Corrections to {ital O}{bold (}{alpha}{sup {bold 7}}(ln{alpha}){ital mc}{sup {bold 2}}{bold )} fine-structure splittings and {ital O}{bold (}{alpha}{sup {bold 6}}(ln{alpha}){ital mc}{sup {bold 2}}{bold )} energy levels in helium
- Department of Physics, University of Windsor, Windsor, Ontario, N9B 3P4 (CANADA)
Fully relativistic formulas for the energy-level shifts arising from no-pair exchange diagrams of two transverse photons plus an arbitrary number of Coulomb photons are derived in closed form within the external potential Bethe-Salpeter formalism. {ital O}{bold (}{alpha}{sup 7}(ln{alpha}){ital mc}{sup 2}{bold )} corrections to the fine-structure splittings of helium are obtained and expressed in terms of expectation values of nonrelativistic operators. {ital O}({alpha}{sup 7}{ital mc}{sup 2}) operators from exchange diagrams are found in nonrelativistic approximation. {ital O}({alpha}{sup 6}{ital m}{sup 2}{ital c}{sup 2}/{ital M}) nucleus-electron operators contributing to the fine-structure splittings are derived. Nonrelativistic operators of {ital O}({alpha}{sup 6}{ital mc}{sup 2}) corrections to the triplet levels of helium are presented. Nonrelativistic operators of {ital O}{bold (}{alpha}{sup 6}(ln{alpha}){ital mc}{sup 2}{bold )} corrections to the helium singlet levels and to positronium {ital S} levels are derived. {ital O}({alpha}{sup 6}{ital m}{sup 2}{ital c}{sup 2}/{ital M}) hydrogen and {ital O}({alpha}{sup 6}{ital mc}{sup 2}) positronium {ital P} levels, and {ital O}{bold (}{alpha}{sup 6}(ln{alpha}){ital mc}{sup 2}{bold )} corrections of first order to positronium {ital S} levels, are calculated using the derived operators for helium, in agreement with those obtained previously by others, except for one term in corrections to positronium {ital P} levels. In addition, the {ital O}({alpha}{sup 6}{ital mc}{sup 2}) Dirac energies for hydrogenic non-{ital S} levels are exactly reproduced in a perturbative calculation. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 286608
- Journal Information:
- Physical Review A, Vol. 54, Issue 2; Other Information: PBD: Aug 1996
- Country of Publication:
- United States
- Language:
- English
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