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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 3, p.263-269
https://doi.org/10.15407/ujpe62.03.0923    Paper

Kharchenko V.F.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14-b, Metrolohichna Str., Kyiv 03143, Ukraine; e-mail: vkharchenko@bitp.kiev.ua)

Solution of the Lippmann–Schwinger Equation for a Partial Wave Transition Matrix with Repulsive Coulomb Interaction

Section: General Problems of Theoretical Physics
Original Author's Text:  Ukrainian

Abstract: A special case where the Lippmann–Schwinger integral equation for the partial wave two-body Coulomb transition matrix for likely charged particles with a negative energy has an analytical solution has been considered. Analytical expressions for the partial s-, p-, and d-wave Coulomb transition matrices for repulsively interacting particles at the ground-state energy have been derived, by using the Fock method of stereographic projection of the momentum space onto a four-dimensional unit sphere.

Key words: partial wave transition matrix, Coulomb interaction, Lippmann–Schwinger equation, Fock method, analytical solution.