Advanced Relativistic Energy Approach
in Spectroscopy of Autoionization States
of Multielectron Atomic Systems
Alexander V. Glushkov
Abstract We present the generalized energy approach to relativistic calculation of
the autoionization decay (resonances) energies and probabilities (widths) in the neutral multielectron atomic systems and multicharged ions. The approach is based on
the Gell-Mann and Low S-matrix formalism and the relativistic many-body perturbation theory (PT) with using the optimized one-quasiparticle representation and an
accurate account of the relativistic and correlation. In relativistic case the Gell-Mann
and Low formula expresses an energy shift E through the electrodynamical scattering matrix including the interaction with as the laser field as the photon vacuum
field. The last case is corresponding to definition of the radiative and autoionization
decays probabilities for atomic systems. As illustration, the results of relativistic calculation of the autoionization states energies and widths are presented for a number
of atoms (helium, barium) and discussed from viewpoint of the correct accounting
for the relativistic and exchange-correlation effects.
Keywords Autoionization states · Multielectron atomic systems · Advanced
relativistic energy approach · Resonances energies and widths
1 Introduction
Accurate radiative and autoionization decay widths and probabilities for atomic systems are needed for example in astrophysics and quantum physics, atomic and molecular spectroscopy, laboratory and thermonuclear plasma diagnostics, fusion research,
laser physics, quantum electronics etc. [1–113]. Traditionally, advanced modeling
is important and of current interest in the theory of atomic spectra and associated
spectral lines. Spectral lines are usually characterized by their wavelength and width.
Typically, autoionization and radiative decay probabilities and widths are known less
accurately than wavelengths. Moreover, for many spectral lines of heavy atoms and
especially multicharged ions the radiative and autoionization decay probabilities are
not reliably known at all.
A. V. Glushkov (B)
Odessa State Environmental University, L’vovskaya str., bld. 15, Odessa 65016, Ukraine
© Springer Nature Switzerland AG 2020
L. Mammino et al. (eds.), Advances in Quantum Systems in Chemistry,
Physics, and Biology, Progress in Theoretical Chemistry and Physics 32,
https://doi.org/10.1007/978-3-030-34941-7_1
3
in Spectroscopy of Autoionization States
of Multielectron Atomic Systems
Alexander V. Glushkov
Abstract We present the generalized energy approach to relativistic calculation of
the autoionization decay (resonances) energies and probabilities (widths) in the neutral multielectron atomic systems and multicharged ions. The approach is based on
the Gell-Mann and Low S-matrix formalism and the relativistic many-body perturbation theory (PT) with using the optimized one-quasiparticle representation and an
accurate account of the relativistic and correlation. In relativistic case the Gell-Mann
and Low formula expresses an energy shift E through the electrodynamical scattering matrix including the interaction with as the laser field as the photon vacuum
field. The last case is corresponding to definition of the radiative and autoionization
decays probabilities for atomic systems. As illustration, the results of relativistic calculation of the autoionization states energies and widths are presented for a number
of atoms (helium, barium) and discussed from viewpoint of the correct accounting
for the relativistic and exchange-correlation effects.
Keywords Autoionization states · Multielectron atomic systems · Advanced
relativistic energy approach · Resonances energies and widths
1 Introduction
Accurate radiative and autoionization decay widths and probabilities for atomic systems are needed for example in astrophysics and quantum physics, atomic and molecular spectroscopy, laboratory and thermonuclear plasma diagnostics, fusion research,
laser physics, quantum electronics etc. [1–113]. Traditionally, advanced modeling
is important and of current interest in the theory of atomic spectra and associated
spectral lines. Spectral lines are usually characterized by their wavelength and width.
Typically, autoionization and radiative decay probabilities and widths are known less
accurately than wavelengths. Moreover, for many spectral lines of heavy atoms and
especially multicharged ions the radiative and autoionization decay probabilities are
not reliably known at all.
A. V. Glushkov (B)
Odessa State Environmental University, L’vovskaya str., bld. 15, Odessa 65016, Ukraine
© Springer Nature Switzerland AG 2020
L. Mammino et al. (eds.), Advances in Quantum Systems in Chemistry,
Physics, and Biology, Progress in Theoretical Chemistry and Physics 32,
https://doi.org/10.1007/978-3-030-34941-7_1
3