Radiative corrections to the hyperfine-structure splitting of hydrogenlike systems

Sunnergren, Per; Persson, Hans; Salomonson, Sten; Schneider, Simon; Lindgren, Ingvar; Soff, G.

doi:10.1103/physreva.58.1055

Cited by 100 publications

(77 citation statements)

References 52 publications

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“…It was calculated in several papers and the results are consistent [11,[16][17][18][19]. In [19] it was shown that ∆E QED is insensitive to details of the magnetization distribution. They give for ∆E QED the value ∆E QED = −0.0298(3) eV for 209 Bi 82+ and ∆E QED = −0.00726(7) eV for 207 Pb 81+ .…”

Section: Effects Of the Core Polarizationmentioning

confidence: 69%

“…The leading QED corrections originate from the one-loop self-energy and vacuum-polarization effects. The one-loop QED effects for hfs have been calculated by different groups and the results are consistent [11,[16][17][18][19].…”

Section: Introductionmentioning

confidence: 80%

“…There are two principal corrections to the Fermi-Breit formulae that is necessary to take into account: the magnetic moment distribution within the nucleus [9][10][11][12][13][14][15] and radiative corrections [11,[16][17][18][19]. Both of these corrections are of comparable magnitude.…”

Section: Introductionmentioning

confidence: 99%

“…High experimental precision attained in the laser spectroscopic measurement of the ground-state hfs in hydrogen-like 209 Bi 82+ [1] stimulates considerable theoretical activity in this field (see, e.g., [11][12][13][14][15][16][17][18][19] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Nuclear magnetization distribution and hyperfine splitting in Bi82+ ion

Sen'kov

Дмитриев

2002

Nuclear Physics A

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Hyperfine splitting in Bi 82+ and Pb 81+ ions was calculated using continuum RPA approach with effective residual forces. To fix the parameters of the theory the nuclear magnetic dipole moments of two one-particle and two one-hole nuclei around 208 Pb were calculated using the same approach. The contribution from velocity dependent two-body spin-orbit residual interaction was calculated explicitly. Additionally, the octupole moment of 209 Bi and the hfs in muonic bismuth atom were calculated as well in the same approach. All the calculated observables, except the electronic hfs in 209 Bi, are in good agreement with the data. We argue for more accurate measurement of the octupole moment and the muonic hfs for 209 Bi.

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Section: Effects Of the Core Polarizationmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nuclear magnetization distribution and hyperfine splitting in Bi82+ ion

Sen'kov

Дмитриев

2002

Nuclear Physics A

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“…Similar situation persists in calculations of self-energy corrections to higher orders of perturbation theory. In such calculations, the convergence of the partial-wave expansion also worsens with decrease of Z and increase of n. In particular, a slow convergence of this expansion turned out to be the factor limiting the accuracy in evaluations of the self-energy correction to the 1s and 2s hyperfine splitting in low-Z ions [28,29,30]. This convergence also posed serious problems in calculations of the self-energy correction to the boundelectron g factor in light H-like ions [31,32,33,34].…”

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confidence: 99%

One-loop self-energy correction in a strong binding field

2005

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Numerical electronic structure calculations for atoms. II. Generalized variable transformation and relativistic calculations

Andrae

Hinze

2000

Int. J. Quantum Chem.

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ABSTRACT:The pairs of radial functions P i and Q i , which are part of the four-component single-particle spinors in the relativistic description of the electronic structure of bound states of atoms, are usually determined as solutions of eigenvalue problems. The latter constitute two-point boundary value problems which involve coupled pairs of first-order ordinary radial differential equations. To introduce a suitable notation, the theory involved in relativistic electronic structure calculations for atoms is briefly reviewed, including a general treatment of arbitrary transformations for the radial variable. Such variable transformations must be specified then, either explicitly (by a transformation function) or implicitly (by the solution method itself), for any actual calculation, though initially the variable transformation is almost completely independent of the numerical method to be applied. We consider suitable transformation functions out of which an actual choice can be made within wide limits. In our approach, the resulting transformed radial differential equations are discretized then with finite-difference methods. Since the accuracy and efficiency of these methods is increased when a constant step size h between contiguous points (in the transformed variable) is used, it is only here where the careful choice of the variable transformation is important. The resulting system of linear equations is solved for the radial functions with standard linear algebra methods rather than "shooting" methods. The present work extends the general study of variable transformations, given recently for nonrelativistic electronic structure calculations in Part I, to the relativistic case. Important results following from the present work are (i) a discretization scheme for first-order ordinary differential equations similar to the ANDRAE, REIHER, AND HINZE well-known standard Numerov scheme used within the nonrelativistic framework, (ii) a consistent numerical algorithm with an overall truncation error of order h 4 , (iii) a method for handling effective potentials behaving singularly like r −1 at the origin (as encountered, e.g., when the atomic nucleus is represented by a pointlike charge density distribution), and, in connection with this last point, (iv) the avoidance of nonanalytic short-range behavior of the solutions to be obtained from the differential equations.

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Radiative corrections to the hyperfine-structure splitting of hydrogenlike systems

Cited by 100 publications

References 52 publications

Nuclear magnetization distribution and hyperfine splitting in Bi82+ ion

Nuclear magnetization distribution and hyperfine splitting in Bi82+ ion

One-loop self-energy correction in a strong binding field

Numerical electronic structure calculations for atoms. II. Generalized variable transformation and relativistic calculations

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