Measurement of the Lamb Shift in Hydrogen,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>

Lundeen, S. R.; Pipkin, F. M.

doi:10.1103/physrevlett.46.232

Cited by 261 publications

(158 citation statements)

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“…One is the classic 2S 1/2 -2P 1/2 Lamb shift measured by several groups [20], [21], [19], and the second is the combined Lamb shift L(4S − 2S) − 1 4 L(2S − 1S) as measured by the Hänsch group (for a review see [22]). The experimental value of 2S Lamb shift can be extracted from E(2S-2P 1/2 ) having the precise value for 2P 1/2 Lamb shift, and can also be determined from the combined Lamb shift through the formula…”

Section: Results and Conclusionmentioning

confidence: 99%

Higher-order binding corrections to the Lamb shift of 2Pstates

1996

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We present an improved calculation of higher order corrections to the oneloop self energy of 2P states in hydrogen-like systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon energy into a high and a low energy part. The high energy part is calculated by an expansion of the electron propagator in powers of the Coulomb field. The low energy part is simplified by the application of a FoldyWouthuysen transformation. This transformation leads to a clear separation of the leading contribution from the relativistic corrections and removes higher order terms. The method is applied to the 2P 1/2 and 2P 3/2 states in atomic hydrogen. The results lead to new theoretical values for the Lamb shifts and the fine structure splitting.

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Section: Results and Conclusionmentioning

confidence: 99%

Higher-order binding corrections to the Lamb shift of 2Pstates

1996

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“…A natural way to obtain a self-consistent value of the 1S Lamb shift independent of the experimental data on the 2S −2P splitting, is provided by the theoretical relation between the 1S and 2S Lamb shifts discussed above in Section XXXIX C. An important advantage of the self-consistent method is that it produces an unbiased value of the L(1S) Lamb shift independent of the widely scattered experimental data on the 2S − 2P interval. Spectacular experimental progress in the frequency measurement now allows one to obtain self-consistent values of 1S Lamb shift from the experimental data [3], with comparable or even better accuracy (see five lines in Table XXI below the theoretical values in the middle of the Table) than in the method based on experimental results of the classic Lamb shift in [320,316]. The original experimental numbers from [3,311] in the fourth and fifth lines in Table XXI are averages of the self-consistent values and the values based on the classic Lamb shift.…”

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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“…6 confirms the presence of two irreducible submatrices of H Fz =0 . Indeed, the two uncoupled subspaces are spanned by the states |Ψ i with i = 1, 2, 5, 7,8,11,15,16,18,21,22, 24 (subspace I), and |Ψ j with j = 3, 4,6,9,10,12,13,14,17,19,20,23 (subspace II). An ordering of the eigenvalues reveals that one can have coupling among the S-S and P -P states (distributed among atoms A and B), forming submanifold I, and among all S-P and P -S states (distributed among atoms A and B), forming submanifold II.…”

Section: S-2s Interaction In Hydrogenmentioning

confidence: 99%

Adjacency Graphs and Long-Range Interactions of Atoms in Quasi-degenerate States: Applied Graph Theory

Adhikari¹,

Debierre²

2018

Exploring the World With the Laser

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We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.

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Measurement of the Lamb Shift in Hydrogen,n=2

Abstract: A measurement based on the fast-atomic-beam separated-oscillatory-field method of sub-natural-linewidth spectroscopy gives, for the Lamb shift in hydrogen, S(w =2) = 1057.845(9) MHz. The result is not in good agreement with theory.

Cited by 261 publications

References 10 publications

Higher-order binding corrections to the Lamb shift of 2Pstates

Higher-order binding corrections to the Lamb shift of 2Pstates

Theory of light hydrogenlike atoms

Adjacency Graphs and Long-Range Interactions of Atoms in Quasi-degenerate States: Applied Graph Theory

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