atoms are provided by a correct consideration of the nuclear, relativistic, radiative
and inter-electron correlation corrections. Using different schemes for accounting of
these correlations explains a difference between calculation results, obtained within
the Klein-Gordon-Fock approach. To reach the further improvement of the computed data one should take into account more correctly the spatial distribution of the
Table 10 Theoretical and experimental data for the 4f level widths (keV) provided by the strong
pion-nuclear interaction for a number of pionic atoms (see text)
ε 4f , Γ 4f
Exp
H-like
Func.
Tau 1
ξ = 0
Tau 2
ξ = 1
Bat
ξ = 1
Sek
ξ = 1
Laat
ξ = 1
Srg-Sha
ξ = 1
Our
ξ = 1
165
Ho: Γ 0.21 ± 0.02 0.08
0.13
0.12
0.13
0.11
0.13
0.20
0.21
169
Tm: Γ –
–
–
–
–
–
–
–
0.23
173
Yb: Γ –
–
–
–
–
–
–
–
0.26
175
Lu: Γ 0.27 ± 0.07 0.14
0.23
0.22
0.24
0.20
0.24
0.28
0.28
181
Ta: Γ 0.31 ± 0.05 0.16
0.31
0.30
0.31
0.27
0.31
0.30
0.31
197
Au: Γ 0.77 ± 0.04 –
0.73
0.68
0.69
0.58
0.67
0.75
0.77
208
Pb: Γ 0.98 ± 0.05 –
1.18
1.04
1.03
0.86
0.98
0.97
0.99
209
Bi: Γ
1.24 ± 0.09 –
1.35
1.18
1.17
0.99
1.10
1.22
1.25
Table 11 Theoretical and experimental data for the 3d level shifts and widths (keV) provided by
the strong pion-nuclear interaction for a number of pionic atoms (see text)
3d
Еxp.
Tau 1
ξ = 0
Tau 2
ξ = 1
Bat
ξ = 1
Sek
ξ = 1
Laat
ξ = 1
Srg-Sha
ξ = 1
Odes
ξ = 1
93
Nb: ε
0.74 ± 0.02
0.66
0.67
0.73
0.66
0.75
0.75
0.73
169
Tm: ε
–
–
–
–
–
–
–
11.0
173
Yb: ε
–
–
–
–
–
–
–
12.4
175
Lu: ε
–
–
–
–
–
–
–
13.9
181
Ta: ε
16.2 ± 1.3
19.6
16.4
10.4
4.4
14.4
16.3
16.1
197
Au: ε
20.6 ± 1.9
27.9
22.5
13.2
5.0
20.3
21.1
20.3
208
Pb: ε
22.7 ± 2.2
34
25
13
3
18
22.8
22.6
209
Bi: ε
20 ± 3
37
27
17
5
19
23
21.1
93
Nb: Γ
0.40 ± 0.02
0.405
0.413
0.459
0.404
0.452
0.42
0.41
169
Tm: Γ
–
–
–
–
–
–
–
15.7
173
Yb: Γ
–
–
–
–
–
–
–
17.6
175
Lu: Γ
–
–
–
–
–
–
–
19.4
181
Ta: Γ
20,1 ± 1,5
40,5
37,5
33,4
26,2
27,6
20.3
20.2
197
Au: Γ
34±3.6
68
62
53
41
42
36.2
35.6
208
Pb: Γ
47.1 ± 3.6
88
78
65
51
51
47.2
47.0
209
Bi: Γ
52 ± 3.6
97
86
72
57
56
53.6
53.4
Relativistic Quantum Chemistry and Spectroscopy of Exotic …
87
and inter-electron correlation corrections. Using different schemes for accounting of
these correlations explains a difference between calculation results, obtained within
the Klein-Gordon-Fock approach. To reach the further improvement of the computed data one should take into account more correctly the spatial distribution of the
Table 10 Theoretical and experimental data for the 4f level widths (keV) provided by the strong
pion-nuclear interaction for a number of pionic atoms (see text)
ε 4f , Γ 4f
Exp
H-like
Func.
Tau 1
ξ = 0
Tau 2
ξ = 1
Bat
ξ = 1
Sek
ξ = 1
Laat
ξ = 1
Srg-Sha
ξ = 1
Our
ξ = 1
165
Ho: Γ 0.21 ± 0.02 0.08
0.13
0.12
0.13
0.11
0.13
0.20
0.21
169
Tm: Γ –
–
–
–
–
–
–
–
0.23
173
Yb: Γ –
–
–
–
–
–
–
–
0.26
175
Lu: Γ 0.27 ± 0.07 0.14
0.23
0.22
0.24
0.20
0.24
0.28
0.28
181
Ta: Γ 0.31 ± 0.05 0.16
0.31
0.30
0.31
0.27
0.31
0.30
0.31
197
Au: Γ 0.77 ± 0.04 –
0.73
0.68
0.69
0.58
0.67
0.75
0.77
208
Pb: Γ 0.98 ± 0.05 –
1.18
1.04
1.03
0.86
0.98
0.97
0.99
209
Bi: Γ
1.24 ± 0.09 –
1.35
1.18
1.17
0.99
1.10
1.22
1.25
Table 11 Theoretical and experimental data for the 3d level shifts and widths (keV) provided by
the strong pion-nuclear interaction for a number of pionic atoms (see text)
3d
Еxp.
Tau 1
ξ = 0
Tau 2
ξ = 1
Bat
ξ = 1
Sek
ξ = 1
Laat
ξ = 1
Srg-Sha
ξ = 1
Odes
ξ = 1
93
Nb: ε
0.74 ± 0.02
0.66
0.67
0.73
0.66
0.75
0.75
0.73
169
Tm: ε
–
–
–
–
–
–
–
11.0
173
Yb: ε
–
–
–
–
–
–
–
12.4
175
Lu: ε
–
–
–
–
–
–
–
13.9
181
Ta: ε
16.2 ± 1.3
19.6
16.4
10.4
4.4
14.4
16.3
16.1
197
Au: ε
20.6 ± 1.9
27.9
22.5
13.2
5.0
20.3
21.1
20.3
208
Pb: ε
22.7 ± 2.2
34
25
13
3
18
22.8
22.6
209
Bi: ε
20 ± 3
37
27
17
5
19
23
21.1
93
Nb: Γ
0.40 ± 0.02
0.405
0.413
0.459
0.404
0.452
0.42
0.41
169
Tm: Γ
–
–
–
–
–
–
–
15.7
173
Yb: Γ
–
–
–
–
–
–
–
17.6
175
Lu: Γ
–
–
–
–
–
–
–
19.4
181
Ta: Γ
20,1 ± 1,5
40,5
37,5
33,4
26,2
27,6
20.3
20.2
197
Au: Γ
34±3.6
68
62
53
41
42
36.2
35.6
208
Pb: Γ
47.1 ± 3.6
88
78
65
51
51
47.2
47.0
209
Bi: Γ
52 ± 3.6
97
86
72
57
56
53.6
53.4
Relativistic Quantum Chemistry and Spectroscopy of Exotic …
87