Lamb Shift in the Helium Atom

Schwartz, Charles

doi:10.1103/physrev.123.1700

Cited by 271 publications

(146 citation statements)

References 13 publications

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“…In order to regularize the divergence introduced by the centrifugal terms (for J > 0), it is necessary to factorize the radial wave functions. A general method of factorization was derived in [13]. One obtains, for P o states :…”

Section: Factorization Of the Radial Partmentioning

confidence: 99%

High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2

Karr

Hilico

2006

J. Phys. B: At. Mol. Opt. Phys.

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Section: Factorization Of the Radial Partmentioning

confidence: 99%

High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2

Karr

Hilico

2006

J. Phys. B: At. Mol. Opt. Phys.

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“…where ln k 0 is the so-called Bethe logarithm [73,90], D 1 and D 2 are the values of the one-and two-electron Darwin corrections (including the factor of α 2 ). The term H AS is the Araki-Sucher contribution, given by the following expectation value…”

Section: Relativistic Qed and Adiabatic Correctionsmentioning

confidence: 99%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

et al. 2015

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In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order α 2 are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0 ± 1.9 cm −1 , in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

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“…[47] for a comprehensive review) and hydrogen molecular ion [61][62][63][64][65]. Beyond that, very accurate results are available for the helium atom [66][67][68][69][70][71][72][73][74][75][76][77], hydrogen molecule [78][79][80][81][82][83], and their isotopomers. Remarkably, corrections of the order α 4 have been derived and evaluated recently [72,83,84,89].…”

Section: Introductionmentioning

confidence: 99%

Calculation of Araki-Sucher correction for many-electron systems

2017

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In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

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Lamb Shift in the Helium Atom

Cited by 271 publications

References 13 publications

High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2

High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

Calculation of Araki-Sucher correction for many-electron systems

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Lamb Shift in the Helium Atom

Cited by 271 publications

References 13 publications

High accuracy results for the energy levels of the molecular ions H+2, D+2and HD+, up toJ= 2

High accuracy results for the energy levels of the molecular ions H+2, D+2and HD+, up toJ= 2

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

Calculation of Araki-Sucher correction for many-electron systems

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High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2

High accuracy results for the energy levels of the molecular ions H⁺₂, D⁺₂and HD⁺, up toJ= 2