High Precision Calculation of Fine Structure Splittings in Helium and He-Like Ions

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

doi:10.1103/physrevlett.74.4791

Cited by 84 publications

(66 citation statements)

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“…In the present work, we show that it is possible to choose a single basis set for the construction of pseudostates such that the sums in (2) can be calculated directly to high accuracy. The basic ideas for the method are contained in earlier papers by Goldman and Drake [6], Goldman [7], and Yan and Drake [8]. A recent paper by Bhatia and Drachman [9] attempts a similar direct evaluation of (2) for the ground state of helium, but their choice of basis sets limited the final accuracy they could obtain.…”

Section: Introductionmentioning

confidence: 97%

Bethe logarithms for Ps, H, and heliumlike atoms

Drake¹,

Goldman²

2000

Can. J. Phys.

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A new method is presented for the calculation of the mean excitation energy (Bethe logarithm) for helium and other two-electron systems. The method requires only a single matrix diagonalization within a correlated Hylleraas basis set extended to contain a wide range of distance scales. High-precision results are obtained for the ground states of Ps − and H − , and all the S-and P-states of heliumlike ions up to n = 5, including finite mass corrections. The results are used to calculate revised values for the quantum electrodynamic shifts for helium, and a comparison with experiment is presented. PACS Nos.: 31.15Pf, 31.30Jv, and 32.10HqRésumé : Nous proposons une nouvelle méthode pour calculer l'énergie moyenne d'excitation (logarithme de Bethe) pour l'hélium et d'autres systèmes à deux électrons. La méthode ne requiert que la diagonalisation d'une matrice dans une base correlée de Hylleraas étendue pour contenir plusieurs échelles de portée. Nous obtenons des résultats de haute précision pour le fondamental de Ps − et de H − , ainsi que pour tous les états S-et P-des ions de type hélium jusqu'à n = 5, incluant les corrections pour la masse finie. Ces résultats sont utilisés pour refaire les calculs de déplacement QED dans l'hélium, que nous comparons aux mesures expérimentales.[Traduit par la rédaction]

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Section: Introductionmentioning

confidence: 97%

Bethe logarithms for Ps, H, and heliumlike atoms

Drake¹,

Goldman²

2000

Can. J. Phys.

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“…coming from the Breit interaction taken to second order, and the Douglas and Kroll terms [15]. By way of comparison, these contribute 0.000 270 6 cm 21 to the 2 3 P 2 2 2 3 P 0 interval of helium [1,2], which would be more than enough to account for the discrepancy in lithium.…”

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confidence: 96%

“…For helium, theoretical calculations for the fine structure splittings in 1s 2p 3 P J states have recently been performed up to O͑a 7 ln a͒ mc 2 [1,2]. With future progress in both theory and experiment, comparisons with high precision measurements will potentially yield an atomic physics determination of the fine structure constant a.…”

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confidence: 98%

Lithium Fine Structure in the1s22p2P<

Yan

Drake

1997

Phys. Rev. Lett.

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The first fully correlated calculations of fine structure in lithium are presented. For the 1s 2 2p 2 states the fine structure is calculated to a computational accuracy of 1 part in 10 6 , including relativistic and QED terms up to O͑a 4 mc 2 ͒, O͑ ͑ ͑͑m͞M͒a 4 mc 2 ͒ ͒ ͒, O͑a 5 mc 2 ͒, and O͑ ͑ ͑͑m͞M͒a 5 mc 2 ͒ ͒ ͒. A comparison is made with other calculations and experiments. A residual discrepancy between theory and experiment of ͑65 6 2͒ 3 10 26 cm 21 is found due to higher-order QED terms. [S0031-9007(97)03922-7] PACS numbers: 31.15. Pf, 31.30.Jv, 32.10.Fn Atomic fine structure is a fundamental testing ground for relativistic and QED effects. For helium, theoretical calculations for the fine structure splittings in 1s 2p 3 P J states have recently been performed up to O͑a 7 ln a͒ mc 2 [1,2]. With future progress in both theory and experiment, comparisons with high precision measurements will potentially yield an atomic physics determination of the fine structure constant a. For lithium, using the level crossing technique, Brog et al.[3] measured the fine structure splitting in 1s 2 2p 2 P J states with an accuracy of 20 ppm (parts per million). The most precise measurement reported in the literature for this splitting was done by Orth et al. [4], using the optical double resonance method. The precision they achieved is 6 ppm. Very recently, Scherf et al.[5] remeasured the 1s 2 2p 2 P J fine structure using the laser-atomic beam spectroscopy method. The precision they obtained is 20 ppm. All these measurements are in excellent agreement. On the theoretical side, there has been a long-standing problem in precise calculations for the lithium 1s 2 2p 2 P J fine structure, including the lowest-order relativistic terms a 4 mc 2 (or a 2 in atomic units) and ͑m͞M͒ a 4 mc 2 , where m is the electron reduced mass and M is the nuclear mass, and the lowestorder QED terms a 5 mc 2 and ͑m͞M͒ a 5 mc 2 . However, recent advances [6-10] in high-precision variational calculations for the lithium atom, using multiple basis sets in Hylleraas coordinates, now make it possible to perform a well-converged calculation for the 1s 2 2p 2 P J fine structure splitting. The purpose of this Letter is to report the first significant theoretical progress in fully correlated calculations for lithium fine structure studies. The key advance is the development of techniques for handling the more highly singular integrals required to calculate matrix elements of the Breit interaction in Hylleraas coordinates.The spin-dependent fine structure splitting can be written in the form [11,12] (in atomic units throughout)where C is a nonrelativistic wave function and H fs is defined by

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“…Drake and co-workers, using matrix elements of operators derived from the Bethe-Salpeter equation, evaluated with high-precision nonrelativistic wave functions, aim to complete calculations to order a 5 a.u. (or a 7 m e c 2 ) [2][3][4]. Independent calculations of the effective operators are also being carried out by Pachucki [5].…”

mentioning

confidence: 99%

Precision Measurement of the1s2pP32
Myers
¹
,
Margolis
²
,
Thompson
³

et al. 1999
Phys. Rev. Lett.
44
2
11
0
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Using Doppler-tuned fast-beam laser spectroscopy with co-and counterpropagating beams we have measured the three hyperfine components of the 1s2p 3 P 2 -3 P 1 fine structure interval in 19 F 71 . Our result for the centroid is 957.6679͑10͒ cm 21 . Allowing for the hyperfine interaction the "pure" fine structure interval is determined to be 957.8730͑12͒ cm 21 . This result tests O͑a 7 m e c 2 ͒ quantum electrodynamic corrections to high precision calculations which will be used to obtain a new value for the fine structure constant from the fine structure of helium. [S0031-9007 (99)09157-7] PACS numbers: 32.10.Fn, 06.20.JrThe fine structure constant, a, is the fundamental constant which expresses the elementary charge in dimensionless form and hence plays a crucial role in unifying an enormous range of physical phenomena [1]. There is now a program to obtain a new value for a from comparison of theory and experiment for the 1s2p 3 P J2J 0 fine structure of atomic helium. Drake and co-workers, using matrix elements of operators derived from the Bethe-Salpeter equation, evaluated with high-precision nonrelativistic wave functions, aim to complete calculations to order a 5 a.u. (or a 7 m e c 2 ) [2-4]. Independent calculations of the effective operators are also being carried out by Pachucki [5]. This is expected to result in a theoretical value for the larger, approximately 29.6 GHz, J 0 1 interval in helium to better than 61 kHz. Combined with measurements aimed at exceeding this precision [6-9], this should yield a value for a at the 16 ppb (parts per 10 9 ) level. This would be of interest for comparison with the result obtained from QED theory and experiment for the electron magnetic moment, and with results obtained from the various other phenomena reviewed in Ref. [1].Compared to other methods dependent on QED theory for obtaining a, helium fine structure has an advantage in that the theory, in particular, the evaluation of the complex higher-order relativistic and QED corrections, FIG. 1. Schematic of the experimental arrangement. G is a diffraction grating, W is a window, L is a lens, M1, M2 are mirrors, EM1, EM2 are electromagnets, PM is a permanent magnet, and PC is a proportional counter.can be independently tested. This is because there are two 2 3 P fine structure intervals and because the same methods used for helium can be used to calculate fine structure in moderate Z heliumlike ions where the relative magnitudes of these higher-order terms are larger. Hence fine structure measurements in moderate Z heliumlike ions [10-15], even though less precise than measurements in helium, can provide sensitive tests of the theory. Here we report a measurement of the three hyperfine components of the 19 F 71 1s2p 3 P 2 -3 P 1 fine structure interval, obtained by directly inducing the M1 transitions using a CO 2 laser, in a fast, foil stripped fluorine ion beam. A novel Doppler shift cancellation technique was used which measures products of the transition energies in pairs. Our result, with a precision of 61 ppm ...

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High Precision Calculation of Fine Structure Splittings in Helium and He-Like Ions

Cited by 84 publications

References 30 publications

Bethe logarithms for Ps, H, and heliumlike atoms

Bethe logarithms for Ps, H, and heliumlike atoms

Lithium Fine Structure in the1s22p2P<

Precision Measurement of the1s2pP32
Myers
¹
,
Margolis
²
,
Thompson
³

et al. 1999
Phys. Rev. Lett.
44
2
11
0
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High Precision Calculation of Fine Structure Splittings in Helium and He-Like Ions

Cited by 84 publications

References 30 publications

Bethe logarithms for Ps, H, and heliumlike atoms

Bethe logarithms for Ps, H, and heliumlike atoms

Lithium Fine Structure in the1s22p2P<

Precision Measurement of the1s2pP32Myers1, Margolis2, Thompson3 et al. 1999Phys. Rev. Lett.442110View full textAdd to dashboardCite

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Bethe logarithms for Ps, H, and heliumlike atoms

Bethe logarithms for Ps, H, and heliumlike atoms

Precision Measurement of the1s2pP32
Myers
¹
,
Margolis
²
,
Thompson
³

et al. 1999
Phys. Rev. Lett.
44
2
11
0
View full text Add to dashboard Cite