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On the scattering problem for a potential decreasing as the inverse square of distance. / Градусов, Виталий Александрович; Яковлев, Сергей Леонидович.

In: Theoretical and Mathematical Physics, Vol. 217, No. 2, 27.11.2023, p. 1777-1787.

Research output: Contribution to journal › Article › peer-review

Harvard

Градусов, ВА & Яковлев, СЛ 2023, 'On the scattering problem for a potential decreasing as the inverse square of distance', Theoretical and Mathematical Physics, vol. 217, no. 2, pp. 1777-1787. https://doi.org/10.1134/s0040577923110120

APA

Градусов, В. А., & Яковлев, С. Л. (2023). On the scattering problem for a potential decreasing as the inverse square of distance. Theoretical and Mathematical Physics, 217(2), 1777-1787. https://doi.org/10.1134/s0040577923110120

Vancouver

Градусов ВА, Яковлев СЛ. On the scattering problem for a potential decreasing as the inverse square of distance. Theoretical and Mathematical Physics. 2023 Nov 27;217(2):1777-1787. https://doi.org/10.1134/s0040577923110120

Author

Градусов, Виталий Александрович ; Яковлев, Сергей Леонидович. / On the scattering problem for a potential decreasing as the inverse square of distance. In: Theoretical and Mathematical Physics. 2023 ; Vol. 217, No. 2. pp. 1777-1787.

BibTeX

@article{afc1c8b9da5c4b07a759add24a8a0f4f,
title = "On the scattering problem for a potential decreasing as the inverse square of distance",
abstract = "Abstract: A solution of the scattering problem is obtained for the Schr{\"o}dinger 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). An integral equation for the wave function 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–antiproton system.",
keywords = "dipole interaction, scattering of charged particles",
author = "Градусов, {Виталий Александрович} and Яковлев, {Сергей Леонидович}",
year = "2023",
month = nov,
day = "27",
doi = "10.1134/s0040577923110120",
language = "English",
volume = "217",
pages = "1777--1787",
journal = "Theoretical and Mathematical Physics (Russian Federation)",
issn = "0040-5779",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - On the scattering problem for a potential decreasing as the inverse square of distance

AU - Градусов, Виталий Александрович

AU - Яковлев, Сергей Леонидович

PY - 2023/11/27

Y1 - 2023/11/27

N2 - Abstract: 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). An integral equation for the wave function 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–antiproton system.

AB - Abstract: 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). An integral equation for the wave function 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–antiproton system.

KW - dipole interaction

KW - scattering of charged particles

UR - https://www.mendeley.com/catalogue/7d70aee6-642e-3271-a2ee-c69728183de1/

U2 - 10.1134/s0040577923110120

DO - 10.1134/s0040577923110120

M3 - Article

VL - 217

SP - 1777

EP - 1787

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -

ID: 114572527