Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy

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...

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Bibliographic Details
Published in:Annals of physics 2016-11, Vol.374, p.16-26
Main Author: Kharchenko, V.F.
Format: Article
Language:English
Subjects:
Analysis
Analytical solution
Energy
Fock method
Lippmann–Schwinger equation
Matrix
Partial wave Coulomb transition matrix
Physics
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Summary: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. •A new description for off-shell partial Coulomb scattering amplitudes based on Fock’s method.•Direct solution of the Lippmann–Schwinger equation for partial Coulomb transition matrix.•New analytical expressions for partial wave Coulomb t-matrices at ground state energy.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2016.08.004