Nonrelativistic QED expansion for the electron self-energy

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonrelativistic QED expansion for the electron self-energy

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Nonrelativistic QED expansion for the electron self-energy

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Physical Review A

ISSN

2469-9926

e-ISSN

—

Svazek periodika

95

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

—

Kód UT WoS článku

000399495600008

EID výsledku v databázi Scopus

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