QED PT formalism [29, 30, 53, 54, 59, 60] allows to reach a physically reasonable
description of the radiative and other contributions to the transition energies,
especially, for high-Z ions of the Li-like isoelectronic sequence.
It is known that the standard relativistic PT usually fails to provide (or the total
accuracy is significantly decreased) the accurate results for low-Z and intermediateZ ions and neutral atoms of astrophysical (laser physics, physics of plasma etc.)
interest. In order to check the possibilities of a new approach (within the QED PT
[45–47, 59, 60]), we have studied the Li-like ions of argon, iron and krypton. These
ions are of the great practical interest for X-ray laser physics etc. (look, for example,
[88–92, 95–101] and Refs. therein). Analyzing the obtained data, in particular, for
the Li-like ions of iron and krypton, one could conclude that the approach presented
(with using the consistent relativistic PT [29, 30, 53–60]) can provide sufficiently
high accuracy and physically reasonable description of the corresponding energy
and spectral parameters of the multicharged ions.
Acknowledgments One of authors (A.V.G.) would like to thank Professor Marco Nascimento for
the invitation to present the invited lecture at the International workshop on Quantum Systems in
Chemistry, Physics and Biology (QSCP-XVIII; Paraty, Rio de Janeiro, Brazil). The help in editing
the manuscript by Ms. Radhika Sree V. is very much appreciated.
References
1. Feynman RP (1949) Phys Rev 76:749
2. Stueckelberg ECG, Rivier D (1949) Helv Phys Acta 13:215
3. Sakurai JJ (1967) Advanced quantum mechanics. Addison-Wesley, New York
4. Sakurai JJ (2011) Physics 221B quantum mechanics. Notes 34 green’s functions in quantum
mechanics. University of California, Berkeley
5. Itzykson C, Zuber J-B (1980) Em quantum field theory. McGraw-Hill Inc., New York
6. Landau LD, Lifshits EM, Pitaevsky LP (1985) Quantum electrodynamics. Nauka, Mposcow
7. Schweber SS (1961) An introduction to relativistic quantum field theory. Evanston, Illinois
8. Bjorken JD, Drell SD (1965) Relativistic quantum field theory. McGraw-Hill, New York
9. Braun MA, Gurchumeliya AD, Safronova UI (1984) Relativistic theory of atom. Nauka,
Moscow, pp 1–268
Table 3 Energy (in 10 cm
−1
)
of 2s 1/2 -2p 1/2 transition in the
spectra of Li-like ions of iron
and krypton (see text)
Li-like ion
Z = 26
Z = 36
RPT [86]
39,158
57,628
PT [87]
39,335
57,628
DF [39, 40]
39,335
57,628
PT DF [45–47]
39,296
57,455
QED PT [55, 56]
39,205
57,461
QED DF L [57, 58]
39,199
39,604*
57,463
58,718*
Exp.
39,199; 39,201
57,460; 57,463
Note *The electron structure values without accounting for the
QED corrections
214
A.V. Glushkov et al.
description of the radiative and other contributions to the transition energies,
especially, for high-Z ions of the Li-like isoelectronic sequence.
It is known that the standard relativistic PT usually fails to provide (or the total
accuracy is significantly decreased) the accurate results for low-Z and intermediateZ ions and neutral atoms of astrophysical (laser physics, physics of plasma etc.)
interest. In order to check the possibilities of a new approach (within the QED PT
[45–47, 59, 60]), we have studied the Li-like ions of argon, iron and krypton. These
ions are of the great practical interest for X-ray laser physics etc. (look, for example,
[88–92, 95–101] and Refs. therein). Analyzing the obtained data, in particular, for
the Li-like ions of iron and krypton, one could conclude that the approach presented
(with using the consistent relativistic PT [29, 30, 53–60]) can provide sufficiently
high accuracy and physically reasonable description of the corresponding energy
and spectral parameters of the multicharged ions.
Acknowledgments One of authors (A.V.G.) would like to thank Professor Marco Nascimento for
the invitation to present the invited lecture at the International workshop on Quantum Systems in
Chemistry, Physics and Biology (QSCP-XVIII; Paraty, Rio de Janeiro, Brazil). The help in editing
the manuscript by Ms. Radhika Sree V. is very much appreciated.
References
1. Feynman RP (1949) Phys Rev 76:749
2. Stueckelberg ECG, Rivier D (1949) Helv Phys Acta 13:215
3. Sakurai JJ (1967) Advanced quantum mechanics. Addison-Wesley, New York
4. Sakurai JJ (2011) Physics 221B quantum mechanics. Notes 34 green’s functions in quantum
mechanics. University of California, Berkeley
5. Itzykson C, Zuber J-B (1980) Em quantum field theory. McGraw-Hill Inc., New York
6. Landau LD, Lifshits EM, Pitaevsky LP (1985) Quantum electrodynamics. Nauka, Mposcow
7. Schweber SS (1961) An introduction to relativistic quantum field theory. Evanston, Illinois
8. Bjorken JD, Drell SD (1965) Relativistic quantum field theory. McGraw-Hill, New York
9. Braun MA, Gurchumeliya AD, Safronova UI (1984) Relativistic theory of atom. Nauka,
Moscow, pp 1–268
Table 3 Energy (in 10 cm
−1
)
of 2s 1/2 -2p 1/2 transition in the
spectra of Li-like ions of iron
and krypton (see text)
Li-like ion
Z = 26
Z = 36
RPT [86]
39,158
57,628
PT [87]
39,335
57,628
DF [39, 40]
39,335
57,628
PT DF [45–47]
39,296
57,455
QED PT [55, 56]
39,205
57,461
QED DF L [57, 58]
39,199
39,604*
57,463
58,718*
Exp.
39,199; 39,201
57,460; 57,463
Note *The electron structure values without accounting for the
QED corrections
214
A.V. Glushkov et al.