Measurement of the Lamb shifts in singlet levels of atomic helium

Lichten, William; Shiner, David; Zhou, Zhi-Xiang

doi:10.1103/physreva.43.1663

Cited by 67 publications

(46 citation statements)

References 15 publications

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“…We use the method of the two-time Green's function, which handles quasidegenerate atomic states. From these expression one can evaluate energy corrections to, e.g., 1s2p 3 P1 and 1s2p 1 P1 in helium and twoelectron ions, to all orders in Zα.In the last ten years, experiments in the spectroscopy of helium [1][2][3][4][5] have become two orders of magnitude more precise than the best theoretical energy level calculations available (see, e.g., Refs. [6,7] and references therein).…”

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confidence: 99%

“…All the subsequent derivations of H (2) nn ′ will thus be done with (1) appears only in the second-order matrices K (2) and P (2) in Eq. (2).…”

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confidence: 99%

“…All the subsequent derivations of H (2) nn ′ will thus be done with (1) appears only in the second-order matrices K (2) and P (2) in Eq. (2). As usual, we must calculate a reducible and an irreducible contribution; as can be seen in subsequent calculations, it turns out that the correct extension of these notions to quasidegenerate states is the following: in the first diagram of Eq.…”

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confidence: 99%

“…Let us introduce some notations in order to express this hamiltonian. The second-order contribution H (2) to this hamiltonian H = H (0) + H (1) + H (2) + . .…”

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confidence: 99%

“…(2) between states of different energies E (0) n and E (0) n ′ , and put them in a form that readily displays the limiting case of identical energies; we checked by a direct calculation of the diagonal matrix elements that they can be obtained from non-diagonal elements H (2) nn ′ by taking the formal limit E (0)…”

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Contribution of the screened self-energy to the Lamb shift of quasidegenerate states

2001

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Expressions for the effective Quantum Electrodynamics (QED) Hamiltonian due to self-energy screening (self-energy correction to the electron-electron interaction) are presented. We use the method of the two-time Green's function, which handles quasidegenerate atomic states. From these expression one can evaluate energy corrections to, e.g., 1s2p 3 P1 and 1s2p 1 P1 in helium and twoelectron ions, to all orders in Zα.In the last ten years, experiments in the spectroscopy of helium [1][2][3][4][5] have become two orders of magnitude more precise than the best theoretical energy level calculations available (see, e.g., Refs. [6,7] and references therein). Several experiments are now focusing on Helium and heliumlike ions 1s2p 3 P J fine structure [8][9][10][11][12], with the aim of providing a new determination of the fine structure constant and of checking higher-order effects in the calculations. In this case the theory is again a limiting factor. In this context a direct determination of all α 2 contributions to all order in Zα is necessary to improve reliability and accuracy of theoretical calculations (α being the fine structure constant, and Z the charge of the nucleus).A difficulty in the study of the (1s2p 1/2 ) 1 and (1s2p 3/2 ) 1 levels is that they are quasidegenerate for low and middle Z ions [13]; this precludes the use of the Gell-Man-Low and Sucher method [14,15] to evaluate QED energy shifts of atomic levels. In fact, this method has two important drawbacks: it does not handle quasidegenerate energy levels, and it leads to a difficult renormalization procedure when applied to degenerate states. (The latter problem has only been tackled up to second-order in α [16,17].)We use the method of the two-time Green's function [18][19][20], rigorously derived from QED (for the most detailed description of this method, see [21]). To the best of our knowledge, only the method recently proposed by Lindgren [22], closely modeled to multireference-state Many-body perturbation techniques, is designed to work for quasidegenerate states.We evaluate the contribution of the screened self-energy diagramsto quasidegenerate energy levels in heliumlike ions. Our results can be easily extended to ions with more than two electrons along lines similar to those found in [23]. First approximate evaluations of the contribution of these diagrams for isolated states in two-and three-electron ions were performed in Refs. [24][25][26][27]. Accurate calculations from the first principles of QED were accomplished in Refs. [28][29][30] for the ground state of heliumlike ions and in Refs. [31,32] for the 2s and 2p 1/2 states of lithiumlike ions. The other two α 2 corrections to the electron-electron interaction have also been calculated for isolated states in twoand three-electron ions: the vacuum-polarization screening [13,29,30,33,34], and the two-photon exchange diagrams [35][36][37][38]. In [13], the vacuum polarization screening for quasidegenerate states of heliumlike ions was evaluated as well. Some results for the direct contrib...

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confidence: 99%

“…All the subsequent derivations of H (2) nn ′ will thus be done with (1) appears only in the second-order matrices K (2) and P (2) in Eq. (2).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Let us introduce some notations in order to express this hamiltonian. The second-order contribution H (2) to this hamiltonian H = H (0) + H (1) + H (2) + . .…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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