Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

QED corrections

For a many-electron atom, the total QED shift of order a Ry consists of two parts—an electron-nucleus part El,i (the Kabir-Salpeter term [32]), and an electron-electron term El,2 originally obtained by Araki [33] and Sucher [34]. The El,2 term is relatively small and stright-forward to calculate. The principal computational challenges come from the El,i term given by (in atomic units) [Pg.44]

The foregoing equations are virtually identical to the corresponding one-electron (hydrogenic) case, except that there the 5-function matrix elements can be replaced by their hydrogenic value [Pg.44]

FIGURE 4.2 Feynman diagram for the electron self energy. [Pg.44]

FIGURE4.3 Differential contributions to the Bethe logarithm for the ground state of hydrogen. Each point represents the contribution from one pseudostate. [Pg.45]

However, this is slowly convergent, and expensive in computer time since a matrix diagonalization must be performed at each integration point. Despite this, results of useful accuracy for the lowest-lying S- and P-states have been obtained by this method in Refs. [36-38]. [Pg.45]


Coulomb-Breit potential gives the following set of operators, where the QED correction to the electronic spin has been introduced by means of the ge pa factor. [Pg.211]

If not otherwise stated the four-component Dirac method was used. The Hartree-Fock (HF) calculations are numerical and contain Breit and QED corrections (self-energy and vacuum polarization). For Au and Rg, the Fock-space coupled cluster (CC) results are taken from Kaldor and co-workers [4, 90], which contains the Breit term in the low-frequency limit. For Cu and Ag, Douglas-Kroll scalar relativistic CCSD(T) results are used from Sadlej and co-workers [6]. Experimental values are from Refs. [91, 92]. [Pg.190]

Cu, Ag and Au) and coupled cluster data (Rg) are from Refs. [4, 91]. Forthe P3 2/ Pi/2Dirac-Hartree-Fockcalculations including Breit and QED corrections. [Pg.192]

Indelicato, P. and Lindroth, E. (1992) Relativistic effects, correlation, and QED corrections on Ka transitions in medium to very heavy atoms. Physical Review A, 46, 2426-2436. [Pg.225]

Mohr, P.J., Plunien, G. and Soff, G. (1998) QED corrections in heavy atoms. Physics Reports-Review Section of Physics Letters, 293, 227-369. [Pg.225]

The definitions of the first and second order magnetic perturbation operators are given helow. In the nonrelativistic formalism these operators are two-component operators, in the Kutzelnigg formalism all operators are to he multiplied hy the four-component matrix. All operators are given in the atomic unit system and we do not apply QED corrections so that the free electron g-factor is precisely equal to 2. [Pg.380]

TABLE 2. QED corrections (in cm ) to the energy of Li-like ions in linlj- states. [Pg.295]

Here D(rjtj,r2t2) is the photon propagator jcv, jpv, jfw are the four-dimensional components of the operator of current for the considered particles core, proton, muon x = (vc, Vp, r, t) includes the space coordinates of the three particles plus time (equal for all particles) and y is the adiabatic parameter. For the photon propagator, it is possible to use the exact electrodynamical expression. Below we are limited by the lowest order of QED PT, i.e., the next QED corrections to Im E will not be considered. After some algebraic manipulation we arrive at the following expression for the imaginary part of the excited state energy as a sum of contributions ... [Pg.304]

Relativity is expected to play an important role in several types of radiative processes in atoms. Its influence on the atomic levels fine structure has been most thoroughly investigated as its signature is easily evidenced in atomic x-ray spectra, [1], [2], [3], It manifests itself also in some delicate aspects of the chemical reactivity of the elements, [4], These effects arise from both the standard Dirac-like properties of electrons and from more sophisticated QED corrections. One of the major objective of the present paper is to show that the overall picture has dramatically changed recently, as a consequence of the considerable advances made in the design of ultra intense laser sources operated at intensities well beyond the so-called atomic unit of intensity la = 3.5 xlO16 W/cm2, [5]. [Pg.107]

The aim of this section is to extract from the measurements the values of the Rydberg constant and Lamb shifts. This analysis is detailed in the references [50,61], More details on the theory of atomic hydrogen can be found in several review articles [62,63,34], It is convenient to express the energy levels in hydrogen as the sum of three terms the first is the well known hyperfine interaction. The second, given by the Dirac equation for a particle with the reduced mass and by the first relativistic correction due to the recoil of the proton, is known exactly, apart from the uncertainties in the physical constants involved (mainly the Rydberg constant R0c). The third term is the Lamb shift, which contains all the other corrections, i.e. the QED corrections, the other relativistic corrections due to the proton recoil and the effect of the proton charge distribution. Consequently, to extract i oo from the accurate measurements one needs to know the Lamb shifts. For this analysis, the theoretical values of the Lamb shifts are sufficiently precise, except for those of the 15 and 2S levels. [Pg.36]

These experimental advances are inspiring renewed theoretical efforts to calculate higher order QED corrections, as discussed elsewhere in these Proceedings. [Pg.40]

The spectrum of hydrogen is composed of a major structure, determined by the Rydberg constant, QED corrections like the Lamb shift and finally nuclear shape... [Pg.54]


See other pages where QED corrections is mentioned: [Pg.195]    [Pg.285]    [Pg.9]    [Pg.370]   
See also in sourсe #XX -- [ Pg.44 ]

See also in sourсe #XX -- [ Pg.3 , Pg.16 , Pg.17 , Pg.18 , Pg.19 , Pg.20 , Pg.21 ]




SEARCH



QED Corrections in Heavy Atoms

QED corrections in many-electron atoms

QED corrections in many-electron system

QED corrections to one-electron energy levels

© 2024 chempedia.info