Advanced Relativistic Energy Approach in Spectroscopy …
5
has been also tested in the 6pnf manifold of barium for J = 1–5 total angular momentum Rydberg series by Abutaleb et al. (1991); experimentally the autoinization rates
of the 6pnf J states were found to be up to a factor of two larger than calculated
values. Accounting for 6p 3/2 nf-6p 1/2 εl fine structure autoinization resulted in only
minor changes of 10–20% in the rates of autoionization. Poirier compared his computation of autoionization rates of 6p 3/2 ng J = 5 levels with experimental linewidths
measured by Jaffe et al. (e.g. [22–24, 35]). For the K = 9/2 level good agreement
was found but for K = 11/2 level the calculated autoionization rates was found to be
three times lower than the experimental value. Van Leuwen et al. [22] investigated
5dng states in barium considering a possibility to use these states as intermediates
for the excitation of higher lying doubly-excited states with large orbital angular
momentum (Jones 1991). Luc Koenig et al. [23, 24] has performed accurate measurements of the autoionization widths of 5d5g levels of barium coupled to theoretical
computation, based on the eigenchannel R-matrix method and multichannel quantum defect theory. Besides, this investigation allowed to understand the quadrupolar
autoionization mechanism. It was found that the direct polarization of the inner
electron by the outer one was important correction to the Coulomb repulsion that
causes autoionization. Besides, it is worth to note that these authors proved that
the dielectronic polarization interaction significantly influences the autoionization
widths. According to Ref. [23], the occurrence of these polarization effects in the
5d5g double excited states with nonoverlapping valence electron results in a significant narrowing of their widths and explains the failure of the single-configuration
model for high-l Rydberg levels. Ivanova, Ivanov et al. [113–120] have performed the
detailed computing energies and widths of the autoionization resonances, Rydberg
levels for ytterbium and thallium. The positions and widths of the autoionization
states belonging to the 7s6p, 6p5d, 6p
2 , and 5d
2 configurations were calculated
using the method of relativistic perturbation theory (PT) with the model potential
zeroth approximation [113–135]. The advanced version of this approach has been
presented and used in Refs. [113, 118–122] to get more exact data for radiative and
autoionization characteristics in the lanthanides atoms. In Refs. [131–135] it has been
discovered a principally new spectroscopic effect of a giant broadening autoionization resonances of the lanthanides atoms (thulium, gadolinium) in sufficiently weak
external electric (laser) field. In general, a problem of studying highly excited Rydberg atomic states and autoionization resonances in an external electromagnetic field
attracts a great interest and importance. In fact, a problem of treating parameters of
autoionization resonances in a field is obviously close to the problem of describing
resonances in general and the Stark resonances in particular. So, here it is worth to
remind about a great number of different approaches such as the Pade and then Borel
summation of the divergent Rayleigh-Schrödinger perturbation theory (PT) series
(Franceschini et al. 1985; Popov et al. 1990), expansions of the wave function over
finite basis (Benassi ans Grecchi 1980; Maquet et al. 1983; Kolosov 1987; Telnov
1989; Anokhin-Ivanov 1994), operator perturbation method by Glushkov-Ivanov,
complex-scaling method by Reinhardt, Chu, Rao, Liu and Li, Rao-Li et al. [64–
110], the Weyl’s theory by Hehenberger-McIntosh-Brändas and the Weyl’s theory
and the complex-rotation method by Brändas, Rittby, Elander and Froelich (1977)
5
has been also tested in the 6pnf manifold of barium for J = 1–5 total angular momentum Rydberg series by Abutaleb et al. (1991); experimentally the autoinization rates
of the 6pnf J states were found to be up to a factor of two larger than calculated
values. Accounting for 6p 3/2 nf-6p 1/2 εl fine structure autoinization resulted in only
minor changes of 10–20% in the rates of autoionization. Poirier compared his computation of autoionization rates of 6p 3/2 ng J = 5 levels with experimental linewidths
measured by Jaffe et al. (e.g. [22–24, 35]). For the K = 9/2 level good agreement
was found but for K = 11/2 level the calculated autoionization rates was found to be
three times lower than the experimental value. Van Leuwen et al. [22] investigated
5dng states in barium considering a possibility to use these states as intermediates
for the excitation of higher lying doubly-excited states with large orbital angular
momentum (Jones 1991). Luc Koenig et al. [23, 24] has performed accurate measurements of the autoionization widths of 5d5g levels of barium coupled to theoretical
computation, based on the eigenchannel R-matrix method and multichannel quantum defect theory. Besides, this investigation allowed to understand the quadrupolar
autoionization mechanism. It was found that the direct polarization of the inner
electron by the outer one was important correction to the Coulomb repulsion that
causes autoionization. Besides, it is worth to note that these authors proved that
the dielectronic polarization interaction significantly influences the autoionization
widths. According to Ref. [23], the occurrence of these polarization effects in the
5d5g double excited states with nonoverlapping valence electron results in a significant narrowing of their widths and explains the failure of the single-configuration
model for high-l Rydberg levels. Ivanova, Ivanov et al. [113–120] have performed the
detailed computing energies and widths of the autoionization resonances, Rydberg
levels for ytterbium and thallium. The positions and widths of the autoionization
states belonging to the 7s6p, 6p5d, 6p
2 , and 5d
2 configurations were calculated
using the method of relativistic perturbation theory (PT) with the model potential
zeroth approximation [113–135]. The advanced version of this approach has been
presented and used in Refs. [113, 118–122] to get more exact data for radiative and
autoionization characteristics in the lanthanides atoms. In Refs. [131–135] it has been
discovered a principally new spectroscopic effect of a giant broadening autoionization resonances of the lanthanides atoms (thulium, gadolinium) in sufficiently weak
external electric (laser) field. In general, a problem of studying highly excited Rydberg atomic states and autoionization resonances in an external electromagnetic field
attracts a great interest and importance. In fact, a problem of treating parameters of
autoionization resonances in a field is obviously close to the problem of describing
resonances in general and the Stark resonances in particular. So, here it is worth to
remind about a great number of different approaches such as the Pade and then Borel
summation of the divergent Rayleigh-Schrödinger perturbation theory (PT) series
(Franceschini et al. 1985; Popov et al. 1990), expansions of the wave function over
finite basis (Benassi ans Grecchi 1980; Maquet et al. 1983; Kolosov 1987; Telnov
1989; Anokhin-Ivanov 1994), operator perturbation method by Glushkov-Ivanov,
complex-scaling method by Reinhardt, Chu, Rao, Liu and Li, Rao-Li et al. [64–
110], the Weyl’s theory by Hehenberger-McIntosh-Brändas and the Weyl’s theory
and the complex-rotation method by Brändas, Rittby, Elander and Froelich (1977)