data by Laat-Konijn et al. [38, 39], obtained with using the relativistic
Klein-Gordon-Fock model and Hartree-Fock approximation.
3.3 Transition Energies and Energy Shift and Widths Due
to the Strong Interaction in the Spectra of in Some π
− A
Systems
In Figs. 2 and 3 there are presented the parts of the X-ray spectra of the
165 Ho
(Fig. 2),
181 Ta (Fig. 3) and positions of the hyperfine structure components (5 g-4f
transition; experimental data from [13]).
In Tables 9a and 10 we present theoretical and experimental data (in keV) for the
4f level shift (a) and widths (b) provided by the strong pion-nuclear interaction for a
number of pionic atoms. The shortened designation of the parameter sets for the
strong π
−
N interaction potential: Tauscher—Tau1; Tauscher, Tau2; Batty et al.—
Bat; Seki et al.—Sek; de Laat-Konijin et al.—Laat, this work—Srg-Sha [16–22, 38,
39, 76–79]. In our parameterization of the strong p
− N interaction potential the most
reliably defined (B 0 , c 0 , c 1 , C 0 ) parameters are remained unchanged, and the
parameters whose values differ greatly in different sets, in particular, b 1
(b 1 = −0.094) plus still not included ones ImB 1 , ImC 1 have been optimized by
computing dependencies of the strong shifts upon the parameters b 1 , ImB 1 , ImC 1
for π
−
−
20 Ne,
24 Mg,
93 Nb,
133 Cs,
175 Lu,
181
Ta,
197 Au,
208 Pb atoms. Further we have
chosen the values which satisfy the smallest standard deviation of reliable experimental values.
In Table 11 the analogous theoretical and experimental data (in keV) for the 3d
level shift (a) and widths for different pionic atoms are listed [16–22, 38, 39,
76–79].
In Table 12 data on the 4f-3d, 5g-4f transition energies for pionic atoms of the
93 Nb,
173 Yb,
181 Ta,
197 Au are presented. There are also listed the measured values
Table 8 The radiation widths of the 3d, 4f, 5g levels in some π
− A systems
Nucleus
Γ
1
rad
(5g) [38, 39]
Γ
2
rad (5g)
[79]
Γ
1
rad (4f)
[38, 39]
Γ
2
rad (4f) [79]
Γ
1
rad (3d)
[38, 39]
Γ
2
rad (3d)
[79]
165
Ho
–
15.2
–
56.1
–
228.8
173
Yb
–
17.9
–
66.8
–
275.4
175
Lu
–
20.7
–
77.5
–
320.3
181
Ta
25.7
23.5
90.9
88.6
369.9
366.1
203
Tl
–
37.2
–
136.8
–
557.2
208
Pb
41.5
39.4
146.8
143.2
587.6
583.8
209
Bi
43.7
41.5
156.2
153.1
617.3
613.7
84
O. Yu. Khetselius et al.
Klein-Gordon-Fock model and Hartree-Fock approximation.
3.3 Transition Energies and Energy Shift and Widths Due
to the Strong Interaction in the Spectra of in Some π
− A
Systems
In Figs. 2 and 3 there are presented the parts of the X-ray spectra of the
165 Ho
(Fig. 2),
181 Ta (Fig. 3) and positions of the hyperfine structure components (5 g-4f
transition; experimental data from [13]).
In Tables 9a and 10 we present theoretical and experimental data (in keV) for the
4f level shift (a) and widths (b) provided by the strong pion-nuclear interaction for a
number of pionic atoms. The shortened designation of the parameter sets for the
strong π
−
N interaction potential: Tauscher—Tau1; Tauscher, Tau2; Batty et al.—
Bat; Seki et al.—Sek; de Laat-Konijin et al.—Laat, this work—Srg-Sha [16–22, 38,
39, 76–79]. In our parameterization of the strong p
− N interaction potential the most
reliably defined (B 0 , c 0 , c 1 , C 0 ) parameters are remained unchanged, and the
parameters whose values differ greatly in different sets, in particular, b 1
(b 1 = −0.094) plus still not included ones ImB 1 , ImC 1 have been optimized by
computing dependencies of the strong shifts upon the parameters b 1 , ImB 1 , ImC 1
for π
−
−
20 Ne,
24 Mg,
93 Nb,
133 Cs,
175 Lu,
181
Ta,
197 Au,
208 Pb atoms. Further we have
chosen the values which satisfy the smallest standard deviation of reliable experimental values.
In Table 11 the analogous theoretical and experimental data (in keV) for the 3d
level shift (a) and widths for different pionic atoms are listed [16–22, 38, 39,
76–79].
In Table 12 data on the 4f-3d, 5g-4f transition energies for pionic atoms of the
93 Nb,
173 Yb,
181 Ta,
197 Au are presented. There are also listed the measured values
Table 8 The radiation widths of the 3d, 4f, 5g levels in some π
− A systems
Nucleus
Γ
1
rad
(5g) [38, 39]
Γ
2
rad (5g)
[79]
Γ
1
rad (4f)
[38, 39]
Γ
2
rad (4f) [79]
Γ
1
rad (3d)
[38, 39]
Γ
2
rad (3d)
[79]
165
Ho
–
15.2
–
56.1
–
228.8
173
Yb
–
17.9
–
66.8
–
275.4
175
Lu
–
20.7
–
77.5
–
320.3
181
Ta
25.7
23.5
90.9
88.6
369.9
366.1
203
Tl
–
37.2
–
136.8
–
557.2
208
Pb
41.5
39.4
146.8
143.2
587.6
583.8
209
Bi
43.7
41.5
156.2
153.1
617.3
613.7
84
O. Yu. Khetselius et al.