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

Abstract

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...

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

“…[158]. The second-order two-electron diagrams for quasidegenerate states of heliumlike ions are studied in [44,75]. In Ref.…”

“…For the case of quasidegenerate states, the corresponding formulas are derived by the TTGF method in Refs. [44,75].…”

QED calculation of then=1andn=2energy levels in He-like ions

“…Formal expressions for this correction in case of quasi-degenerate states were obtained previously in Ref. [46] by the TTGF method. Here we present only the final expressions for this correction.…”

QED theory of the spectral line profile and its applications to atoms and ions

“…Concerning the energy corrections, it remains to be mentioned, that the screening corrections (see Fig. 7) to two-and three-electron configurations of HCI were calculated in [189][190][191][192][193][194][195][196][197][198].…”