Nonrelativistic QED expansion for the electron self-energy

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10367393" target="_blank" >RIV/00216208:11320/17:10367393 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1103/PhysRevA.95.012507" target="_blank" >http://dx.doi.org/10.1103/PhysRevA.95.012507</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevA.95.012507" target="_blank" >10.1103/PhysRevA.95.012507</a>

Result language

angličtina

Original language name

Nonrelativistic QED expansion for the electron self-energy

Original language description

The recently proposed relativistic multipole expansion (RME) of the self-energy effect suggests some observations on the nonrelativistic expansion of the effect. First, the nature of the series for the one-loop self-energy of an electron bound by the Coulomb field of the nucleus is clarified. It is shown that the expansion of the energy shift caused by the self-energy effect contains terms of the form alpha(Z alpha)(7) ln(Z alpha), alpha(Z alpha)(8) ln(3)(Z alpha), alpha(Z alpha)(9) ln(2)(Z alpha), alpha(Z alpha)(10) ln(4)(Z alpha), and so on. Here Z is the charge of the nucleus. The origin of these terms is traced back to the logarithmic divergence of the Dirac S-wave function at the origin. These terms eventually lead to breakdown of the nonrelativistic quantum electrodynamics approach. Second, at leading order relativistic multipole expansion requires an evaluation of the &quot;extended Bethe logarithm&quot; (EBL). When expanded in series in Z alpha EBL reduces at leading order to the ordinary Bethe logarithm. However, it is argued that it is both more accurate and easier to calculate the EBL than the ordinary Bethe logarithm. Both variants of the Bethe logarithm can be calculated by means of the pseudostate method. An improvement of this method is suggested. Finally, the contribution of the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen for the 1s-4s and 2p-4p states by means of the EBL is calculated. For cases that had already been calculated the results reported here are more accurate than the previous ones.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physical Review A

ISSN

2469-9926

e-ISSN

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Volume of the periodical

95

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

13

Pages from-to

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UT code for WoS article

000399495600008

EID of the result in the Scopus database

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