Gauge-Invariant QED Perturbation Theory Approach to Calculating Nuclear Electric Quadrupole Moments, Hyperfine Structure Constants for Heavy Atoms and Ions

Study of spectra for lanthanides atoms with relativistic many- body perturbation theory: Rydberg resonances

“…In the relativistic case, the GellMann and Low formula expressed an energy shift ΔE through the QED scattering matrix including the interaction of the photon vacuum field and of the laser field. The wave function zeroth basis is found from the Dirac equation with a potential, which includes ab initio optimized model potentials (IvanovIvanova type [6]) or DF potentials, the electric potential of a nucleus -we usually use the Gaussian form of the charge distribution in a nucleus [4]. The correlation corrections of the perturbation theory of second and higher orders are taken into account with the polarization and screening potentials (see Refs.…”

“…In this approach, the whole calculation of the energies and decay probabilities of a non-degenerate excited state is reduced to the calculation and diagonalization of the complex matrix M. In published work by different authors, the Re{ΔE} calculation procedure has been generalized for the case of nearly degenerate states, whose levels form a more or less compact group. One of these variants has been introduced previously [4,13,14]: For a system with a dense energy spectrum, a group of nearly degenerate states is extracted and their matrix M is calculated and diagonalized. If the states are well separated in energy, the matrix M reduces to one term, equal to ΔE.…”

“…However, the necessary experimental quantities are not often available. The first two order corrections to Re{M (2) } have been analyzed [4] using Feynman diagrams. The contributions of the first-order diagrams have been completely calculated.…”

“…This is investigated in detail by Grant, Armstrong, Aymar and Luc-Koenig, Glushkov-Ivanov et al, see Refs. [1][2][3][4][9][10][11][12][13][14][15]. Grant has investigated the gauge connection with the limiting non-relativistic form of the transition operator and has formulated the conditions for approximate functions of the states, in which the amplitudes of the photo processes are gauge invariant.…”

“…In essence, special attention should be given to two very general and important computer systems for relativistic and Quantum Electro-Dynamics (QED) calculations of atomic and molecular properties developed at Oxford, UK, known as GRASP ("GRASP", "Dirac"; "BERTHA") (see Refs. [1][2][3][4] and references therein). Relativistic many-body perturbation theory is effectively applied to the computation of spectra of low-lying states for lanthanides atoms [5][6][7][8][9][10].…”