Approximate recalculation of the contribution to the self-energy effect on hydrogenic states with a multipole expansion

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Published inAnnals of physics Vol. 328; p. 139
Main Author Zamastil, J
Format Journal Article
LanguageEnglish
Published New York Elsevier BV 01.01.2013
Subjects
APPROXIMATIONS
ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
CORRECTIONS
COULOMB FIELD
ELECTRONS
GROUND STATES
MULTICHARGED IONS
QUANTUM ELECTRODYNAMICS
SELF-ENERGY
VIRTUAL STATES
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AbstractList A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order . The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in for up to 6 parts in for . The complete terms of the order are identified. The accuracy of the result for the ground state of the hydrogen is 2 ppm. The separation into the low and high energy regions and their matching is avoided.
Highlights
A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order {alpha}(Z{alpha}){sup 5}. The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order {alpha}(Z{alpha}){sup 5} to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in 10{sup 6} for Z=1 up to 6 parts in 10{sup 4} for Z=10. - Highlights: Black-Right-Pointing-Pointer The complete terms of the order {alpha}(Z{alpha}){sup 5} are identified. Black-Right-Pointing-Pointer The accuracy of the result for the ground state of the hydrogen is 2 ppm. Black-Right-Pointing-Pointer The separation into the low and high energy regions and their matching is avoided.
Author Zamastil, J
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Snippet Highlights
A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context...
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SubjectTerms APPROXIMATIONS
ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
CORRECTIONS
COULOMB FIELD
ELECTRONS
GROUND STATES
MULTICHARGED IONS
QUANTUM ELECTRODYNAMICS
SELF-ENERGY
VIRTUAL STATES
Title Approximate recalculation of the contribution to the self-energy effect on hydrogenic states with a multipole expansion
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