Advanced Relativistic Energy Approach in Spectroscopy …
19
In Table 3 we present the measured and calculated AS width (cm
−1 ) for 5d5g AS
Ba with J < 6: (3) Experiment; (4) Theory: HF method with partial accounting for the
correlations (Van Leeuwen et al. [53]); (5) R-matrix method without accounting for
the polarization effect of the shells (Luc-Koenig et al.); (6) R-method with accounting
the polarization of shells and without accounting for dielectronic interaction (LucKoenig et al.); (7) R-method with full accounting for the polarization and dielectronic
correlation effects (Luc-Koenig et al. [23, 24]); (8,9) our theory without accounting
for the correlation (polarization) effects and with full accounting the cited corrections.
In Table 4 we present the measured and calculated AS energies (theoretical data
by Van Leeuwen et al. [22] and this approach). The analysis of 5d5g barium levels, the channels 6s 1/2 εl 1 j 1 are open, 55d j2 n 1 l 1 j 1 are closed, and p j2 np j1 are closed.
The double excited states of 6p2 and 6p7p lie on the energy scale far from 5dng
states, respectively below the 6s 1/2 threshold and above the 5d 5/2 threshold. Therefore, it is quite enough to take into account the general connection of 5dng-6pnp
channels. All 6pnf J = 1–5 states are located at least 8000 cm
−1 above the 5d 5/2
threshold and, thus, the 6p j2 nf j1 channels are closed. The R-matrix method of LucKoenig et al. [24], taking into account polarization effects, is based on the use of the
empirical single-particle polarization potential of the Dalgarno form. In our theory,
the essentially multi-particle polarization operators of [182] act as an analogue of
the Dalgarno polarization potential. These potentials are derived by summing the
sequence of Feynman diagrams corresponding to the second and higher orders of
Rayleigh-Schrödinger PT in the density functional approximation (Thomas-Fermi)
and, accordingly, are initially more correct.
In any case to get a physically reasonable agreement between theoretical and
experimental data one should accurately take the complex exchange-correlation
(polarization, dielectronic interaction etc.) effects into account under using the optimized one-quasiparticle representation (with adding the Sturm expansions) in the
relativistic many-body PT theory zeroth approximation.
Very interesting in Ba spectroscopy is the study of the Rydberg AS that correspond
to transitions in the state 4fnf, in particular, 4f 5/2 n’f J = 6, 5, 4, excited from the initial
5d 3/2 15f J = 5 state [28, 64]. The method of laser spectroscopy method is applied to
study the corresponding 4f 5/2 n’f J = 6, 5, 4, states, excited from the initial 5d 3/2 15f J
= state, and 4f 5/2,7/2 n’f J = 6, 5, 4 one speakers (the initial state is 5d 3/220 20 f J = 4).
As illustration, in Table 5 we present experimental energy values (cm
−1 ) of 4fnf, n
= 15 autoionization resonances, n = 15 (averaged over the fine structure) measured
experimentally, as well as calculated on the basis of relativistic energy approach
(REA; combined with the PT with the DKS approximation) [4, 64] and the multichannel quantum defect method (MCQD) with empirical fitting (de Graaff et al.)
[28].
One should note that the use of the MCQD is possible provided that its parameters
are reliably determined (quantum defects either on the basis of empirical information
or the simplest screening models).
An analysis of the data presented in Table 5 shows that both the methods (MCQD
with an empirical fitting and our theory with a correct accounting for the exchangepolarization effects), provide a physically reasonable description of the energies of
19
In Table 3 we present the measured and calculated AS width (cm
−1 ) for 5d5g AS
Ba with J < 6: (3) Experiment; (4) Theory: HF method with partial accounting for the
correlations (Van Leeuwen et al. [53]); (5) R-matrix method without accounting for
the polarization effect of the shells (Luc-Koenig et al.); (6) R-method with accounting
the polarization of shells and without accounting for dielectronic interaction (LucKoenig et al.); (7) R-method with full accounting for the polarization and dielectronic
correlation effects (Luc-Koenig et al. [23, 24]); (8,9) our theory without accounting
for the correlation (polarization) effects and with full accounting the cited corrections.
In Table 4 we present the measured and calculated AS energies (theoretical data
by Van Leeuwen et al. [22] and this approach). The analysis of 5d5g barium levels, the channels 6s 1/2 εl 1 j 1 are open, 55d j2 n 1 l 1 j 1 are closed, and p j2 np j1 are closed.
The double excited states of 6p2 and 6p7p lie on the energy scale far from 5dng
states, respectively below the 6s 1/2 threshold and above the 5d 5/2 threshold. Therefore, it is quite enough to take into account the general connection of 5dng-6pnp
channels. All 6pnf J = 1–5 states are located at least 8000 cm
−1 above the 5d 5/2
threshold and, thus, the 6p j2 nf j1 channels are closed. The R-matrix method of LucKoenig et al. [24], taking into account polarization effects, is based on the use of the
empirical single-particle polarization potential of the Dalgarno form. In our theory,
the essentially multi-particle polarization operators of [182] act as an analogue of
the Dalgarno polarization potential. These potentials are derived by summing the
sequence of Feynman diagrams corresponding to the second and higher orders of
Rayleigh-Schrödinger PT in the density functional approximation (Thomas-Fermi)
and, accordingly, are initially more correct.
In any case to get a physically reasonable agreement between theoretical and
experimental data one should accurately take the complex exchange-correlation
(polarization, dielectronic interaction etc.) effects into account under using the optimized one-quasiparticle representation (with adding the Sturm expansions) in the
relativistic many-body PT theory zeroth approximation.
Very interesting in Ba spectroscopy is the study of the Rydberg AS that correspond
to transitions in the state 4fnf, in particular, 4f 5/2 n’f J = 6, 5, 4, excited from the initial
5d 3/2 15f J = 5 state [28, 64]. The method of laser spectroscopy method is applied to
study the corresponding 4f 5/2 n’f J = 6, 5, 4, states, excited from the initial 5d 3/2 15f J
= state, and 4f 5/2,7/2 n’f J = 6, 5, 4 one speakers (the initial state is 5d 3/220 20 f J = 4).
As illustration, in Table 5 we present experimental energy values (cm
−1 ) of 4fnf, n
= 15 autoionization resonances, n = 15 (averaged over the fine structure) measured
experimentally, as well as calculated on the basis of relativistic energy approach
(REA; combined with the PT with the DKS approximation) [4, 64] and the multichannel quantum defect method (MCQD) with empirical fitting (de Graaff et al.)
[28].
One should note that the use of the MCQD is possible provided that its parameters
are reliably determined (quantum defects either on the basis of empirical information
or the simplest screening models).
An analysis of the data presented in Table 5 shows that both the methods (MCQD
with an empirical fitting and our theory with a correct accounting for the exchangepolarization effects), provide a physically reasonable description of the energies of