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.
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Notes
We have chosen the formulation of the scattering problem leading to a real solution. Other equivalent formulations are obtained by simple renormalization.
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Funding
This work was carried out within the framework of the Russian Science Foundation project No. 23-22-00109 using the equipment of the Resource Center “Computer Center of Saint-Petersburg State University” (http://cc.spbu.ru).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 217, pp. 416–429 https://doi.org/10.4213/tmf10568.
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Gradusov, V.A., Yakovlev, S.L. On the scattering problem for a potential decreasing as the inverse square of distance. Theor Math Phys 217, 1777–1787 (2023). https://doi.org/10.1134/S0040577923110120
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DOI: https://doi.org/10.1134/S0040577923110120