High Resolution Spectroscopy of the Hydrogen Atom: Determination of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi mathvariant="italic">S</mml:mi></mml:math>Lamb Shift

Bourzeix, S.; Beauvoir, B. de; Nez, F.; Plimmer, Mark; Tomasi, F. De; Julién, L.; Biraben, F.; Stacey, D. N.

doi:10.1103/physrevlett.76.384

Cited by 125 publications

(77 citation statements)

References 21 publications

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“…Then we obtain an equality between a linear combination of the 1S, 2S and 8D linear combination of the Lamb shifts in 1S and 2S states may be directly expressed in terms of the experimental data. All other recent measurements of the 1S Lamb shift [311,[323][324][325] also end up with an experimental number for a linear combination of the 1S, 2S and higher level Lamb shifts. An unbiased extraction of the 1S Lamb shift from the experimental data remains a problem even after an experimental decoupling of the Lamb shift measurement from the measurement of the Rydberg constant.…”

Section: Comparison Of Theory and Experimentsmentioning

confidence: 99%

Theory of light hydrogenlike atoms

2001

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The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion He + , and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium. *

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Section: Comparison Of Theory and Experimentsmentioning

confidence: 99%

Theory of light hydrogenlike atoms

2001

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“…The Dirac equation extends the analysis to a full relativistic description, but still requires further adjustment via quantum electrodynamics (QED) theory to account properly for the Lamb shift in order to agree with direct experimental measurements of the 1S-2S transition frequency. Currently, the measurement of this transition by laser spectroscopy, relative to the Cs primary standard, has an uncertainty of 1.4 parts in 10 14 [21], and, when combined with measurements of other hydrogen transitions [22] to account for the Lamb shift, gives a Rydberg constant value with the lowest uncertainty of 6.6 parts in 10 12 .…”

Section: Possible Algorithms For a Redefinition Of The Secondmentioning

confidence: 99%

When should we change the definition of the second?

Gill

2011

Phil. Trans. R. Soc. A.

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The microwave caesium (Cs) atomic clock has formed an enduring basis for the second in the International System of Units (SI) over the last few decades. The advent of laser cooling has underpinned the development of cold Cs fountain clocks, which now achieve frequency uncertainties of approximately 5 × 10 −16 . Since 2000, optical atomic clock research has quickened considerably, and now challenges Cs fountain clock performance. This has been suitably shown by recent results for the aluminium Al + quantum logic clock, where a fractional frequency inaccuracy below 10 −17 has been reported. A number of optical clock systems now achieve or exceed the performance of the Cs fountain primary standards used to realize the SI second, raising the issues of whether, how and when to redefine it. Optical clocks comprise frequency-stabilized lasers probing very weak absorptions either in a single cold ion confined in an electromagnetic trap or in an ensemble of cold atoms trapped within an optical lattice. In both cases, different species are under consideration as possible redefinition candidates. In this paper, I consider options for redefinition, contrast the performance of various trapped ion and optical lattice systems, and point to potential limiting environmental factors, such as magnetic, electric and light fields, collisions and gravity, together with the challenge of making remote comparisons of optical frequencies between standards laboratories worldwide.

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“…For the 1S Lamb shift the uncertainty [29] was estimated to be about 40 kHz. This number is the linear sum of a 8 kHz uncertainty in the self energy correction, the 16 kHz uncertainty caused by the unknown α 2 (Zα) 6 terms and the 16 kHz uncertainty due to unknown α 3 (Zα) 4 terms. The result of Ref.…”

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Three-Loop Slope of the Dirac Form Factor and the1SLamb Shift in Hydrogen

2000

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The last unknown contribution to hydrogen energy levels at order mα 7 , due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n 3 kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius rp = 0.883 ± 0.014 fm.Precision experiments with hydrogen and, more generally, with hydrogen-like atoms serve as an excellent laboratory to test theoretical approaches to bound state QED (for a recent review see, e.g. [1]). These experiments address a number of features of the simplest atoms, such as the energy levels of the ground and excited states, and the corresponding lifetimes.In recent years we have seen remarkable progress in the experimental study of the hydrogen atom. In particular the accuracy of the 1S Lamb shift measurements has increased dramatically over the years [2][3][4][5][6][7]. All measurements are consistent with each other and the most accurate value so far was determined in Ref. [7]:This result was obtained by analysing the most precise measurements for the transition frequencies in hydrogen (see [7] for details). Theoretically, since the ratio of the electron mass m to the proton mass M is very small, it is convenient to write hydrogen energy levels as a double expansion in α and m/M . The corrections which survive in the limit M → ∞ are known as non-recoil corrections, the other corrections are called recoil ones. It is further convenient to organize non-recoil corrections in powers of α n (Zα) l , assigning an auxiliary notation Z for the proton charge. In this case the correction α n (Zα) l describes a contribution of all diagrams with l − 3 Coulomb photons exchanged between the electron and the proton and with * e-mail: melnikov@slac.stanford.edu † e-mail: timo@particle.physik.uni-karlsruhe.de n photons emitted and absorbed by the electron. The general expression for the nS-level shift can be written as:where we have also added a contribution of muons and hadrons to photon vacuum polarization and a contribution due to the proton structure (see a discussion below). We begin with non-recoil corrections. These corrections can be parameterized as (see e.g. [8][9][10]):where m r = mM/(m + M ) is the reduced mass of the electron and L = log m/(m r (Zα) 2 ) and the function A(Zα) contains all higher order terms in the expansion in Zα. We have also indicated that the higher order corrections contain a logarithm of the fine structure constant in the third power [11]. All the terms in the above equation, with the exception for C 40 , are currently known. It is the purpose of this paper to report on the calculation of the last missing ingredient in C 40 , the slope of the Dirac form factor at zero momentum transfer.The hydrogen atom is formed because of a Coulomb interaction of the proton with the electron. The interaction of the virtual photon with the electron on its mass shell can be parameterized by the so-called Dirac and Pauli form facto...

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High Resolution Spectroscopy of the Hydrogen Atom: Determination of the1SLamb Shift

Cited by 125 publications

References 21 publications

Theory of light hydrogenlike atoms

Theory of light hydrogenlike atoms

When should we change the definition of the second?

Three-Loop Slope of the Dirac Form Factor and the1SLamb Shift in Hydrogen

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