arXiv subjects

S. L. Yakovlev

Publications and source records attributed to S. L. Yakovlev.

At least 19 recordsLinked to original sources

arXiv2024

Scattering in $e^- -(pe^-)$ and $μ^- -(pμ^-)$ systems: mass dependent and mass independent features of cross sections above the degenerated thresholds

Ab initio calculation of low energy scattering of electrons (muons) off hydrogen (muonic hydrogen) are performed on the basis of Faddeev-Merkuriev (FM) equations. The explicit contribution of induced dipole interaction in the asymptotic behavior of the wave function components has been incorporated into FM formalism. Elastic and inelastic cross sections have been calculated with high energy resolution in the vicinity of $n=2,3$ exited states thresholds of respective atoms. The Gailitis-Dumburg oscillations are discovered in some of calculated cross sections.

physics.atom-ph↗

arXiv2023

The Gailitis-Damburg oscillations in the three-body $e^-e^+\bar{p}$ system

We study the near threshold behavior of cross sections of low-energy antiproton scattering off the ground and excited states of positronium with zero total orbital momentum $L=0$. In our computational experiment, the existence of singularities called the Gailitis-Damburg oscillations above the thresholds of excited states of positronium and antihydrogen atoms is confirmed. In the future the obtained results can be useful for developing proposals for improving the conditions of experiments with antimatter.

hep-ph↗

arXiv2023

On scattering problem off the potential, decreasing as inverse square of distance

A solution of the scattering problem is obtained for the Schrödinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident charged particle with a complex of charged particles (for example, in the collision of electrons with atoms). For the wave function, an integral equation is constructed for an arbitrary value of the orbital momentum of relative motion. By solving this equation, an exact integral representation for the $K$-matrix of the problem is obtained in terms of the wave function. This representation is used to analyze the behavior of the $K$-matrix at low energies and to obtain comprehensive information on its threshold behavior for various values of the dipole momentum. The resulting solution is applied to study the behavior of the scattering cross sections in the electron, positron and antiproton system.

physics.atom-ph↗

arXiv2022

Wave function asymptotics for scattering of three-particles with Coulomb interaction

The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schrödinger equation to a system of partial wave one-dimensional equations. Asymptotic solutions of this system are constructed by direct asymptotic methods.

math-ph↗

arXiv2021

Theoretical study of reactions in the three body $e^-e^+\bar{p}$ system and antihydrogen formation cross sections

We apply a new highly efficient method of solving Faddeev-Merkuriev equations to multi-channel scattering calculations of the antihydrogen formation cross section for antiproton scattering off the ground and excited states of the positronium. Our results demonstrate good agreement with the known data on total and partial cross sections for all the reaction channels. Using moderate computational resources we have achieved a supreme energy resolution.

physics.atom-ph↗

arXiv2020

Weak asymptotics of wave function for N-particle system and asymptotic filtering

Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the asymptotic representations are expressed in terms of the $N$-particle scattering matrix. The phenomenon of asymptotic filtration is discovered, which consists in the fact that only scattering processes contribute to the leading terms of such an asymptotic representation, in which all particles are free both before and after interaction. The obtained representations are used to construct the correct asymptotics of the partial components of the wave function of $N$ particles in the hyperspherical representation.

math-ph↗

arXiv2020

Multichannel Coulomb Scattering with Asymptotic Non-adiabatic Coupling

The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-zero asymptotic behavior at large internuclear separations. The asymptotic solutions at large inter-nuclear distances are {therefore} constructed. The asymptotic boundary conditions with S-matrix and K-matrix for the scattering problem are formulated on the basis of constructed asymptotic solutions.

physics.atom-ph↗

arXiv2019

Potential splitting approach for molecular systems

In order to describe few-body scattering in the case of the Coulomb interaction, an approach based on splitting the reaction potential into a finite range part and a long range tail part is presented. The solution to the Schrödinger equation for the long range tail is used as an incoming wave in an inhomogeneous Schrödinger equation with the finite range potential. The resulting equation with asymptotic outgoing waves is then solved with the exterior complex scaling. The potential splitting approach is illustrated with calculations of scattering processes in the H${}^+$ -- H${}^+_2$ system considered as the three-body system with one-state electronic potential surface.

physics.atom-ph↗

arXiv2019

On formal scattering theory for differential Faddeev equations

The formal scattering theory is developed for the three-particle differential Faddeev equations. The theory is realised along the same line as in the standard two-body case. The solution of the scattering problem is expressed in terms of the matrix T-operator constructed from the matrix resolvent of the differential Faddeev equations. The relationships of the matrix T-operator with elements of transition operators and Faddeev T-matrix components have been established.

nucl-th↗

arXiv2016

Potential splitting approach to e-H and e-He${}^+$ scattering with zero total angular momentum

An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schrödinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schrödinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.

physics.atom-ph↗

arXiv2015

Excitons in square quantum wells: microscopic modeling and experiment

The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schroedinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the high-order finite-difference scheme. The microscopic calculations are compared with the results obtained by the standard variational approach. The exciton binding energies found by two methods coincide within 0.1 meV for the wide range of QW widths. The radiative decay rate is calculated for QWs of various widths using the exciton wave functions obtained by direct and variational methods. The radiative decay rates are confronted with the experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW heterostructures grown by molecular beam epitaxy. The calculated and measured values are in good agreement, though slight differences with earlier calculations of the radiative decay rate are observed.

cond-mat.mes-hall↗

arXiv2015

Decomposition method for block-tridiagonal matrix systems

The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations for its parallel and serial parts. The computational speedup with respect to the conventional sequential Thomas algorithm is assessed for various types of the application of the method. It is observed that the maximum of the analytical speedup for a given number of blocks on the diagonal is achieved at some finite number of parallel processors. The values of the parameters required to reach the maximum computational speedup are obtained. The benchmark calculations show a good agreement of analytical estimations of the computational speedup and practically achieved results. The application of the method is illustrated by employing the decomposition method to the matrix system originated from a boundary value problem for the two-dimensional integro-differential Faddeev equations. The block-tridiagonal structure of the matrix arises from the proper discretization scheme including the finite-differences over the first coordinate and spline approximation over the second one. The application of the decomposition method for parallelization of solving the matrix system reduces the overall time of calculation up to 10 times.

physics.comp-ph↗

arXiv2014

A potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion

The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrödinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

physics.atom-ph↗

arXiv2012

Zero range potential for particles interacting via Coulomb potential: application to electron positron annihilation

The zero range potential is constructed for a system of two particles interacting via the Coulomb potential. The singular part of the asymptote of the wave function at the origin which is caused by the common effect of the zero range potential singularity and of the Coulomb potential is explicitly calculated by using the Lippmann-Schwinger type integral equation. The singular pseudo potential is constructed from the requirement that it enforces the solution to the Coulomb Schrödinger equation to possess the calculated asymptotic behavior at the origin. This pseudo potential is then used for constructing a model of the imaginary absorbing potential which allows to treat the annihilation process in positron electron collisions on the basis of the non relativistic Schrödinger equation. The functional form of the pseudo potential constructed in this paper is analogous to the well known Fermi-Breit-Huang pseudo potential. The generalization of the optical theorem on the case of the imaginary absorbing potential in presence of the Coulomb force is given in terms of the partial wave series.

physics.atom-ph↗

arXiv2011

Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation

In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schrödinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The boundary conditions at infinity for this set of equations have been proven to be purely outgoing waves. The formulation {presented here} is based on splitting the interaction potential into a finite range core part and a long range tail part. The conventional matching procedure coupled with the integral Lippmann-Schwinger equations technique are used in the formal theoretical basis of this approach. The reformulated scattering problem is suitable for application in the exterior complex scaling technique: the practical advantage is that after the complex scaling the problem is reduced to a boundary problem with zero boundary conditions. The Coulomb wave functions are used only at a single point: if this point is chosen to be at a sufficiently large distance, on using the asymptotic expansion of Coulomb functions, one may completely avoid the Coulomb functions in the calculations. The theoretical results are illustrated with numerical calculations for two models.

physics.atom-ph↗

arXiv2011

Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schrödinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.

physics.atom-ph↗

arXiv2006

Closed form representation for a projection onto infinitely dimensional subspace spanned by Coulomb bound states

The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the $n^2$ dimensional subspace corresponding to the $n$-th eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of $n$-th and $(n-1)$-th order. The latter allows us to derive an analog of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two body subsystems is one of the most difficult technical problems.

physics.atom-ph↗

arXiv2005

Positron annihilation in $e^+ -$H collision above the Positronium formation threshold

A long-standing problem to account for the electron-positron annihilation in positron Hydrogen scattering above the Positronium formation threshold has been resolved by the use of the three-body Faddeev formalism. The multichannel three-body theory for scattering states in presence of a complex absorbing potential is developed in order to compute the direct $e^+ e^-$ annihilation amplitude, the amplitude of Positronium formation and respective cross sections. A number of $e^+ e^-$ direct annihilation cross sections and Positronium formation cross sections in the energy gap between Ps$(1s)$ and H$(n=2)$ thresholds are reported for both the positron-Hydrogen incoming channel as well as the proton-Positronium incoming channel.

physics.atom-ph↗