Erratum: High Precision Atomic Theory for Li and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Be</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>: QED Shifts and Isotope Shifts [Phys. Rev. Lett.<b>100</b>, 243002 (2008)]

Yan, Zong-Chao; Nörtershäuser, W.; Drake, G. W. F.

doi:10.1103/physrevlett.102.249903

Cited by 72 publications

(149 citation statements)

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“…One of the main difficulties and long-standing problems was the calculation of the so-called Bethe logarithm, which is the dominant part of the electron self-energy. Its calculation for hydrogenlike [8] and helium-like systems [9] was recently followed by the report of the complete calculation of QED terms up to the order of α 3 Ry [2,7,10] for lithium atoms. In [10] Yan and Drake calculated the Bethe logarithm ln k 0 to a relative accuracy of 10 −6 , and in [11] Pachucki reports on the Bethe logarithm of the four-electron system beryllium with a relative accuracy of 10 −5 .…”

Section: Introductionmentioning

confidence: 99%

“…The non-relativistic energies and lowest-order relativistic corrections can now be calculated to spectroscopic accuracy [2]- [7], but the QED corrections still limit the overall accuracy. One of the main difficulties and long-standing problems was the calculation of the so-called Bethe logarithm, which is the dominant part of the electron self-energy.…”

Section: Introductionmentioning

confidence: 99%

“…The most accurate treatments available solve the non-relativistic Schrödinger equation variationally in multiple-basis sets in Hylleraas coordinates [10,11] and use the resulting wave functions to calculate relativistic and QED corrections perturbatively. Table 1, summarized from [2,7,20], lists the different contributions to the 1s 2 2s 2 S 1/2 − 1s 2 3s 2 S 1/2 transitions in 7 Li. The non-relativistic contributions include the first-and second-order mass polarization term.…”

Section: Introductionmentioning

confidence: 99%

“…In these experiments, the change in the transition frequency between the isotopes A Table 1. Contributions of the various expansive terms to the absolute 2S-3S transition energy in 7 Li. All values are in given MHz.…”

Section: Introductionmentioning

confidence: 99%

“…Values from [2] are based on table III in this reference. Term Yan et al [7] a Puchalski and Pachucki [ and A (the isotope shift δν A,A ) was accurately measured. After subtracting the calculated massdependent shift, the so-called field shift is obtained, which is due to the change in the nuclear charge distribution between the isotopes A and A .…”

Section: Introductionmentioning

confidence: 99%

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Absolute frequency measurements on the 2S→3S transition of lithium-6,7

Sánchez¹,

Žáková²,

Andjelkovic³

et al. 2009

New J. Phys.

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Abstract. The frequencies of the 2S-3S two-photon transition for the stable lithium isotopes were measured by cavity-enhanced Doppler-free laser excitation that was controlled by a femtosecond frequency comb. The resulting values of 815 618 181.57(18) and 815 606 727.59(18) MHz, respectively, for 7 Li and 6 Li are in agreement with previous measurements but are more accurate by an order of magnitude. There is still a discrepancy of about 11.6 and 10.6 MHz from the latest theoretical values. This is comparable to the uncertainty in the theoretical calculations, while uncertainty in our experimental values is more than a hundred-fold smaller. More accurate theoretical calculation of the transition frequencies would allow extraction of the absolute charge radii for these stable isotopes, which in turn could improve nuclear charge radii values for the unstable lithium isotopes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Absolute frequency measurements on the 2S→3S transition of lithium-6,7

Sánchez¹,

Žáková²,

Andjelkovic³

et al. 2009

New J. Phys.

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Recursion relations for the three‐electron subsidiary integral W (l, m, n; α, β, γ)

Wang

Zhou

2012

Int J of Quantum Chemistry

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The subsidiary integral W (l, m, n; a, b, c) is a key integral that appears in the variational calculation of a threeelectron atomic system using Hylleraas coordinates. For the case where the ratio a/(a þ b þ c) $ 1, an important special situation that may occur in the evaluation of the Bethe logarithm, existing approaches for calculating the W integral become impractical due to the problem of slow convergence. In this article, we present a computationally efficient and numerical stable method, in which the W integral can be expressed in terms of either a finite series or a finite recursion relation. Numerical tests are given.

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