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

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 t...

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Bibliographic Details
Published in:Annals of physics 2015-04, Vol.355, p.153-169
Main Author: Kharchenko, V.F.
Format: Article
Language:English
Subjects:
ANALYTICAL SOLUTION
BOUND STATE
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Electric multipole polarizability
EXCITED STATES
GROUND STATES
HYDROGEN
Hydrogen-like atom
Inhomogeneous integral equation
INTEGRAL EQUATIONS
Matrix
MULTIPLE SCATTERING
Particle physics
POLARIZABILITY
POLARIZATION
Quantum physics
Transition-matrix formalism
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Summary: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. •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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2015.02.007