Breit term

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]. 

The Breit term can be derived from QED, but can also be obtained in a simpler... 

The terms etc. represent the one-body mean-field potential, which approximates the two-electron interaction in the Hamiltonian, as is the practice in SCF schemes. In the DFB equations this interaction includes the Breit term (3) in addition to the electron... 

While including the Breit term has a rather small effect on the excitation energies of Pr " ", it improves the fine-structure splittings (table 7). This is a general phenomenon, and may be traced to including the spin-other-spin interaction in the two-electron Breit term [62]. 

The demonstration here of the efficacy of the integral formulation and the propagator techniques may be used in further attempts at approximating the more awkward terms in the electron-electron interactions, such as exchange and Breit terms(19), albeit giving rise to rather involved integrals. 

Once the electrons mass is known to a better accuracy it may be possible to derive a new value for the fine structure constant a from g factor measurements. The leading bound state correction to the g factor is the Breit term (Eq. 2). From that we deduce... 

In the case of normal hydrogen [14] the difference is mainly determined by a relativistic contribution of order (Za)2Ep (so-called Breit term [15]). In muonic atoms the leading effect is due to vacuum polarization and it is of order aEp. 

The computations of 2p-core ionization energies were performed using a pattern similar to that used for Is- and 2s-core ionization energies [9]. Here again we have used Bruneau s multiconfiguration Dirac-Fock (MCDF) ab initio program [26-28], which is based on a numerical resolution of the Dirac equation corrected for Breit terms, vacuum polarization, and radiative (qed) contributions, and nuclear size and motion (nuc) effects. 

The fully self-consistent handling is compared with a perturbative evaluation of only the beyond-Breit terms and a perturbative treatment of the complete Ej. Even for the heaviest atoms the perturbative evaluation of the retardation corrections to the Breit term seems to be sufficient. On the other hand, use of first-order perturbation theory for the complete Ej leads to errors of the order of 1 eV for heavy atoms. An accurate description of inner shell transitions in these systems requires the inclusion of second-order Breit corrections. 

A less demanding, but still useful, approximation is the configuration average model, which is an adaptation of the closed shell DHF scheme. The starting point of this scheme is the closed shell expression (95) which, after dropping the Breit terms, takes the form... 

The terms etc. in (10) represent the one-body mean-field potential, which approximates the two-electron interaction in the Hamiltonian, as is the practice in SCF schemes. In the DFB equations this interaction includes the Breit term (4) in addition to the electron repulsion l/rjj. The radial functions Pn ( ) and Qn/c( ) may be obtained by mmierical integration [20,21] or by expansion in a basis (for more details see recent reviews [22,23]). Since the Dirac Hamiltonian is not bound from below, failure to observe correct boundary conditions leads to variational collapse [24,25], where admixture of negative-energy solutions may yield energies much below experimental. To avoid this failure, the basis sets used for expanding the large and small components must maintain kinetic balance [26,27]. In the nonrelativistic limit (c oo), the small component is related to the large component by [24]... 

Eka-actinium (E121) —- when is the Breit term important ... 

The first-order correction is known as the Breit term, and ai and velocity operators. Physically, the first term in the Breit correction corresponds to magnetic interaction between the two electrons, while the second term describes a retardation effect, since the interaction between distant particles is delayed relative to interactions between close particles, owing to the finite value of c (in atomic units, c -137). 

Although in the Dirac-Coulomb Hamiltonian the one-particle operator is correct to all orders in a, the two-particle interaction is only correct to a°. The Dirac-Coulomb Hamiltonian is not invariant under Lorentz transformations, however it can be considered as the leading term of a yet unknown relativistic many-electron Hamiltonian which fulfills this requirement. An operator which also takes into account the leading relativistic corrections for the two-electron terms is the Coulomb-Breit term (Breit 1929,1930,1932, 1938),... 

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