72
O. Yu. Khetselius et al.
where g = r/(αZ). A More correct and consistent approach is presented in Refs. [3,
10, 60, 68, 81–86]. Taking into account the nuclear finite size effect modifies the
potential (16) as follows [3]:
U F S (r ) = −
2α 2
3π
d 3 r
∞
1
dt exp
−2t
r − r
/α Z
×
1 +
1
2t 2
t 2 − 1
t 2
ρ
r
r − r
.
(17)
Other details of the general method and PC code are described in Refs. [3, 4, 10,
50, 53–102]. All calculations are performed with using the numeral codes SuperAtom
(Nucleus) (modified versions 93).
3 Results and Conclusions
As the first illustration (the test), we consider
133 Cs and present the results (Table 1) of
calculation of the hyperfine structure (hfs) parameters for Cs. In Table 1 the experimental (A
Exp ) and our (A
N−Qed ) data for magnetic dipole constant A (MHz) for
valent states of
133 Cs (I = 7/2, g i = 0.7377208) are presented. The calculation results
within standard (A
RHF ) RHF and RHF with accounting for the second and higher
PT corrections, the MCDF approximation and QED formalism are given too (from
Refs. [3, 22–33, 62, 68]). The following notations are used: A
RCC —calculation by
relativistic cluster-coupled (RCC) method; A
DF —DF method; A
RHF —RHF method
and A
QED —the QED calculation; A
N−Qed is the result of this work. The key quantitative factor of physically reasonable agreement between theory and experimental data
is connected with the correct accounting for the inter electron correlations, nuclear,
Breit and QED radiative corrections.
In Table 2 the PNC amplitudes (in units of 10
−11 iea B (−Q W )/N) are listed
and calculated on the basis of the different methods (without the Breit corrections): DF, RHF, MCDF, MBPT and nuclear-RMBPT results (data from Refs.
[3, 22–33, 62, 68]).
In Table 3 we present the Breit correction (in units of 10
−11 (−Q W )/N) to the
PNC amplitude, which are calculated by the different methods (without the Breit
corrections): DF, RHF, MCDF, and nuclear-RMBPT (data from Refs. [3, 22–33, 62,
68]). Let us note that the radiative corrections to the PNC amplitude, provided by the
Table 1 The values (MHZ) of the hfs constant A for valent states of 133 Cs: A Exp —experiment;
A RHF , dA RHF —RHF calculation plus the second and higher PT orders contribution [A QED —data];
A N−Qed —this work
State
A MCDF
A RHF
A RHF + dA
A Qed
A N−Qed
A Exp
6s 1/2
1736.9
1426.81
2291.00
2294.45
2296.78
2298.16(13)
6p 1/2
209.6
161.09
292.67
292.102
292.118
291.90(13)
O. Yu. Khetselius et al.
where g = r/(αZ). A More correct and consistent approach is presented in Refs. [3,
10, 60, 68, 81–86]. Taking into account the nuclear finite size effect modifies the
potential (16) as follows [3]:
U F S (r ) = −
2α 2
3π
d 3 r
∞
1
dt exp
−2t
r − r
/α Z
×
1 +
1
2t 2
t 2 − 1
t 2
ρ
r
r − r
.
(17)
Other details of the general method and PC code are described in Refs. [3, 4, 10,
50, 53–102]. All calculations are performed with using the numeral codes SuperAtom
(Nucleus) (modified versions 93).
3 Results and Conclusions
As the first illustration (the test), we consider
133 Cs and present the results (Table 1) of
calculation of the hyperfine structure (hfs) parameters for Cs. In Table 1 the experimental (A
Exp ) and our (A
N−Qed ) data for magnetic dipole constant A (MHz) for
valent states of
133 Cs (I = 7/2, g i = 0.7377208) are presented. The calculation results
within standard (A
RHF ) RHF and RHF with accounting for the second and higher
PT corrections, the MCDF approximation and QED formalism are given too (from
Refs. [3, 22–33, 62, 68]). The following notations are used: A
RCC —calculation by
relativistic cluster-coupled (RCC) method; A
DF —DF method; A
RHF —RHF method
and A
QED —the QED calculation; A
N−Qed is the result of this work. The key quantitative factor of physically reasonable agreement between theory and experimental data
is connected with the correct accounting for the inter electron correlations, nuclear,
Breit and QED radiative corrections.
In Table 2 the PNC amplitudes (in units of 10
−11 iea B (−Q W )/N) are listed
and calculated on the basis of the different methods (without the Breit corrections): DF, RHF, MCDF, MBPT and nuclear-RMBPT results (data from Refs.
[3, 22–33, 62, 68]).
In Table 3 we present the Breit correction (in units of 10
−11 (−Q W )/N) to the
PNC amplitude, which are calculated by the different methods (without the Breit
corrections): DF, RHF, MCDF, and nuclear-RMBPT (data from Refs. [3, 22–33, 62,
68]). Let us note that the radiative corrections to the PNC amplitude, provided by the
Table 1 The values (MHZ) of the hfs constant A for valent states of 133 Cs: A Exp —experiment;
A RHF , dA RHF —RHF calculation plus the second and higher PT orders contribution [A QED —data];
A N−Qed —this work
State
A MCDF
A RHF
A RHF + dA
A Qed
A N−Qed
A Exp
6s 1/2
1736.9
1426.81
2291.00
2294.45
2296.78
2298.16(13)
6p 1/2
209.6
161.09
292.67
292.102
292.118
291.90(13)