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

V. A. Gradusov   ; S. L. Yakovlev

Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 416-429

Résumé

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.

Détail

Keywords: scattering of charged particles
Mots-clés : dipole interaction.

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