where ρ
0
c is the core electron density (without account for the quasiparticle), X is
numerical coefficient, c is the light velocity. The contribution of the ladder diagrams
(these diagrams describe the immediate interparticle interaction) is summarized by a
modification of the perturbation theory zeroth approximation mean-field central
potential (look [35, 65]), which include the screening (anti-screening) of the core
potential of each particle by the two others. The details of calculating this contribution can be found in Refs. [63, 65–76]. All computing was performed with using
the modified PC code “Superatom-ISAN” (version 93).
3 Results and Conclusions
In Tables 1 and 2 we present the experimental and theoretical values (in atomic
units: a.u.) of the reduced dipole transition matrix elements for the Fr and Cs atoms:
experimental data—Exp; theoretical data: perturbation theory (PT)-DF
SD
—PT with
the Dirac-Hartree-Fock zeroth approximation (single-double SD approximation in
which single and double excitations of Dirac-Hartree-Fock wave functions are
Table 1 The reduced dipole transition matrix elements for Fr (see text)
Transition/
method
PT-DF
SD
PT-DF
SD
(corr)
EMP PT-RHF
(corr)
PT-RHF DF
RPT-EA Exp.
7p 1/2 -7s
4.256
–
–
4.279
4.304
4.179 4.272,
4.274
4.277
8p 1/2 -7s
0.327
0.306
0.304 0.291
0.301
–
0.339
9p 1/2 -7s
0.110
0.098
0.096 –
–
–
0.092
10p 1/2 -7s
–
–
–
–
–
–
0.063
7p 3/2 -7s
5.851
–
–
5.894
5.927
5.791 5.891
5.898
8p 3/2 -7s
0.934
0.909
0.908 0.924
–
–
0.918
–
9p 3/2 -7s
0.436
0.422
0.420 –
–
–
0.426
–
10p 3/2 -7s
–
–
–
–
–
–
0.284
–
7p 1/2 -8s
4.184
4.237
4.230 4.165
4.219
4.196 4.228
–
8p 1/2 -8s
10.02
10.10
10.06 10.16
10.00
10.12
–
9p 1/2 -8s
0.985
–
0.977 –
–
–
0.972
–
10p 1/2 -8s
–
–
–
–
–
–
0.395
–
7p 3/2 -8s
7.418
7.461
7.449 7.384
7.470
7.472 7.453
–
8p 3/2 -8s
13.23
13.37
13.32 13.45
13.26
13.35
–
9p 3/2 -8s
2.245
–
2.236 –
–
–
2.232
–
10p 3/2 -8s
–
–
–
–
–
–
1.058
–
7p 1/2 -9s
1.016
–
1.010 –
–
–
1.062
–
8p 1/2 -9s
9.280
–
9.342 –
–
–
9.318
–
9p 1/2 -9s
17.39
–
17.40 –
–
–
17.42
–
(continued)
Spectroscopy of Radiative Decay Processes …
235
0
c is the core electron density (without account for the quasiparticle), X is
numerical coefficient, c is the light velocity. The contribution of the ladder diagrams
(these diagrams describe the immediate interparticle interaction) is summarized by a
modification of the perturbation theory zeroth approximation mean-field central
potential (look [35, 65]), which include the screening (anti-screening) of the core
potential of each particle by the two others. The details of calculating this contribution can be found in Refs. [63, 65–76]. All computing was performed with using
the modified PC code “Superatom-ISAN” (version 93).
3 Results and Conclusions
In Tables 1 and 2 we present the experimental and theoretical values (in atomic
units: a.u.) of the reduced dipole transition matrix elements for the Fr and Cs atoms:
experimental data—Exp; theoretical data: perturbation theory (PT)-DF
SD
—PT with
the Dirac-Hartree-Fock zeroth approximation (single-double SD approximation in
which single and double excitations of Dirac-Hartree-Fock wave functions are
Table 1 The reduced dipole transition matrix elements for Fr (see text)
Transition/
method
PT-DF
SD
PT-DF
SD
(corr)
EMP PT-RHF
(corr)
PT-RHF DF
RPT-EA Exp.
7p 1/2 -7s
4.256
–
–
4.279
4.304
4.179 4.272,
4.274
4.277
8p 1/2 -7s
0.327
0.306
0.304 0.291
0.301
–
0.339
9p 1/2 -7s
0.110
0.098
0.096 –
–
–
0.092
10p 1/2 -7s
–
–
–
–
–
–
0.063
7p 3/2 -7s
5.851
–
–
5.894
5.927
5.791 5.891
5.898
8p 3/2 -7s
0.934
0.909
0.908 0.924
–
–
0.918
–
9p 3/2 -7s
0.436
0.422
0.420 –
–
–
0.426
–
10p 3/2 -7s
–
–
–
–
–
–
0.284
–
7p 1/2 -8s
4.184
4.237
4.230 4.165
4.219
4.196 4.228
–
8p 1/2 -8s
10.02
10.10
10.06 10.16
10.00
10.12
–
9p 1/2 -8s
0.985
–
0.977 –
–
–
0.972
–
10p 1/2 -8s
–
–
–
–
–
–
0.395
–
7p 3/2 -8s
7.418
7.461
7.449 7.384
7.470
7.472 7.453
–
8p 3/2 -8s
13.23
13.37
13.32 13.45
13.26
13.35
–
9p 3/2 -8s
2.245
–
2.236 –
–
–
2.232
–
10p 3/2 -8s
–
–
–
–
–
–
1.058
–
7p 1/2 -9s
1.016
–
1.010 –
–
–
1.062
–
8p 1/2 -9s
9.280
–
9.342 –
–
–
9.318
–
9p 1/2 -9s
17.39
–
17.40 –
–
–
17.42
–
(continued)
Spectroscopy of Radiative Decay Processes …
235