantum electrodynamics. It is the purpose of this paper to discuss the directions in which either the methods or the concepts of quantum electrodynamics have to be generalized and to point out possible novel and unexpected phenomena.
In these lectures I discuss some properties of large magnetic dipole fields, the phenomenon of magnetic resonances in dipole fields, and a dynamical model of hadrons and heavy leptons based on magnetic resonances.
In this chapter we begin a study of Dirac’s equation for a single particle in the presence of other particles and fields. This study actually commenced with the derivation of the bound-state energy levels in a fixed Coulomb field, although it was noted that the picture was not yet complete. For example, there are relativistic corrections to the hyperfine structure which can be obtained by accounting for nuclear mass, spin, and magnetic moment. Indeed, it is usually the finite size of the nucleus which is invoked to resolve the large-Z difficulties. Similarly, relativistic corrections to magnetic-field splitting arise in the form of the anomalous Zeeman effect. Many of these correction terms are readily evaluated by straightforward perturbation theory (e.g., Rose, 1961; Berestetskii, et al, 1971), and others will be developed more rigorously in Chapter 8.
The lower levels of the discrete spectrum of a hydrogen-like atom are calculated within the point-like nucleus approximation with nonperturbative consideration for the Schwinger interaction of the radiative component of the magnetic moment of a free electron with the Coulomb field of a nucleus. The behavior of the 1s
1/2, 2s
1/2, 2p
1/2, and 2p
3/2 levels is investigated depending on the nuclear charge values, including the range of Z > 137, where the Dirac Hamiltonian continues to be self adjoint in the presence of the Schwinger term. It is shown that the Schwinger interaction for large Z causes significant changes in the properties of the discrete spectrum; in particular, the first level that reaches the threshold of a negative continuum is 2p
1/2 and this occurs at Z = 147. The behavior of the g-factor of an electron for the 1s
1/2 and 2p
1/2 states as a function of Z is considered as well and it is shown that for extremely large charges the correction to the g-factor due to the Schwinger term becomes a very significant effect.
Bound states of a composite system consisting of a charged spin-0 and a charged spin- 1/2 constituent interacting via minimal electrodynamics are investigated using the Bethe–Salpeter equation in the ladder approximation (single photon exchange). Although the interaction involves derivative couplings, in the limit that the four-momentum is zero, it is possible to solve the integral equation by performing a Wick rotation and employing a method due to Fock. The eigenvalue spectrum of the coupling constant is found to be discrete.
It is proved that both the standard minimal coupling, epsigammamupsiAmu, and the anomalous Pauli coupling, apsisigma muvpsiFmuv, of quantumelectrodynamics are locally invariant under the one-parameter local U(1) gauge transformations omega+/- = exp[ietheta(x) + 1/2ia (1 +/- gamma5)gammamuthetamu(x)], with theta(x) = 0, applied to Dirac bispinors. Under omega+/- both couplings are necessary. Further natural generalizations are pointed out. On study leave from Mathematical Institute, University of Kent at Canterbury, Kent CT2 7NF, UK.
The general effective radial potentials for a spin- 1/2 particle interacting with scalar, electric, and magnetic potentials are given. In the m=0 limit, it is shown that the magnetic potential provides a well deep enough to confine the massless particle. In particular, there are exact zero-energy solutions in which two of the four components of the massless particle are confined; only two can leak out into the asymptotic region. The scattering amplitude is analytic in the entire j plane, hence consists only of Regge poles.
Positive-energy, numerical solutions are obtained in the ladder approximation to the Bethe-Salpeter equation describing a
spinor and a scalar with arbitrary, nonzero masses that are bound by minimal electrodynamics. These solutions are a first
step in exploring the possibility that leptons, quarks or both might be highly relativistic bound states. Attention is restricted
to solutions obeying boundary conditions of the general form for which zero-energy solutions have been found. Because the
calculated value of the coupling constant is sensitive to the behavior of the solution at large momenta, an iterative procedure
is used to ensure that the input boundary conditions and the boundary conditions actually obeyed by each solution agree. Although
the solutions discussed here could not describe leptons or quarks because the coupling constant required to create strongly
bound states is much larger than the electromagnetic fine structure constant, the numerical technique used here to obtain
solutions can be used to analyze additional solutions that may exist.
For the system consisting of a neutral Dirac particle with anomalous magnetic moment, interacting with a fixed magnetic monopole, zero-energy bound states are constructed for each possible value of the total angular momentum. Results of Kazama and Yang for the charge--monopole system are used to deduce the existence of other bound states for this system, when the mass of the bound particle is nonzero. In the zero-mass case, there are no other bound states, but there are resonant states, and these are determined exactly. A noncompact, so(3,2) symmetry algebra of the zero-energy bound states is given for the finite-mass case and for the zero-mass case. In each case the infinite number of such states is associated with an irreducible Majorana representation of the algebra.
The short time (~10 minutes) high voltage electrolysis of nitrate bismuth solution was performed. After electrolysis about 30 mg of electrolyte have been dried up on a thin polyethylene film. The sample obtained was placed into the detecting system (Si detector and plastic detector). Alpha-radioactivity of the sample was measured. The results showed that alpha-radioactivity increased about 100 times to the base level. The radioactivity decreasing was about 2 times for 50 minutes. Some signals from the Si detector was accompanied by a signal from the electron detector (22 events). The signal from the plastic detector for all the events the electron recorded preceded the Si detector signal with delay less than 1.4 musec. The conclusion was made that beta-decay of nuclei 212Bi and the subsequent alpha-decay of nuclei 212Po were recorded. The effect was reproduced in 28 experiments. The possible explanation of the phenomenon was given.
An exothermal reaction has been observed when submitting metallic uranium to the combined action of a magnetic field and an electrical current. The set-up used to study the phenomenon is described and results are given. A tentative explanation is given, based on the possible existence of a still hypothetical proton/electron resonance.
An explicit non-relativistic mathematical analysis of a model proposed by Vigier to interpret (within the present frame of quantum theory, i.e. in terms of spin-orbit and magnetic interactions appearing in dense media) excess heat observed in the so-called “cold fusion” phenomena based only on hydrogen is presented. The existence of new “tight” Bohr orbits is demonstrated in this case.
It is demonstrated that the short distance singularities of the relativistic interaction Hamiltonian of two spin particles with electromagnetic interactions have an effect on the muon-proton overlap in the ground state of pmu-atoms of the order of 1-2% that may be important for the interpretation of high-accuracy measurements of the rate of muon capture by protons in hydrogen. On leave from the Institute for Nuclear Research and Nuclear Energy, Boulevard Tsarigradsko Shosse 72, Sofia 1784, Bulgaria.
We have studied the possible existence of quasibound states of an electron-positron pair due to their magnetic interaction in the framework of the equations suggested by Barut et al. [5]. We derive radial equations for all angular quantum numbers of thee
−-e
+ system and show, in detail, that Barut's equations doe not give a consistent, physically satisfactory description of positronium, except in the non-relativistic approximation (up to terms of orderm α2). Moreover, we donot find evidence that the effective potentials occurring in the radial equations support magnetic resonances of the e−-e
+ system at short particle distances (“micropositronium”).
The possibility of tight bound states in quantum mechanics has been often emphasized [1]. Two different mechanisms are proposed
for their occurrence: strong magnetic interactions at small distances and creation of the “anti-Born-Oppenheimer” states,
corresponding to rapid motion of the heavy particles around almost fixed electrons. The observed “excess heat” in cold fusion
experiments could be explained by these new tightly bound states [1]. In the present paper both ideas are analyzed.
ince 1989, many experimenters worked on low-energy nuclear reactions (LENR). They face both an experimental and a theoretical dilemma: how to design simple and convincing experiments in a complex system and if the phenomenon has a nuclear origin, why do they observe no radiation. A rather simple water mass flow calorimeter was designed to study this phenomenon under different experimental conditions. First results indicate that a high-density current induced an exothermic reaction in a hydrogen processed palladium wire. A working hypothesis is presented to solve the theoretical dilemma. This working hypothesis is based on the possible existence of a still hypothetical proton/electron resonance. We underline that a working hypothesis is not a theory presented to explain the phenomenon; this is just a conceptual scheme to drive the authors to build experiments.
Recent work on the perturbation theory for the central-field Dirac equation is extended to include potential coupling of the anomalous-magnetic-moment type. A combination of general parity-conserving central fields is also considered. A method of transforming such a general perturbation to a specific type of perturbation is also demonstrated. All corrections to the energies and wave functions, including corrections to the positions of the nodes in excited states, are expressed in quadrature in a hierarchical scheme, without the use of either the Green's function or the sum over intermediate states.
We formulate the problem of finding the narrow positive energy resonances in a deep potential well as an eigenvalue problem (thereby extending the scope of the discrete spectrum problem). We determine the number of resonances in an exactly soluble case. The method is then applied to a nonperturbative treatment of the magnetic resonances occurring in charge‐dipole interactions, and the existence of the previously conjectured high mass narrow resonances in this model is proved.
We present a nonperturbative theory of superpositronium, the highly
massive very narrow resonance states in the electron-positron system due
to anomalous-magnetic-moment interactions. From basic coupled equations
of quantum electrodynamics we show that the form-factor corrections play
a role only at distances smaller than the superpositronium size,
α2m, in such a way as to precisely induce the formation
of the superpositronium.
An exact expression for the magnetic part of the Lamb shift in hydrogen for a point nucleus is derived which reduces to the usual formula in the non-relativistic limit. It contains an additional strong Z-dependence which is not present in the non-relativistic case.
The theory of classical relativistic spinning particles with c-number internal spinor variables, modelling accurately the Dirac electron, is generalized to particles with anomalous magnetic moments. The equations of motion are derived and the problem of spin precession is discussed and compared with other theories of spin.
A low energy phenomenon in quantum theories with extra dimensions is studied. The method of Bohr and Sommerfeld is used to compute the relativistic bound state energy spectrum for hydrogen-like atoms in the flat, five-dimensional Kaluza-Klein model.
The authors show that the explicit inclusion of the effect of the anomalous magnetic moment for the electron in the electron-proton scattering cross section leads to contradictions with experimental data.
We give an exact solution of the Dirac equation with an additional Pauli coupling in an external field Aμ which is a function of the phase = kμ xμ only. A Weyl representation is used to obtain a completely covariant description.
We present exact solutions of the Dirac equation for two
electromagnetic potentials, i.e. the vector and the scalar potentials.
These solutions are written in terms of the known
solutions of the Schrödinger equation. The presentation is within the
two-component relativistic description. Mainly the bound state
solutions have been obtained.
The 16 × 16 spinor equations of two fermions interacting with their charges and anomalous magnetic moments have been separated first covariantly into center of mass and relative coordinates, then completely into angular and radial parts. The 16 radial equations reduce by a symmetry into two sets of 8 equations, four of which are algebraic. The final result is a set of four first order equations or two coupled second order equations.
We derive relativistic equations for two-fermion systems from quantum field theory, taking into account the form factors of the particles. When theq
2-dependence of the form factors is disregarded, we obtain, in the static approximation, the two-fermion equations with Coulomb and anomalous-magnetic-moment interactions. Separating the angular variables, we finally obtain a sixteen-component relativistic radial equation.
Upper and lower limits for the number of bound states in a given central potential are obtained. They imply that for strongly attractive potentials the number of bound states of given angular momentum increases as the square root of the strength of the potential.
We have solved the Dirac equation for a lepton with an anomalous magnetic moment in the Coulomb field of the antilepton. We demonstrate the existence of resonance states of hadronic size and of energies of a few GeV due to the interplay of effective attractive and repulsive dynamical potentials of the r-2, r-3 and r-4-type. No new parameters are involved. We predict almost similar resonances in the lepton-lepton systems for opposite values of the quantum number kappa.