Addendum to ‘‘Effects of transverse photon exchange in helium Rydberg states: Corrections beyond the Coulomb-Breit interactions’’

Au, C. K.; Mesa, Manuel A.

doi:10.1103/physreva.41.2848

Cited by 22 publications

(10 citation statements)

References 5 publications

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“…In fact, the suggestion that such physics (specifically the Casimir or retardation interactions) might be present in these large-sized atoms was the initial motivation for this series [12 -14] of helium Rydberg measurements. Detailed calculations [17,18,30,31] of the dipole retardation contributions have been carried out by a number of techniques and it is clear that for the high-L, large-sized states, methods that go beyond the standard approximation of atomic theory are required. This fact is illustrated, for instance, by the contributions of AV, ", , shown in Table X, which cannot be obtained from standard atomic theory calculations.…”

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confidence: 99%

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Fast-beam measurements of the 10D-10Ffine-structure intervals in helium

1995

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Four fine-structure intervals separating the n =10, L =2 and 3 Rydberg states of helium have been measured using a fast-beam microwave-optical technique. These are found to agree both with previous measurements of these intervals and with high-precision calculations. The experimental results for the four intervals are 10 'D2 -10+F3, 10 918.826(37) MHz; 10 D 1 -10 F2, 15 760.667(17) MHz; 10 D2 -10 F3, 15770.704(15) MHz; and 10 D3 -10 F4, 15781.991(11)MHz. The +F ( F) state is the mixed singlet-triplet state of higher (lower) energy. The result for the spin-averaged 10D-10Finter-val in helium is 14 560.650(13) MHz, which has an experimental uncertainty of better than one part per million. The good agreement with theory breaks the pattern of discrepancies between theory and experiment observed in measurements of the higher-L n =10 helium fine structure. Possible explanations for those discrepancies are discussed.PACS number(s): 32.30.8v, 31.30.Jv

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confidence: 99%

“…The column labeled 6V, ", , is the portion of the retardation contribution thought not be implicitly included in Drake s calculations (taken from Ref. [31]). …”

Section: Most Of the Results Listed Inmentioning

confidence: 99%

Fast-beam measurements of the 10D-10Ffine-structure intervals in helium

1995

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“…New theoretical techniques have been developed for calculating the nonrelativistic eigenvalues and relativistic corrections of these states, 2,3 and for evaluating the predicted retardation effects for specific states. 4 " 6 Experimental results of increasing precision have come from fast-beam microwave-optical experiments. 7 " 10 We report here a new set of measurements which determine the mean energy intervals separating n = 10, L =4-8 states of helium with a precision of about ±0.4 kHz, which is sufficient to clearly resolve the predicted retardation effects.…”

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Precision spectroscopy of high-L,n=10 Rydberg helium: An improved test of relativistic, radiative, and retardation effects

et al. 1990

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“…The largest uncertainty in the theoretical predictions was due to the uncertainty in the selfenergy contribution to the energy, specifically the Bethelogarithm contribution to the Lamb shift. Results for the variational calculation of the electric dipole polarizability contribution to the Bethe logarithm were published recently [3], eliminating the gap between the uncertaintainties in the theoretical predictions and experimental results and pointing to discrepancies between both that cannot be accounted for by residual Casimir-Polder retardation corrections [4]. It is still necessary to add to that calculation the electric quadrupole and (of the same order) the nonadiabatic dipole polarizability contributions to the Bethe logarithm in order to have an estimate of the uncertainty in the theoretical results.…”

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Calculation of the Bethe logarithm for the Rydberg states of helium

Goldman

1994

Phys. Rev. A

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A very efficient technique for the finite-basis-set calculation of logarithmic sums is introduced. The basis sets contain sequences of nonlinear parameters determined by the zeros of Laguerre polynomials. It is shown that one can easily obtain convergence to 12 digits in fast calculations involving small basis sets. The method is then applied to calculations of the asymptotic expansion of the Bethe logarithm for the Rydberg states of helium. As pertubation calculations of the sums involved diverge, the present method is used to obtain accurate results for atoms in dipole and quadrupole fields from which the adiabatic contributions are extracted. A discussion of gauges in the multipole case and the suppression of roundoK errors by working in a mixed gauge is presented. A strategy for handling the nonadiabatic contributions to sums is presented and used to obtain preliminary bounds on these contributions. PACS number(s): 31.30.Jv, 31.20.Di, 31.50.+w I. THE BETHE LOGARITHMIn the past few years, experimental measurements [1] and theoretical predictions [2] of transition frequencies among the Rydberg states of helium have advanced substantially in accuracy to the point that they are sensitive to both /ED contributions and Casimir-Polder retardation corrections. The largest uncertainty in the theoretical predictions was due to the uncertainty in the selfenergy contribution to the energy, specifically the Bethelogarithm contribution to the Lamb shift. Results for the variational calculation of the electric dipole polarizability contribution to the Bethe logarithm were published recently [3], eliminating the gap between the uncertaintainties in the theoretical predictions and experimental results and pointing to discrepancies between both that cannot be accounted for by residual Casimir-Polder retardation corrections [4]. It is still necessary to add to that calculation the electric quadrupole and (of the same order) the nonadiabatic dipole polarizability contributions to the Bethe logarithm in order to have an estimate of the uncertainty in the theoretical results. In this paper we present the details of the difficult calculations that yield the dipole corrections to the Bethe logarithm, as well as results for the quadrupole contribution and an estimate of the nonadiabatic dipole correction with a discussion of the difficulties one encounters in this last case.Following Kabir and Salpeter [5], the lowest-order Lamb shift for a two-electron ion in an nI.S state can be written as b, EI", = n'Z D -+ In-[(crZ) '] 3' 30 + ln[Z A~/k(nLS, Z)]+2.296vra 2 + -CM where D = , (b(r, ) + b (r2)) is independent of Z in the hydrogenic limit and (p/M)CM involves finite-mass terms. There is in (1) a term that is difficult to calculate: the two-electron Bethe logarithm (BL from now on) defined for a state with energy Eo by

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Addendum to ‘‘Effects of transverse photon exchange in helium Rydberg states: Corrections beyond the Coulomb-Breit interactions’’

Cited by 22 publications

References 5 publications

Fast-beam measurements of the 10D-10Ffine-structure intervals in helium

Fast-beam measurements of the 10D-10Ffine-structure intervals in helium

Precision spectroscopy of high-L,n=10 Rydberg helium: An improved test of relativistic, radiative, and retardation effects

Calculation of the Bethe logarithm for the Rydberg states of helium

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