Corrections radiatives des etats de Rydberg

Poquérusse, A.

doi:10.1016/0375-9601(81)90194-8

Cited by 10 publications

(13 citation statements)

References 5 publications

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“…, 10, thereby confirming the asymptotic limits obtained in Ref. [46] (see Table V). A comparison to the numerical values obtained in the current investigation indicates excellent agreement with the asymptotic values as n → ∞ (see Fig.…”

Section: Discussionsupporting

confidence: 86%

Calculation of hydrogenic Bethe logarithms for Rydberg states

Mohr

2005

Phys. Rev. A

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We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n ≤ 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schrödinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schrödinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.

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Section: Discussionsupporting

confidence: 86%

Calculation of hydrogenic Bethe logarithms for Rydberg states

Mohr

2005

Phys. Rev. A

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“…The final results for b L are in Table II. Based on the trend of the data in Table II, we conjecture here that in the limit n → ∞, the two-loop Bethe logarithms for a given l should approach a constant in the same way as the one-loop Bethe logarithms [16][17][18]. Also, the data in Table II indicate that the two-loop Bethe logarithms, just like their one-loop counterparts, become smaller in magnitude for increasing orbital angular momentum.…”

Section: Asymptotics Of the Integrandmentioning

confidence: 86%

“…The calculation of this contribution is done separately, by writing it in terms of a sum over virtual states, which are calculated as a basis set on a lattice in coordinate space. Numerical values are compiled in Table I, where the name "loop-after-loop" should be taken cum grano salis because the negative-energy virtual states are excluded from expression (16). The final results for b L are in Table II.…”

Section: Asymptotics Of the Integrandmentioning

confidence: 99%

Two-loop Bethe logarithms for non-Slevels

Jentschura

2006

Phys. Rev. A

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Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of α 8 me c 2 , where me is the electron mass and c is the speed of light, and scale as Z 6 , where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (α/π) 2 (Zα) 6 ln[(Zα) −2 ] me c 2 for D states and all states with higher angular momenta. For higher excited P and D states, a number of poles from lower-lying levels have to subtracted in the numerical evaluation. We find that, surprisingly, the corrections of the "squared decayrate type" are the numerically dominant contributions in the order (α/π) 2 (Zα) 6 me c 2 for states with large angular momenta, and provide an estimate of the entire B60-coefficient for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.

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“…It would be very interesting to verify this limit by an explicit calculation, e.g., using the techniques outlined in Ref. [29].…”

Section: Asymptotics For High Quantum Numbersmentioning

confidence: 96%

“…For the Bethe logarithm ln k 0 , such a study has recently been completed (see Refs. [29,30]). The asymptotics of the generalized Bethe logarithm ln k 3 have not yet been determined.…”

Section: Asymptotics For High Quantum Numbersmentioning

confidence: 99%

Mass measurements and the bound-electron g factor

Jentschura

Czarnecki

Pachucki

et al. 2006

International Journal of Mass Spectrometry

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The accurate determination of atomic masses and the high-precision measurement of the bound-electron g factor are prerequisites for the determination of the electron mass, which is one of the fundamental constants of nature. In the 2002 CODATA adjustment [P.J. Mohr, B.N. Taylor, Rev. Mod. Phys. 77 (2005) 1], the values of the electron mass and the electron–proton mass ratio are mainly based on g factor measurements in combination with atomic mass measurements. In this paper, we briefly discuss the prospects for obtaining other fundamental information from bound-electron g factor measurements, we present some details of a recent investigation of two-loop binding corrections to the g factor, and we also investigate the radiative corrections in the limit of highly excited Rydberg S states with a long lifetime, where the g factor might be explored using a double resonance experiment

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Corrections radiatives des etats de Rydberg

Cited by 10 publications

References 5 publications

Calculation of hydrogenic Bethe logarithms for Rydberg states

Calculation of hydrogenic Bethe logarithms for Rydberg states

Two-loop Bethe logarithms for non-Slevels

Mass measurements and the bound-electron g factor

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