Dual Kinetic Balance Approach to Basis-Set Expansions for the Dirac Equation

Shabaev, V. M.; Tupitsyn, I. I.; Yerokhin, V. A.; Plunien, G.; Soff, G.

doi:10.1103/physrevlett.93.130405

Cited by 329 publications

(355 citation statements)

References 41 publications

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“…Let us now discuss how do we produce a balanced discrete representation of the one-electron continuum spectrum. In our approach, the one-electron orbitals are taken from the finite basis set representation of the Dirac Hamiltonian with the frozen-core Dirac-Fock potential, obtained by the DKB B-spline method [20]. The B-splines are defined on a radial grid, whose form outside of the nucleus is exponential,…”

Section: Configuration-interaction Methods For Core Excited Statesmentioning

confidence: 99%

“…In our implementation of the CI method, we used the one-particle Dirac Hamiltonian with the frozen-core Dirac-Fock potential. The eigenvalues and eigenfunctions of the Dirac Hamiltonian are constructed by the dual-kinetic-balance (DKB) method [20] from a finite set of B-spline basis functions. This approach yields a discrete representation of the continuum part of the Dirac spectrum, in which the density of the continuum states increases as the number of basis functions is enlarged.…”

Section: Configuration-interaction Methods For Core Excited Statesmentioning

confidence: 99%

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Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
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We present systematic calculations of energy levels of the 1s 2 2l and 1s2l2l ′ states of ions along the lithium isoelectronic sequence from carbon till chlorine. The calculations are performed by using the relativisticconfiguration-interaction method adapted to the treatment of autoionizing core-excited states. The relativistic energies are supplemented with the QED energy shifts calculated within the model QED operator approach. A systematic estimation of the theoretical uncertainties is performed for every electronic state and every nuclear charge. The results are in agreement with existing high-precision theoretical and experimental data for the ground and first excited states. For the core-excited states, our theory is much more accurate than the presently available measurements.

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Section: Configuration-interaction Methods For Core Excited Statesmentioning

confidence: 99%

Section: Configuration-interaction Methods For Core Excited Statesmentioning

confidence: 99%

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
Self Cite
32
10
33
3
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“…The numerical evaluation was performed by solving the Dirac equation with help of the RADIAL package [11] and, independently, by using the B-spline finite basis set method [12]. For calculations in the low-Z region, the RADIAL package was upgraded into the quadruple arithmetics (about 32 digits).…”

Section: Ns Correction To Dirac Energymentioning

confidence: 99%

Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

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The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p 1/2 , and 2p 3/2 states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Zα. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Zα. Extrapolation of the all-order numerical results obtained towards Z = 1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.PACS numbers: 31.30.jf, 12.20.Ds, 31.15.A- IntroductionThe distribution of charge of the nucleus influences the Dirac energies of atomic systems as well as the quantum electrodynamical corrections to the energy levels. This effect, termed as the nuclear size (NS) correction, is important for comparison of theoretical predictions with experimental data for the whole range of the nuclear charges Z, from hydrogen (Z = 1) up to uranium (Z = 92). The NS corrections to the one-loop self energy and vacuum polarization have been previously investigated both within the approach based on the expansion in the nuclear binding strength parameter Zα [1][2][3][4][5][6] (where α is the fine structure constant) and within the numerical approach that accounts the parameter Zα to all orders [7,8]. In the high-Z region, the numerical allorder approach provides accurate predictions for the NS effect on the radiative corrections. For lower Z, however, the NS effect diminishes and becomes increasingly more difficult to identify in a numerical calculation. On the contrary, the Zα-expansion approach provides accurate predictions for the low-Z ions and only the qualitative estimates in the high-Z region. A quantitative cross-check of the two complementary approaches is not simple and has not been accomplished up to now.The NS corrections became of particular interest recently, after the results of the muonic hydrogen Lambshift experiment were announced [9]. It turned out that the value for the proton charge radius r p deduced from the muonic hydrogen differs by five standard deviations from the spectroscopic value of r p derived from the hydrogen atom. This unexplained disagreement stimulates the scientific community to double-check all contributions originating from the nuclear charge distribution, both for the muonic and normal atoms.The aim of the present investigation is to perform an accurate numerical all-order calculation of the NS correction to the one-loop self energy and vacuum polarization and to make a detailed comparison with the Zα-expansion results available.The relativistic units (m = = c = 1) and the charge units α = e 2 /(4π) are used in this paper. I. NS CORRECTION TO DIRAC ENERGYThe leading-order NS correction to the energy levels of a hydrogen-like atom is defined as the difference of the corresponding eigenvalues of the Dirac equation with the point-Coulomb and the extended-nucleus potentials. The two most commonly used models of the nuclear charge distribution are the uniformly charged sphere ("sp...

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“…Numerical evaluation of expressions (1)- (15) was performed by employing the dual-kinetic-balance finite basis set method [26] with basis functions construced from B-splines. The calculation of the zeroth-order contribution, with V (r) constructed as indicated above, yields E PNC =-1.002, in units i×10 −11 Q W /(−N ) a.u.…”

mentioning

confidence: 99%

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

et al. 2005

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The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in 133 Cs is evaluated to all orders in αZ using a local version of the Dirac-Hartree-Fock potential. The calculations are peformed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%, which differs from previous evaluations of this effect. The weak charge of 133 Cs, derived using two most accurate values of the vector transition polarizability β, is QW = −72.57(46) for β = 26.957(51)a 3 B and QW = −73.09(54) for β = 27.15(11)a 3 B . The first value deviates by 1.1σ from the prediction of the Standard Model, while the second one is in perfect agreement with it. PACS numbers: 11.30.Er,31.30.Jv,32.80.Ys Investigations of parity noncoservation (PNC) effects in atomic systems play a prominent role in tests of the Standard Model (SM) and impose constraints on physics beyond it [1,2]. The 6s-7s PNC amplitude in 133 Cs [3] remains one of the most attractive subject for such investigations. The measurement of this amplitude to a 0.3% accuracy [4,5] has stimulated a reanalysis of related theoretical contributions. First, it was found [6,7,8,9] that the role of the Breit interaction had been underestimated in previous evaluations of this effect [10,11]. Then, it was pointed out [12] that the QED corrections may be comparable with the Breit corrections. The numerical evaluation of the vacuum-polarization (VP) correction [13] led to a 0.4% increase of the 6s-7s PNC amplitude in 133 Cs, which resulted in a 2.2σ deviation of the weak charge of 133 Cs from the SM prediction. This has triggered a great interest to calculations of the one-loop QED corrections to the PNC amplitude.While the VP contribution can easily be evaluated to a high accuracy within the Uehling approximation, the calculation of the self-energy (SE) contribution is a much more demanding problem (here and below we imply that the SE term embraces all one-loop vertex diagrams as well). To zeroth order in αZ, it was derived in Refs. [14,15]. This correction, whose relative value equals to −α/(2π), is commonly included in the definition of the nuclear weak charge. The αZ-dependent part of the SE correction to the PNC matrix element between s and p states was evaluated in Refs. [16,17]. These calculations, which are exact to first order in αZ and partially include higher-order binding effects, yield the correction of -0.9(1)% [16, 18] and -0.85% [17]. This restored the agreement with SM.Despite of the close agreement of the results obtained in Refs. [17,18], the status of the QED correction to PNC in 133 Cs cannot be considered as resolved until a complete αZ-dependence calculation of the SE correction to the 6s-7s transition amplitude is accomplished. The reasons for that are the following. First, in case of cesium (Z = 55) the parameter αZ ≈ 0.4 is not small and, therefore, the higher-order corrections can be significant. Second, because the calculations [16,17,18] are performed for the...

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Dual Kinetic Balance Approach to Basis-Set Expansions for the Dirac Equation

Cited by 329 publications

References 41 publications

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
Self Cite
32
10
33
3
View full text Add to dashboard Cite

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
Self Cite
32
10
33
3
View full text Add to dashboard Cite

Nuclear-size correction to the Lamb shift of one-electron atoms

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

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Dual Kinetic Balance Approach to Basis-Set Expansions for the Dirac Equation

Cited by 329 publications

References 41 publications

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′Yerokhin1, Surzhykov2, Müller3 2017Phys. Rev. ASelf Cite3210333View full textAdd to dashboardCite

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′Yerokhin1, Surzhykov2, Müller3 2017Phys. Rev. ASelf Cite3210333View full textAdd to dashboardCite

Nuclear-size correction to the Lamb shift of one-electron atoms

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

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Product

Resources

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Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
Self Cite
32
10
33
3
View full text Add to dashboard Cite

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
Self Cite
32
10
33
3
View full text Add to dashboard Cite