Fine structure of helium and light helium-like ionsThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

Pachucki, Krzysztof; Yerokhin, V. A.

doi:10.1139/p10-050

“…Drake and collaborators [44,[59][60][61][62][63][64] and Pachucki and collaborators [2,[65][66][67][68][69][70][71][72][73][74] have pushed relativistic corrections for regular helium up to order α 5 and beyond using a Hylleraas [26] type basis. Drake [63] matched theoretical and observed energy differences in the J = 0, 1 splitting of the 2 3 P state and determined α −1 = 137.0359893 (23).…”

Section: Mass Polarization and Relativistic Correction Calculationsmentioning

confidence: 99%

Pseudospectral calculation of helium wave functions, expectation values, and oscillator strength

Grabowski

¹

,

Chernoff

²

2011

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We show the pseudospectral method is a powerful tool for finding precise solutions of Schrödinger's equation for two-electron atoms with general angular momentum. Realizing the method's full promise for atomic calculations requires special handling of singularities due to twoparticle Coulomb interactions. We give a prescription for choosing coordinates and subdomains whose efficacy we illustrate by solving several challenging problems. One test centers around the determination of the nonrelativistic electric dipole oscillator strength for the helium 1 1 S → 2 1 P transition. The result achieved, 0.27616499 (27), is comparable to the best in the literature. The formally equivalent length, velocity, and acceleration expressions for the oscillator strength all yield roughly the same accuracy. We also calculate a diverse set of helium ground state expectation values, reaching near state-of-the-art accuracy without the necessity of implementing any specialpurpose numerics. These successes imply that general matrix elements are directly and reliably calculable with pseudospectral methods. A striking result is that all the relevant quantities tested in this paper -energy eigenvalues, S-state expectation values and a bound-bound dipole transition between the lowest energy S and P states -converge exponentially with increasing resolution and at roughly the same rate. Each individual calculation samples and weights the configuration space wave function uniquely but all behave in a qualitatively similar manner. These results suggest that the method has great promise for similarly accurate treatment of few-particle systems.

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Unexpectedly Large Difference of the Electron Density at the Nucleus in the 4p 2P1/2,3/2 Fine-Structure Doublet of Ca+

Shi¹,

Gebert²,

Gorges³

et al. 2018

Exploring the World With the Laser

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We measured the isotope shift in the 2 S1 /2 → 2 P3 /2 (D2) transition in singly-ionized calcium ions using photon recoil spectroscopy. The high accuracy of the technique enables us to resolve the difference between the isotope shifts of this transition to the previously measured isotopic shifts of the 2 S1 /2 → 2 P1 /2 (D1) line. This so-called splitting isotope shift is extracted and exhibits a clear signature of field shift contributions. From the data we were able to extract the small difference of the field shift coefficient and mass shifts between the two transitions with high accuracy. This J-dependence is of relativistic origin and can be used to benchmark atomic structure calculations. As a first step, we use several ab initio atomic structure calculation methods to provide more accurate values for the field shift constants and their ratio. Remarkably, the high-accuracy value for the ratio of the field shift constants extracted from the experimental data is larger than all available theoretical predictions.

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Unexpectedly large difference of the electron density at the nucleus in the $$ 4p\, ^2{\mathrm {P}}_{{1}/{2},{3}/{2}}$$ 4 p 2 P 1 / 2 , 3 / 2 fine-structure doublet of Ca $$^+$$ +

Shi

¹

,

Gebert

²

,

Gorges

³

et al. 2016

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We measured the isotope shift in the 2 S1 /2 → 2 P3 /2 (D2) transition in singly-ionized calcium ions using photon recoil spectroscopy. The high accuracy of the technique enables us to resolve the difference between the isotope shifts of this transition to the previously measured isotopic shifts of the 2 S1 /2 → 2 P1 /2 (D1) line. This so-called splitting isotope shift is extracted and exhibits a clear signature of field shift contributions. From the data we were able to extract the small difference of the field shift coefficient and mass shifts between the two transitions with high accuracy. This J-dependence is of relativistic origin and can be used to benchmark atomic structure calculations. As a first step, we use several ab initio atomic structure calculation methods to provide more accurate values for the field shift constants and their ratio. Remarkably, the high-accuracy value for the ratio of the field shift constants extracted from the experimental data is larger than all available theoretical predictions.

show abstract

Fine structure of helium and light helium-like ionsThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

Cited by 12 publications

References 38 publications

Pseudospectral calculation of helium wave functions, expectation values, and oscillator strength

Pseudospectral calculation of helium wave functions, expectation values, and oscillator strength

Unexpectedly Large Difference of the Electron Density at the Nucleus in the 4p 2P1/2,3/2 Fine-Structure Doublet of Ca+

Unexpectedly large difference of the electron density at the nucleus in the $$ 4p\, ^2{\mathrm {P}}_{{1}/{2},{3}/{2}}$$ 4 p 2 P 1 / 2 , 3 / 2 fine-structure doublet of Ca $$^+$$ +

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