arXiv subjects

A. I. Mikhailov

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

17 recordsLinked to original sources

arXiv2024

On the theory of relativistic Brownian motion

The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener measure as a weak limit of finite-difference approximations. A formula has been proposed for calculating the probability particle transition during relativistic Brownian motion. Calculations were carried out by three different methods with identical results. Along the way, exact and asymptotic formulas for the volume of some parts and sections of an N-1-dimensional unit cube were obtained. They can have independent value.

gr-qc↗

arXiv2020

Relativistic photoeffect for $s$ states in a central field

We study the photoionization of the $s$ states in the systems bound by sufficiently weak central fields $V(r)$ for the large photon energies corresponding to the relativistic photoelectrons. We demonstrate that the energy dependence of the photoionization cross section can be obtained without solving the wave equation. We show that the shape of the energy dependence of the cross section is determined by analytical properties of the binding potential $V(r)$. We find the cross sections for the potentials $V(r)$ which have singularities in the origin, on the real axis and in the complex plane.

hep-ph↗

arXiv2018

Asymptotic behavior of photoionization cross section in a central field. Ionization of the $p$ states

We continue our studies of the high energy nonrelativistic asymptotics for the photoionization cross section of the systems bound by a central field $V(r)$. We consider the bound states with the orbital momentum $\ell=1$. We show, that as well as for the $s$ states the asymptotics can be obtained without solving of the wave equations for the bound and outgoing electrons. The asymptotics of the cross sections is expressed in terms of the asymptotics of the Fourier transform $V(p)$ of the field and its derivative $V'(p)$ by employing the Lippmann--Schwinger equation. The shape of the energy dependence of the cross sections is determined by the analytical properties of the potential $V(r)$. The cross sections exhibit power drop with the increase of the photon energy for the potentials $V(r)$ which have singularities on the real axis. They experience exponential drop if $V(r)$ has poles in the complex plane. We trace the energy dependence of the ratios of the photoionization cross sections for $s$ and $p$ electrons from the states with the same principle quantum number. We apply the results to the physics of fullerenes.

physics.atom-ph↗

arXiv2018

Ionization-excitation of helium-like ions at Compton scattering

Ionization of helium-like ions with simultaneous excitation of the ns-states due to photon scattering is considered. The differential and total cross sections of the process are calculated to leading order of perturbation theory with respect to the interelectron interaction. The formulas obtained are applicable in the nonrelativistic energy range far beyond the ionization threshold.

physics.atom-ph↗

arXiv2018

Photoionization of the bound systems at high energies

We consider photoionization of a system bound by the central potential $V(r)$. We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann--Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential $V(r)$. We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model dependent. We demonstrate that if the fullerene field $V(r)$ is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which as so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster drop of the cross sections becomes important in these cases.

physics.atom-ph↗

arXiv2017

High energy photoionization of fullerenes

We show that the theoretical predictions on high energy behavior of the photoionization cross section of fullerenes depends crucially on the form of the function $V(r)$ which approximates the fullerene field. The shape of the high energy cross section is obtained without solving of the wave equation. The cross section energy dependence is determined by the analytical properties of the function $V(r)$.

physics.atom-ph↗

arXiv2017

Asymptotic behavior of photoionization cross section in a central field

We demonstrate that the high energy nonrelativistic asymptotic for the photoionization cross section in a central field $V(r)$ can be expressed in terms of the asymptotic of the Fourier transform $V(p)$ of the field. We show that the cross sections drop in the same way for the fields with the Coulomb short distance behavior. The character of the cross sections energy behavior is related to the analytical properties of the function $V(r)$. The cross sections exhibit power drop for the potentials which have singularities an the real axis. They suffer the exponential drop if $V(r)$ has singularities in the complex plane.

quant-ph↗

arXiv2016

On neutrinoless double electron capture

We found the probability for the neutrinoless double electron capture in the case of $KK$ capture. We clarified the mechanism of the energy transfer from the nucleus to the bound electrons. This enabled us to obtain the equations for the probability of the $2EC0ν$ process which modify those obtained earlier. We found that the probability of the process is three orders of magnitude larger than it was supposed earlier.

nucl-th↗

arXiv2013

On the dependence of one-photon - two-electron differential cross sections on recoil momenta

We calculate the distributions in recoil momenta and their energy distributions for the high energy non-relativistic double photoionization of helium caused by the quasifree mechanism of the process. The distributions obtain local maxima at small values of the recoil momenta. This is in agreement with the earlier predictions and with recently obtained experimental data. We obtained also the angular correlations, which reach the largest value in the "back-to-back" configuration of the photoelectrons. Our analysis is valid in all high energy nonrelativistic region. Particular equations are true for the case when the wavelength of the photon exceeds strongly the size of the atom. We present numerical results for the photon energies in the region of 1 keV, employed in the recent experiments.

physics.atom-ph↗

arXiv2009

About universal scalings in double K-shell photoionization

We discuss the problem of the universal scalings in the double ionization of atomic K-shell electrons caused by absorption of a single photon. In particular, we envisage the following questions: Under which conditions and up to which accuracy the universal scalings are realized? Does it make sense to talk about different physical mechanisms in the double-ionization process? Finally, we present also the theoretical analysis of recent experimental measurements performed on neutral atoms. As a testing ground, QED perturbation theory is employed.

physics.atom-ph↗

arXiv2009

Differential cross sections for K-shell ionization by electron or positron impact

We have investigated the universal scaling behavior of differential cross sections for the single K-shell ionization by electron or positron impact. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. In the case of low-energy positron scattering, the doubly differential cross section exhibits prominent interference oscillations. The results obtained are valid for arbitrary atomic targets with moderate values of nuclear charge number Z.

physics.atom-ph↗

arXiv2009

Parity nonconservation in electron recombination of multiply charged ions

We discuss a parity nonconserving asymmetry in the cross section of KLL dielectronic recombination of polarized electrons on the hydrogen-like ions with $Z \lesssim 60$. This effect is strongly enhanced because of the near-degeneracy of doubly-excited $2l2l'$ states of opposite parity in He-like ions. For ions with $Z \sim 30$ the asymmetry is of the order of $10^{-9}$. For $Z \approx 48$ a level crossing takes place, leading to the PNC asymmetry of $\pm 5\times 10^{-9}$, which is $10^8$ times greater than the basic strength of the weak interaction in atoms.

physics.atom-ph↗

arXiv2007

Triple coalescence singularity in a dynamical atomic process

We show that the high energy limit for the amplitude of the double electron capture to the bound state of the Coulomb field of a nucleus with emission of a single photon is determined by behavior of the wave function in the vicinity of the singular triple coalescence point.

quant-ph↗

arXiv2007

Single photoeffect on helium-like ions in the non-relativistic region

We present a generalization of the pioneering results obtained for single K-shell photoionization of H-like ions by M. Stobbe [Ann. Phys. 7 (1930) 661] to the case of the helium isoelectronic sequence. The total cross section of the process is calculated, taking into account the correlation corrections to first order of the perturbation theory with respect to the electron-electron interaction. Predictions are made for the entire non-relativistic energy domain. The phenomenon of dynamical suppression of correlation effects in the ionization cross section is discussed.

physics.atom-ph↗

arXiv2006

Formation of ions by high energy photons

We calculate the electron energy spectrum of ionization by a high energy photon, accompanied by creation of electron-positron pair. The total cross section of the process is also obtained. The asymptotics of the cross section does not depend on the photon energies. At the photon energies exceeding a certain value $ω_0$ this appeares to to be the dominant mechanism of formation of the ions. The dependence of $ω_0$ on the value of nuclear charge is obtained. Our results are consistent with experimental data.

quant-ph↗

arXiv2006

Nonrelativistic double photoeffect on lithiumlike ions at high energies

The total cross section for double ionization of lithiumlike ions by a high-energy photon is calculated in leading order of the nonrelativistic perturbation theory. The partial contributions due to simultaneous and sequential emissions of two electrons are taken into account. The cross section under consideration is shown to be related to those for double photoeffect on the ground and excited 2^{1,3}S states of heliumlike ions. The double-to-single ionization ratio is equal to R = 0.288/Z^2 for lithiumlike ions with moderate nuclear charge numbers Z. However, even for the lightest three-electron targets such as Li and Be^+, analytical predictions are found to be in good agreement with the numerical calculations performed within the framework of different rather involved approaches.

physics.atom-ph↗

arXiv2006

Photoionization of helium-like ions in asymptotic nonrelativistic region

The cross section for single K-shell ionization by a high-energy photon is evaluated in the next-to-leading order of the nonrelativistic perturbation theory with respect to the electron-electron interaction. The screening corrections are of particular importance for light helium-like ions. Even in the case of neutral He atom, our analytical predictions turn out to be in good agreement with the numerical calculations performed with the use of the sophisticated wave functions. The universal high-energy behavior is studied for the ratio of double-to-single photoionization cross sections. We also discuss the fast convergence of the perturbation theory over the reversed nuclear charge number 1/Z.

physics.atom-ph↗