our data. The following abbreviations are used: the Uehling-Serber vacuum
polarization correction (VP-US), the Kallen-Sabry correction (VP-KS),
Wichman-Kroll one (PV-WK).
Analysis of data shows that there is physically reasonable agreement between
different theoretical data, namely, data by Schlesser-Indelicato et al. [31, 32, 76–
79]. Naturally, the reason is obvious as the known expansion parameter aZ in the
hydrogen atom is significantly less than one, and the general QED contributions
into the levels energies are not large in comparison with other ones.
In Table 8 we present our calculated (the relativistic Klein-Gordon-Fock theory
combined with energy approach) data on the radiation widths of the 3d, 4f, 5g
levels for a number of the pionic π
− A atoms. There are also listed the analogous
Table 6 The dependence of shifts and widths for the 4f, 3d levels due to the strong pion nuclear
interaction upon the parameter ImC 1 для ядpa
81
Ta
ImC 1
ε
4f
0 (
81
Ta)
Γ
4f
0 (
81
Ta)
ε
3d
0 (
81
Ta)
Γ
3d
0 (
81
Ta)
0.00
0.486
0.334
12.8
33.7
−0.05
0.502
0.325
13.7
30.8
−0.10
0.519
0.313
14.3
28.5
−0.15
0.534
0.302
14.9
25.7
−0.20
0.547
0.274
15.6
23.4
−0.25
0.559
0.268
16.3
20.6
−0.30
0.571
0.255
16.8
19.9
Exp.
0.56 ± 0.04
0.31 ± 0.05
16.2 ± 1.3
20.1 ± 1.5
Table 7 The calculated (in
meV) QED corrections to the
energies of the 1s, 2p, 3p, 4p
states for pionic hydrogen:
data by Indelicato et al., Serga
et al. and our data
QED contr.
1s [31, 32]
1s[76, 77]
1s[79]
VP-US
−3240.802
−3240.799
−3240.801
VP-KS
−24.365
−24.363
−24.365
PV-WK
−4.110
−4.113
−4.112
QED contr.
2p
2p
2p
VP-US
−35.795
−35.793
−35.794
VP-KS
−0.346
−0.343
−0.345
PV-WK
−0.008
−0.010
−0.009
QED contr.
3p
3p
3p
VP-US
−11.407
−11.405
−11.406
VP-KS
−0.108
−0.105
−0.107
PV-WK
−0.002
−0.003
−0.002
QED contr.
4p
4p
4p
VP-US
−4.921
−4.918
−4.920
VP-KS
−0.046
−0.044
−0.045
PV-WK
−0.001
−0.002
−0.001
Relativistic Quantum Chemistry and Spectroscopy of Exotic …
83
polarization correction (VP-US), the Kallen-Sabry correction (VP-KS),
Wichman-Kroll one (PV-WK).
Analysis of data shows that there is physically reasonable agreement between
different theoretical data, namely, data by Schlesser-Indelicato et al. [31, 32, 76–
79]. Naturally, the reason is obvious as the known expansion parameter aZ in the
hydrogen atom is significantly less than one, and the general QED contributions
into the levels energies are not large in comparison with other ones.
In Table 8 we present our calculated (the relativistic Klein-Gordon-Fock theory
combined with energy approach) data on the radiation widths of the 3d, 4f, 5g
levels for a number of the pionic π
− A atoms. There are also listed the analogous
Table 6 The dependence of shifts and widths for the 4f, 3d levels due to the strong pion nuclear
interaction upon the parameter ImC 1 для ядpa
81
Ta
ImC 1
ε
4f
0 (
81
Ta)
Γ
4f
0 (
81
Ta)
ε
3d
0 (
81
Ta)
Γ
3d
0 (
81
Ta)
0.00
0.486
0.334
12.8
33.7
−0.05
0.502
0.325
13.7
30.8
−0.10
0.519
0.313
14.3
28.5
−0.15
0.534
0.302
14.9
25.7
−0.20
0.547
0.274
15.6
23.4
−0.25
0.559
0.268
16.3
20.6
−0.30
0.571
0.255
16.8
19.9
Exp.
0.56 ± 0.04
0.31 ± 0.05
16.2 ± 1.3
20.1 ± 1.5
Table 7 The calculated (in
meV) QED corrections to the
energies of the 1s, 2p, 3p, 4p
states for pionic hydrogen:
data by Indelicato et al., Serga
et al. and our data
QED contr.
1s [31, 32]
1s[76, 77]
1s[79]
VP-US
−3240.802
−3240.799
−3240.801
VP-KS
−24.365
−24.363
−24.365
PV-WK
−4.110
−4.113
−4.112
QED contr.
2p
2p
2p
VP-US
−35.795
−35.793
−35.794
VP-KS
−0.346
−0.343
−0.345
PV-WK
−0.008
−0.010
−0.009
QED contr.
3p
3p
3p
VP-US
−11.407
−11.405
−11.406
VP-KS
−0.108
−0.105
−0.107
PV-WK
−0.002
−0.003
−0.002
QED contr.
4p
4p
4p
VP-US
−4.921
−4.918
−4.920
VP-KS
−0.046
−0.044
−0.045
PV-WK
−0.001
−0.002
−0.001
Relativistic Quantum Chemistry and Spectroscopy of Exotic …
83