Partial-wave Coulomb transition matrices for attractive interaction by Fock's method

2016/10/05 by V.F. Kharchenko, Kharchenko, V. F.
Engineering · Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Photonic Crystals and Applications #Photonic and Optical Devices #Photorefractive and Nonlinear Optics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1610.01431

openalex publication_date 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states. Keywords: Partial wave Coulomb transition matrix; Lippmann-Schwinger equation; Fock method; Analytical solution PACS Nos. 03.65.-w; 03.65.Nk; 34.20.Cf

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