Hyperfine and Electroweak Interactions in Heavy Finite Fermi Systems …
73
Table 2 PNC amplitudes (in units of 10 −11 iea B (-Q W )/N), which are calculated by different
methods (without the Breit corrections): DF, RHF, MCDF, MBPT and nuclear-QED PT
Atom
trans.
Spin
of
Nucl.
Nucl.
Moment
μ N
Radius
(fm) of
nucleus
DF
RHF
MCDF
MBPT
N-RMBPT
85 Rb
5s–6s
5/2
1.3534
4.246
−0.110 −0.138 −0.134 −0.135 −0.132
133 Cs
6s–7s
7/2
2.5826
4.837
−0.741 −0.926
−0.897
−0.904 −0.906
−0.908
−0.903
223 Fr
7s–8s
3/2
1.1703
5.640
−13.72 −16.63 −15.72 −15.56
−15.80
−15.54
211 Fr
7s–8s
9/2
4.0032
5.539
−12.51 −15.16 −14.34 –
−14.17
Table 3 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 results (other data from Refs. [25, 29, 33])
Atom: transition.
DF
RHF
MCDF
N-QED PT
133 Cs 6s–7s
0.0022
0.0018
0.0045
0.0049
223 Fr 7s–8s
0.0640
0.0650
0.1430
0.1703
vacuum-polarization (VP) effect and the self-energy (SE) part are as follows: E PNC
−
133 Cs − VP = 0.38%, SE = −0.74%;
223 Fr − VP = 1.025%, SE = −1.35%.
In Table 4 we list the nuclear spin dependent corrections to PNC (
133 Cs:
6s−7s) amplitude, calculated by different theoretical methods (in units of the
k a,2,hf coefficient): MBPT, DF–PT, the shell model, N-RMBPT (from Refs.
[3, 22–33, 62, 68]).
In Table 5 we present the estimated values of the weak charge Q W for different heavy atoms, predicted in different approaches and determined in the Standard
model (SM) (from Refs. [1–7, 22–33, 62, 68]). The analysis of results shows that in
Table 4 The nuclear spin-dependent corrections to the PNC 133 Cs: 6s-7s amplitude E PNC ,
calculated by different methods (in units of k a,2,hf coeff.): MBPT, DF-PT, shell model, N-RMBPT
(see text)
Correction
MBPT
Shell model DF
N-RMBPT
K (sum)
0.1169
0.1118
0.112
0.1159
k 2 —the Z-boson exchange interaction from
nucleon axial-vector currents (A n V e )
0.0140
0.0140
0.0111
0.0084
0.0138
k hf —the combined action of the hyperfine
interaction and spin-independent Z exchange
0.0049
0.0078
0.0071
0.0078
0.0067
k a —anapole moment
0.0980
0.090
0.0920 0.0954
73
Table 2 PNC amplitudes (in units of 10 −11 iea B (-Q W )/N), which are calculated by different
methods (without the Breit corrections): DF, RHF, MCDF, MBPT and nuclear-QED PT
Atom
trans.
Spin
of
Nucl.
Nucl.
Moment
μ N
Radius
(fm) of
nucleus
DF
RHF
MCDF
MBPT
N-RMBPT
85 Rb
5s–6s
5/2
1.3534
4.246
−0.110 −0.138 −0.134 −0.135 −0.132
133 Cs
6s–7s
7/2
2.5826
4.837
−0.741 −0.926
−0.897
−0.904 −0.906
−0.908
−0.903
223 Fr
7s–8s
3/2
1.1703
5.640
−13.72 −16.63 −15.72 −15.56
−15.80
−15.54
211 Fr
7s–8s
9/2
4.0032
5.539
−12.51 −15.16 −14.34 –
−14.17
Table 3 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 results (other data from Refs. [25, 29, 33])
Atom: transition.
DF
RHF
MCDF
N-QED PT
133 Cs 6s–7s
0.0022
0.0018
0.0045
0.0049
223 Fr 7s–8s
0.0640
0.0650
0.1430
0.1703
vacuum-polarization (VP) effect and the self-energy (SE) part are as follows: E PNC
−
133 Cs − VP = 0.38%, SE = −0.74%;
223 Fr − VP = 1.025%, SE = −1.35%.
In Table 4 we list the nuclear spin dependent corrections to PNC (
133 Cs:
6s−7s) amplitude, calculated by different theoretical methods (in units of the
k a,2,hf coefficient): MBPT, DF–PT, the shell model, N-RMBPT (from Refs.
[3, 22–33, 62, 68]).
In Table 5 we present the estimated values of the weak charge Q W for different heavy atoms, predicted in different approaches and determined in the Standard
model (SM) (from Refs. [1–7, 22–33, 62, 68]). The analysis of results shows that in
Table 4 The nuclear spin-dependent corrections to the PNC 133 Cs: 6s-7s amplitude E PNC ,
calculated by different methods (in units of k a,2,hf coeff.): MBPT, DF-PT, shell model, N-RMBPT
(see text)
Correction
MBPT
Shell model DF
N-RMBPT
K (sum)
0.1169
0.1118
0.112
0.1159
k 2 —the Z-boson exchange interaction from
nucleon axial-vector currents (A n V e )
0.0140
0.0140
0.0111
0.0084
0.0138
k hf —the combined action of the hyperfine
interaction and spin-independent Z exchange
0.0049
0.0078
0.0071
0.0078
0.0067
k a —anapole moment
0.0980
0.090
0.0920 0.0954