Convergence of the Breit interaction in self-consistent and configuration-interaction approaches

Abstract

Much discussion in relativistic atomic physics and quantum optics has related to the interaction of gauge and perturbation of the Hamiltonian or Dirac operator. It has been commented that Lorentz and gauge independence requires different forms of the perturbation operator in shifting from one gauge to another. Equally, it has been commented that gauge convergence is not possible without different operator forms in different bases and without the operator being embedded within the self-consistent kernel. We explore the logic and self-consistency of these arguments, applied to the well-known Breit operator in an area of continuing discussion. We find that convergence is now possible to a remarkable degree including a Breit interaction operator in a form consistent with the gauge for length and velocity relativistic forms of the multipole operator, implemented at the configuration-interaction level. Excellent convergence is obtained for Breit interaction energies, interaction mixing coefficients, interaction transition probabilities and eigenenergies and transition probabilities in complex open shells (transition metal K α transitions and shake satellites), and forbidden transitions.

Characterization of the copperKβx-ray emission profile: anab initiomulti-configuration Dirac–Hartree–Fock approach with Bayesian constraints

“…The degeneracy of the 4s satellite spectrum compared with the diagram line spectrum decreases the number of degrees of freedom and increases the strongly correlated parameters without any improved fit. Therefore, when including 4s satellite in the fitting, fits (6)(7)(8) is only slightly larger than that of fits (3)(4)(5).…”

“…Although using a single CSF gives a good approximation to the exact wavefunction, a linear combination of orthonormal CSFs offers even closer approximation. The mixing coefficients, c r , can be obtained by diagonalizing of the Dirac-Coulomb Hamiltonian In the MCDHF implementation of GRASP2K, the Breit interaction [7], QED corrections for self-energy and vacuum polarization, and finite nuclear mass effects are included perturbatively [8]. Each CSF in equation 1 The orthonormality condition from equation 4gives:…”

Breit and QED contributions in atomic structure calculations of tungsten ions

“…This effect is about 1 eV (0.1-0.3%) in studied cases. However, it has been found that "variational effect" is significantly reduced when active space is expanding [50,51]. The frequency-dependent Breit term is about 2% of frequency-independent one (having opposite sign).…”

Vignetted photon fields, recharacterisation of V Kα, and reducing X‐ray uncertainties by a factor of two

“…X‐ray emission from electron bombardment undergoes many processes with contributions in the spectra from many energy eigenstates (from relativistic multi‐configuration DHF computations) ranging from the tens to the tens‐of‐thousands depending on the transition. Whilst this theory is undergoing great advances at this time (e.g., GRASP2K), [ 5,19–22 ] it is known that convergence is difficult as is comparing a partially resolved spectrum with thousands of eigenvalues and amplitudes. The most detailed current characterisations of experimental spectra are given in the International Tables for Crystallography, Vol.…”