22
A. V. Glushkov
the studied states. Let us also note that according to our data the widths of the
resonances indicated in the table vary extremely irregularly and are in the range of
1.64 × 10
−6
− 1.92 × 10
−5 Ry.
4 Conclusions
To conclude, we presented the generalized energy approach to relativistic calculation
of the autoionization decay (resonances) energies and probabilities (widths) in the
neutral multielectron atomic systems. The approach is based on the Gell-Mann and
Low S-matrix formalism and the relativistic many-body PT with using the optimized
one-quasiparticle representation. 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. The optimized one-electron representation in the PT zeroth
approximation is constructed by means of the correct treating the gauge dependent
multielectron contribution of the lowest PT corrections to the radiation widths of
atomic levels. It is important to note that an approach is universal and, generally
speaking, can be applied to quantum systems of other nature (see, for example,
[57–66] and Refs. therein).
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 point of view of the correct accounting for the relativistic and
exchange-correlation effects. The calculations encourage us to believe that using
energy approach combined with the relativistic many-body PT with the optimal oneelectron basis is quite consistent and effective tool from the point of view of the
theory correctness and results exactness. This fact is confirmed by other calculations
of the oscillator strengths, radiative widths, hyperfine structure constants for atoms
and multicharged ions (see Refs. [4, 6, 27–35, 82, 88, 163–183]). The obtained data
can be used in different applications, namely, astrophysical analysis, laboratory, thermonuclear plasmas diagnostics, fusion research, laser physics, quantum electronics
etc.
Acknowledgements The author would like to thank Professor Jean Maruani and Professor Liliana
Mammino (the organizer of the QSCP-XXIII Workshop) for their invitation to submit contributions
in these Proceedings.
References
1. Grant IP (2007) Relativistic quantum theory of atoms and molecules, theory and computation.
Springer Series on Atomic, Optical, and Plasma Physics, vol 40. Springer, Berlin, pp 587–626
A. V. Glushkov
the studied states. Let us also note that according to our data the widths of the
resonances indicated in the table vary extremely irregularly and are in the range of
1.64 × 10
−6
− 1.92 × 10
−5 Ry.
4 Conclusions
To conclude, we presented the generalized energy approach to relativistic calculation
of the autoionization decay (resonances) energies and probabilities (widths) in the
neutral multielectron atomic systems. The approach is based on the Gell-Mann and
Low S-matrix formalism and the relativistic many-body PT with using the optimized
one-quasiparticle representation. 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. The optimized one-electron representation in the PT zeroth
approximation is constructed by means of the correct treating the gauge dependent
multielectron contribution of the lowest PT corrections to the radiation widths of
atomic levels. It is important to note that an approach is universal and, generally
speaking, can be applied to quantum systems of other nature (see, for example,
[57–66] and Refs. therein).
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 point of view of the correct accounting for the relativistic and
exchange-correlation effects. The calculations encourage us to believe that using
energy approach combined with the relativistic many-body PT with the optimal oneelectron basis is quite consistent and effective tool from the point of view of the
theory correctness and results exactness. This fact is confirmed by other calculations
of the oscillator strengths, radiative widths, hyperfine structure constants for atoms
and multicharged ions (see Refs. [4, 6, 27–35, 82, 88, 163–183]). The obtained data
can be used in different applications, namely, astrophysical analysis, laboratory, thermonuclear plasmas diagnostics, fusion research, laser physics, quantum electronics
etc.
Acknowledgements The author would like to thank Professor Jean Maruani and Professor Liliana
Mammino (the organizer of the QSCP-XXIII Workshop) for their invitation to submit contributions
in these Proceedings.
References
1. Grant IP (2007) Relativistic quantum theory of atoms and molecules, theory and computation.
Springer Series on Atomic, Optical, and Plasma Physics, vol 40. Springer, Berlin, pp 587–626