174
A.V. Glushkov
experiment is good. Our results are obtained in the first PT order, i.e., the first PT
order provides physically reasonable results.
9.4 Conclusions
In this chapter it is presented a new uniform quantum-mechanical approach to the
solution of the non-stationary state problems including the DC strong-field Stark
effect and also scattering problem. New OPT method allows sufficiently exact calculating the complex EE and resonance widths and especially is destined for investigation of the spectral region of an atom near the new continuum boundary in a
strong field. The essence of the method is the inclusion of the well known “distorted
waves approximation” in the frame of the formally exact PT. The method is generalized to provide the description of the DC strong field Stark effect for the non-H
atoms. The results of the calculation of the Stark resonance energies and widths for
the hydrogen and sodium atoms are presented and in a physically reasonable agreement with the best results of the alternative theoretical methods and experiment. It
is noted that the zeroth model approximation, including the potential of a strong external electric field, can be implemented into the general formalism of the formally
exact PT for many-electron atom [6, 12, 59–63, 71–76].
The range of validity of the presented method which uses the Fermi golden rule is
sufficiently wide and it is not restricted to resonances lying far from the continuum
boundary. Let us conclude that the OPT method has been also successfully applied
to correct description of the resonances of the Zeeman effect in a strong magnetic
field, crossed electric and magnetic fields, the resonances in molecular systems, as
well as descriptions of resonant states in nuclear systems such as the resonances of
the compound nucleus and the resonances arising from the collision of heavy ions
(nuclei), accompanied by the electron-positron pairs production (look the details in
Refs. [6, 80, 83–91]).
Acknowledgements The author would like to thank Prof. Jean Maruani and Prof. Matti Hotokka
(the organizer of QSCP XVII-2012, Turku, Finland) for the friendly cooperation and invaluable
advises.
References
1. Stark J (1914) Ann Phys 43:965
2. Bethe HA, Salpeter EE (1957) Quantum mechanics of one- and two-electron atoms. Springer,
Berlin
3. Landau LD, Lifshitz EM (1977) Quantum mechanics. Pergamon, Oxford
4. Stebbings RF, Dunning FB (eds) (1983) Rydberg states of atoms and molecules. Cambridge
University Press, Cambridge
5. Nayfeh MN, Clark CW (eds) (1984) Atomic excitation and recombination in external fields.
NBS, Gaithersburg
6. Glushkov AV (2005) Atom in an electromagnetic field. KNT, Kiev, pp 1–450
A.V. Glushkov
experiment is good. Our results are obtained in the first PT order, i.e., the first PT
order provides physically reasonable results.
9.4 Conclusions
In this chapter it is presented a new uniform quantum-mechanical approach to the
solution of the non-stationary state problems including the DC strong-field Stark
effect and also scattering problem. New OPT method allows sufficiently exact calculating the complex EE and resonance widths and especially is destined for investigation of the spectral region of an atom near the new continuum boundary in a
strong field. The essence of the method is the inclusion of the well known “distorted
waves approximation” in the frame of the formally exact PT. The method is generalized to provide the description of the DC strong field Stark effect for the non-H
atoms. The results of the calculation of the Stark resonance energies and widths for
the hydrogen and sodium atoms are presented and in a physically reasonable agreement with the best results of the alternative theoretical methods and experiment. It
is noted that the zeroth model approximation, including the potential of a strong external electric field, can be implemented into the general formalism of the formally
exact PT for many-electron atom [6, 12, 59–63, 71–76].
The range of validity of the presented method which uses the Fermi golden rule is
sufficiently wide and it is not restricted to resonances lying far from the continuum
boundary. Let us conclude that the OPT method has been also successfully applied
to correct description of the resonances of the Zeeman effect in a strong magnetic
field, crossed electric and magnetic fields, the resonances in molecular systems, as
well as descriptions of resonant states in nuclear systems such as the resonances of
the compound nucleus and the resonances arising from the collision of heavy ions
(nuclei), accompanied by the electron-positron pairs production (look the details in
Refs. [6, 80, 83–91]).
Acknowledgements The author would like to thank Prof. Jean Maruani and Prof. Matti Hotokka
(the organizer of QSCP XVII-2012, Turku, Finland) for the friendly cooperation and invaluable
advises.
References
1. Stark J (1914) Ann Phys 43:965
2. Bethe HA, Salpeter EE (1957) Quantum mechanics of one- and two-electron atoms. Springer,
Berlin
3. Landau LD, Lifshitz EM (1977) Quantum mechanics. Pergamon, Oxford
4. Stebbings RF, Dunning FB (eds) (1983) Rydberg states of atoms and molecules. Cambridge
University Press, Cambridge
5. Nayfeh MN, Clark CW (eds) (1984) Atomic excitation and recombination in external fields.
NBS, Gaithersburg
6. Glushkov AV (2005) Atom in an electromagnetic field. KNT, Kiev, pp 1–450