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Title: Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

Abstract

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.

Authors:
Publication Date:
OSTI Identifier:
22451150
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; BOUND STATE; EXCITED STATES; GROUND STATES; HYDROGEN; INTEGRAL EQUATIONS; MULTIPLE SCATTERING; POLARIZABILITY; POLARIZATION

Citation Formats

Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua. Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.02.007.
Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua. Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms. United States. https://doi.org/10.1016/J.AOP.2015.02.007
Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua. 2015. "Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms". United States. https://doi.org/10.1016/J.AOP.2015.02.007.
@article{osti_22451150,
title = {Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms},
author = {Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua},
abstractNote = {The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.},
doi = {10.1016/J.AOP.2015.02.007},
url = {https://www.osti.gov/biblio/22451150}, journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 355,
place = {United States},
year = {Wed Apr 15 00:00:00 EDT 2015},
month = {Wed Apr 15 00:00:00 EDT 2015}
}