Chapter 9
Operator Perturbation Theory for Atomic
Systems in a Strong DC Electric Field
Alexander V. Glushkov
Abstract A consistent uniform quantum approach to the solution of the nonstationary state problems including the DC (Direct Current) strong-field Stark effect and also scattering problem is presented. It is based on the operator form of the
perturbation theory for the Schrödinger equation. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact
quantum-mechanical procedure. The zero-order Hamiltonian possessing only stationary states is determined only by its spectrum without specifying its explicit form.
The method allows calculating the resonance complex energies and widths plus a
complete orthogonal complementary of the scattering state functions. The calculation results of the Stark resonance energies and widths for the hydrogen and sodium
atoms are presented and compared with other theoretical data.
9.1 Introduction
The Stark effect [1] is one of the best known problems in quantum mechanics, but
at the same time one of the most difficult (outside the weak-field region) [1–8].
A new interest in this effect has been stimulated in the last two decades. A range of
the interesting phenomena to be studied includes: quasi-discrete state mixing; a zoo
of Landau-Zener anticrossings in non-hydrogenic (non-H) atoms; autoionization in
non-H atoms; the effects of potential barriers (shape resonances); new kinds of resonances above threshold etc. [1–63]. The dielectronic recombination involves highly
excited (Rydberg) atomic states, which are very strongly affected by relatively weak
fields [3–6]. In fact these states provide the gateway for ion-electron recombination
processes. Now it is well known that weak-field effects on Rydberg states can cause
the large changes in electron-ion collision cross sections. One subject stands out
quite clearly: possible non-perturbative effects of the electric fields on the autoionization states responsible for dielectronic recombination. It is of a great importance
for a consistent treating the different processes in a laser plasma, astrophysical enA.V. Glushkov (B)
Odessa State University—OSENU, L’vovskaya str., 15, Odessa-9, 65016, Ukraine
e-mail: glushkovav@gmail.com
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_9,
© Springer International Publishing Switzerland 2013
161
Operator Perturbation Theory for Atomic
Systems in a Strong DC Electric Field
Alexander V. Glushkov
Abstract A consistent uniform quantum approach to the solution of the nonstationary state problems including the DC (Direct Current) strong-field Stark effect and also scattering problem is presented. It is based on the operator form of the
perturbation theory for the Schrödinger equation. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact
quantum-mechanical procedure. The zero-order Hamiltonian possessing only stationary states is determined only by its spectrum without specifying its explicit form.
The method allows calculating the resonance complex energies and widths plus a
complete orthogonal complementary of the scattering state functions. The calculation results of the Stark resonance energies and widths for the hydrogen and sodium
atoms are presented and compared with other theoretical data.
9.1 Introduction
The Stark effect [1] is one of the best known problems in quantum mechanics, but
at the same time one of the most difficult (outside the weak-field region) [1–8].
A new interest in this effect has been stimulated in the last two decades. A range of
the interesting phenomena to be studied includes: quasi-discrete state mixing; a zoo
of Landau-Zener anticrossings in non-hydrogenic (non-H) atoms; autoionization in
non-H atoms; the effects of potential barriers (shape resonances); new kinds of resonances above threshold etc. [1–63]. The dielectronic recombination involves highly
excited (Rydberg) atomic states, which are very strongly affected by relatively weak
fields [3–6]. In fact these states provide the gateway for ion-electron recombination
processes. Now it is well known that weak-field effects on Rydberg states can cause
the large changes in electron-ion collision cross sections. One subject stands out
quite clearly: possible non-perturbative effects of the electric fields on the autoionization states responsible for dielectronic recombination. It is of a great importance
for a consistent treating the different processes in a laser plasma, astrophysical enA.V. Glushkov (B)
Odessa State University—OSENU, L’vovskaya str., 15, Odessa-9, 65016, Ukraine
e-mail: glushkovav@gmail.com
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_9,
© Springer International Publishing Switzerland 2013
161