arXiv subjects

S L Yakovlev

Publications and source records attributed to S L Yakovlev.

4 recordsLinked to original sources

arXiv2018

High resolution calculation of low energy scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$ systems via Faddeev-Merkuriev equations

The potential splitting approach incorporated into the framework of Faddeev-Merkuriev equations in the differential form is used for calculations of multichannel scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$ systems. Detailed calculations of all possible S-wave cross-sections are performed %in systems $e^+e^-\bar{p}$ and $e^+e^-\mbox{He}^{++}$ in the low-energy region which supports up to seven open channels including the rearrangement channels of ground and excited states of antihydrogen, positronium and helium ion formations. All known sharp resonances of the systems obtained and approved by a number of authors are clearly reproduced in the calculated cross sections. In cross sections for energies above the threshold corresponding to $n=2$ state of antihydrogen the prominent oscillations of Gailitis Damburg type have been found.

physics.atom-ph↗

arXiv2016

Multichannel Scattering Problem with Non-trivial Asymptotic Non-adiabatic Coupling

The multichannel scattering problem in an adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-trivial constant asymptotic behavior at large internuclear separations. The asymptotic solutions at large internuclear distances are constructed. It is shown that these solutions up to the first order of perturbation theory are identical to the asymptotic solutions of the re-projection approach, which was proposed earlier as a remedy for the electron translation problem in the context of the Born-Oppenheimer treatment.

physics.atom-ph↗

arXiv2010

The impact of sharp screening on the Coulomb scattering problem in three dimensions

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the interior part of the Coulomb potential is left in the Hamiltonian and, secondly, when the long range tail is considered as the potential. The partial wave results are summed up to obtain the wave function in three dimensions. It is shown that in the domains where the wave function is expected to be proportional to the known solutions, the proportionality is given by an operator acting on the angular part of the wave function. The explicit representation for this operator is obtained in the basis of Legendre polynomials. We proposed a driven Schrödinger equation including an inhomogeneous term of the finite range with purely outgoing asymptotics for its solution in the case of the three dimensional scattering problem with long range potentials.

nucl-th↗

arXiv2006

Multichannel Formalism for Positron-Hydrogen Scattering and Annihilation

A problem to account for the direct electron-positron annihilation in positron-hydrogen scattering above the positronium formation threshold has been resolved within the time independent formalism. The generalization of the optical theorem is derived for the case when an absorption potential is present in the Hamiltonian. With this theorem the annihilation cross section is fully determined by scattering amplitudes. This allows us to separate out analytically the contribution of the positronium formation from the overall annihilation cross section. The rest is determined as the direct annihilation cross section. It is done uniformly below as well as above the positronium formation threshold. The multichannel three-body theory for scattering states in the presence of an imaginary absorption potential is developed in order to compute the direct $e^+ e^-$ annihilation amplitude. Special attention has been paid to an accurate definition of the coordinate part of the absorption potential as the properly constructed zero-range potential, which corresponds to the delta-function originated from the first order perturbation theory. The calculated direct annihilation cross section below the positronium formation threshold is in good agreement with results of other authors. The direct annihilation cross section computed with the formalism of the paper shows nonsingular behavior at the positronium formation threshold and is in good agreement with existing data. 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. A sharp increase in the calculated direct annihilation cross section across the resonant energy is found for all first S and P-wave Feshbach resonances.

physics.atom-ph↗