arXiv subjects

A. I. Agafonov

Publications and source records attributed to A. I. Agafonov.

14 recordsLinked to original sources

arXiv2023

Relativistic-kinematic approach to the hydrogen atom. A possible family of two-particle optically-inactive bound states

The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the electron and proton have different scales of intraatomic motions, is predicted. Two two-particle states are obtained numerically and discussed in detail. Radiative processes involving the two-particle bound state, should result in simultaneous changing the electron and the proton states and occur through the simultaneous two-photon emission. These processes will be extremely improbable, in comparison with electronic two-photon transitions, since they will be additionally suppressed by the large proton mass.

physics.gen-ph↗

arXiv2023

The electron-proton bound state in the continuum with the positive binding energy of 1.531 of the electron mass

In the bound states in the continuum (BIC) the binding energy is positive, and the mass of a composite particle is greater than the total mass of its constituents. In this work the BIC state is studied for the electron-proton system with using the ladder Bethe-Salpeter equation. We demonstrate that there are two momentum space regions in which the electromagnetic interaction between the particles is strongly enhanced, and the effective coupling constant is equal to $α\sqrt{m_{p}/m_{e}}=0.313$, where $α$ is the fine structure constant, $m_{p}$ and $m_{e}$ are the proton and the electron masses. This interaction resonance causes the confinement of the pair in the BIC state with the positive binding energy of 1.531 of the electron mass. The integral equation for the bispinor wave function is derived. This normalized wave function which must be complex, was found numerically in the momentum and coordinate spaces. It turned out that in the BIC state, the average radius for the electron is equal to 48Fm, and the average radius for the proton is equal to 1.1Fm. This composite particle can exist exclusively in the free state, in which its properties, such as its form-factors, should only be studied. In bound states with other particles, the composite loses its individuality.

hep-ph↗

arXiv2023

Resonance enhancement of the electromagnetic interaction between two charged particles in the bound state in the continuum

In bound states in the continuum (BIC) the mass of a composite particle is greater than the total mass of its constituents. Using the ladder Bethe-Salpeter equation, the BIC state in a system of two charged particles $a$ and $b$ with different masses ($m_{b}>>m_{a}$) is investigated. We demonstrate that for the positive binding energy, there are two momentum space regions in which the electromagnetic interaction between the particles is strongly enhanced, and the effective coupling constant turns out to be equal to $α\sqrt{m_{b}/m_{a}}$, where $α$ is the fine structure constant. The interaction resonance leads to confinement of the constituents in the BIC state with the positive binding energy which is of the order of the mass of the lighter particle from the pair.

hep-ph↗

arXiv2022

A massive composite fermion from the three electron-like leptons in the bound state in the continuum

In the bound state in continuum (BIC) the mass of a composite particle is greater than the total mass of its constituent particles. The BIC states that are stable due to confinement mechanisms, have been found in various fields but particle physics has evolved without analyzing these states. The work's idea is to apply the BIC phenomenon to some elementary particles. The study focuses on a composite fermion of the three light leptons, $(e^{-}e^{+}e^{\pm})_{BIC}$. In the present theory the free electron and free positron is treated as different particles, each being characterized by the complete set of the Dirac plane waves. Using the Bethe-Salpeter equation, the wave function of the fermion with the mass of 207 electron masses was found numerically. The results obtained predict the particle radius equal to 65.9 Fm. The representation of muons as the composite fermions formed by the three electron-like leptons in the BIC states, is analyzed.

hep-ph↗

arXiv2018

Hydrogen energy-levels shifts induced by the atom motion. Crossover from the Lamb shifts to the motion-induced shifts

When the hydrogen atom moves, the proton current generates a magnetic field which interacts with the hydrogen electron. A simple analyze shows that this interaction between the hydrogen momentum and the electron is of order of $α^3\frac{v}{c}m$, where $α$ is the fine structure constant, $v$ is the atom velocity, $c$ is the speed of light, and $m$ is the electron mass. Using the Bethe-Salpeter equation, the two velocity-dependent operators of this order are derived for the hydrogen velocity $\frac{v}{c}<<α$. As well known, the degeneracy of the energy levels with the same principal quantum number, $n$, and the same quantum number of the total angular momentum, $j$, but the different orbital angular momenta $l=j\pm 1/2$ is removed by the radiative corrections (the Lamb shift) that are proportional to $α^{5}m$. It is shown that the velocity-dependent perturbation interactions remove this degeneracy as well. There is, however, an important difference between the Lamb shifts and the energy-levels shifts induced by the atom motion. The Lamb shift is the diagonal correction to the energy separately for each of the degenerate states. The the velocity-dependent perturbation interactions result in the off-diagonal energy corrections between the mutually degenerate states. The joint effect of these two perturbations which are essentially different in their origin, is analyzed. Given their order of magnitude, the crossover from the Lamb shifts to the motion-induced shifts should occur at the atom velocity $v=kα^2 c$, where $k>>1$ is a numerical factor depended on $n$ and $j$. An experiment used the orbital motion of the Earth, is proposed to test the theory developed.

physics.atom-ph↗

arXiv2017

Massless composite bosons formed by the coupled electron-positron pairs, and two-photon angular correlations in the colliding beam reaction $e^{-}e^{+}\to Bγγ$ with emission of the massless boson

The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED, makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is studied in the ladder approximation. A new branch of the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant, has been found. It has been obtained that: 1) the massless bosons have the normalized complex wave functions, which are transversely compressed plane waves; 2) the transverse radius of the wave functions diverges as the boson energy goes to zero that is, the composite bosons cannot be at rest; 3) the extension of the transverse wave function in the momentum space and the compression of the coordinate wave function are continuously occurred with increasing the boson energy. The reaction $e^{-}e^{+}\to Bγγ$ products of which are the massless composite boson and two photons, is investigated. The cross-section of this reaction is derived for the non-relativistic colliding beams of the spin-polarized electrons and positrons. In this case the $2γ$ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that to establish whether there is the conventional annihilation of singlet electron-positron pair with the two-photon emission or the investigated reaction, products of which are the three particles, experiments with the extremely non-relativistic colliding beams should be conducted.

hep-ph↗

arXiv2016

Massless states and negative mass states of the coupled electron-positron system with completely symmetric representation of the particles

We argue that the free electron and positron can be considered as different, independent particles, each of which is characterized by the complete set of the Dirac plane waves. This completely symmetric representation of the particles makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that currently used in QED. The Bethe-Salpeter equation is studied in the ladder approximation with using these free propagators. A new branch of electron-positron bound states which represent the massless composite bosons, have been found for the actual coupling equal to the fine structure constant. We have obtained that: 1) the massless boson states have the normalized complex wave functions; 2) the average distance between the electron and positron diverges as the boson kinetic energy goes to zero; 3) the spatial contraction of the wave function of the transverse motion of strongly coupled electron-positron pair is continuously occurred with increasing the boson kinetic energy. Unlike the usual annihilation process in which nothing remains from the electron and positron, a similar annihilation-like process in which the reaction products are two or three gamma quanta and the massless boson, is predicted. In this symmetric representation one could expect states, which have a certain symmetry relative to Ps states, but have negative masses. For these states the equal-time bound-state equation was derived neglecting the interaction retardation and interaction through the vector potential. It turned out that the wave functions of the negative mass boson states are not normalized. Beyond these assumptions, the existence of these negative mass states remains unclear.

physics.gen-ph↗

arXiv2015

Phonon residual resistance of pure crystals

Using the Boltzmann transport equation, we study phonon residual resistance of perfect metallic crystals of a finite thickness $d$ along which a weak constant electric field $E$ is applied. This resistance which is $\propto d^{-5}E^{-3}$, is due to scattering of electric field-heated electrons with emission of long-wave acoustic phonons. This electron-phonon interaction is caused by zero-point vibrations of the atoms in the perfect crystal lattice sites. Consideration is carried out for Cu, Ag and Au single crystals with the thickness of about 1 cm, in the fields of the order of 1 mV/cm. Following the Matthiessen rule, the resistance of the pure crystals the thicknesses of which are much larger than the electron mean free path, is represented as the sum of the impurity and phonon residual resistances. The condition on the thickness $d$ and the field $E$ is found at which the phonon scattering of the field-heated electrons dominates. Under this condition, the low-temperature resistances of pure crystals do not depend on the their purity and determine the phonon residual resistivity of the ideal crystals. The calculations are performed for Cu with a purity of at least 99.9999%.

cond-mat.supr-con↗

arXiv2013

Manifestation of the magnetic moments of Cooper pairs in low-temperature properties of superconducting thin-film rings

Experimental determination of the magnetic moment of the Cooper pairs can shed light on the pairing symmetry in cuprates. We argue that the intrinsic magnetic moments of the Cooper pairs can be detected in experiments with superconducting thin-film rings. At sufficiently low temperatures the magnetic field generated by the supercurrent, can cause the ordering of these magnetic moments that produces changes in the supercurrent and magnetic induction distributions, the heat capacity and magnetic moment of the ring. It is shown that the intrinsic magnetic moment of the Cooper pairs can be extracted from low-temperature behaviours of these measurable quantities of the current-carrying rings made of the cuprate superconductors.

cond-mat.supr-con↗

arXiv2011

Two-photon emission from thin superconducting rings irradiated by coherent microwave fields

Superconducting current instability in thin rings, irradiated by a coherent microwave electromagnetic field, is studied. On the regular circular motion of the Cooper pairs in the supercurrent states the field imposes coherent oscillations of the condensate as a whole. The oscillating condensate should emit photons with the energies determined mainly by the discrete values of the superconducting ring energy. For the first time the probability of the supercurrent decay accompanied by the two- photon emission, is derived. The ring thickness is less than both the field skin-depth and the London penetration depth. Numerical results for the energy-angular distributions of the photons, as well as the waiting time of the stimulated two-photon transition depending on both the ring sizes and fluxoid number in the initial current state, are presented.

cond-mat.supr-con↗

arXiv2011

Relativistic bound-state equations for two-fermion systems

We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit, and, therefore, does not satisfy the Lehmann spectral representation for fermions. Proceeding from the Lippmann-Schwinger integral equation, we obtain a two-fermion relativistic wave equation in which the free two-fermion equal-time propagator satisfying the Lehmann representation, is used. This wave equation has been applied to the electron-positron system. In addition to the eigenstates for positronium, we find a solution which describes a deep bound state with the binding energy $\simeq 2m$ and anomalously small mass of the bound system.

math-ph↗

arXiv2011

Electromagnetic-field-induced decay of currents in thin-film superconducting rings with photons emission

It is shown that currents in thin-film superconducting rings irradiated by coherent microwave fields, can discretely decay with photons emission. These quantized jumps of the supercurrent correspond to destruction one or several magnetic flux quanta trapped in the ring. The ring thickness should be less than the skin-depth of the low-frequency field. The probability of the microwave field-induced single-photon decay of the supercurrent states in these rings is obtained. The angle distributions of the photons emitted by superconducting rings, and the current state lifetimes, depending on the ring sizes and the fluxoid numbers in the initial states, are studied.

cond-mat.supr-con↗

arXiv2010

Inelastic scattering of neutrons by superconducting rings

The differential cross section for the inelastic magnetic scattering of neutrons by superconducting rings is derived theoretically taking account of the interaction of the neutron magnetic moment with magnetic field created by the superconducting current. In this scattering process the neutron kinetic energy increases discretely and, respectively, the number of the magnetic flux quanta trapped in the ring, reduces. Quantitative calculations of the scattering cross section for cold neutrons is carried out for thin film rings from type-II superconductors with the film thickness $d<λ$($λ$ is the penetration depth).

cond-mat.supr-con↗

arXiv2010

Massless Wave States of Two-Fermion Systems

It is known that in the ladder approximation the relativistic two-fermion bound-state equation of Bethe and Salpeter has solutions corresponding to the binding energy equal to the total mass of the particles. The study of these massless states has been carried out only for the bound system at rest. Of course, such composite boson can not be in the state of rest. But it is more importantly that this approach for the massless boson can not be interpreted as the limiting case of a nonzero mass system because the phase velocity of the boson wave must equal to the speed of light. Using the Bethe-Salpeter equation in the ladder approximation, we have obtained the wave equation for the massless bound states of two fermions with equal masses and the electromagnetic interaction between them. Neglecting retardation of the interaction, solutions corresponded to the stationary wave states of the composite boson, have been found. The boson wave function can be represented as an infinite, straight thread, the transverse radius of which is more than the Compton wavelength of the fermion. Two energy branches of the bosons with quantized energies have been determined. The appearance of these branches is due to the strong renormalization of the fine structure constant for the massless states.

hep-th↗