Geodesic
On the~scattering problem for a~potential decreasing as the~inverse square of distance
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 416-429

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: scattering of charged particles
Mots-clés : dipole interaction. 
@article{TMF_2023_217_2_a11,
     author = {V. A. Gradusov and S. L. Yakovlev},
     title = {On the~scattering problem for a~potential decreasing as the~inverse square of distance},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {416--429},
     publisher = {mathdoc},
     volume = {217},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a11/}
}
TY  - JOUR
AU  - V. A. Gradusov
AU  - S. L. Yakovlev
TI  - On the~scattering problem for a~potential decreasing as the~inverse square of distance
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 416
EP  - 429
VL  - 217
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a11/
LA  - ru
ID  - TMF_2023_217_2_a11
ER  - 
%0 Journal Article
%A V. A. Gradusov
%A S. L. Yakovlev
%T On the~scattering problem for a~potential decreasing as the~inverse square of distance
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 416-429
%V 217
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a11/
%G ru
%F TMF_2023_217_2_a11
V. A. Gradusov; S. L. Yakovlev. On the~scattering problem for a~potential decreasing as the~inverse square of distance. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 416-429. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a11/