Batygin et al., based on the approximation formulas (10a)–(10c), the Hartree-Fock
data by Penkin et al., as well as experimental data (from Refs. [18–27, 30–35]).
It is noteworthy sufficiently large error for values of the van der Waals constants,
obtained during calculating on the basis of formula (11), as well as within the
standard Hartree-Fock method.
The calculation shows the importance of the quality of the atomic wave functions (using an optimization and correct account for the exchange-correlation effects
and continuum “pressure” etc.) for an adequate description of the corresponding
constants.
In Table 2 there are listed the results of our calculation of the interatomic
interaction potential U(R) and the values of the local shift δω(R) (all values are in
atomic units) of the thallium hyperfine spectral line for different values of the
internuclear distance in the system Tl–He. For comparison, similar results of the
calculation of the potential U(R) and the local shift δω(R) with using the singleconfiguration Dirac-Fock method [25–27] are presented too.
In Table 3 we list the results of our calculation (as all values are given in atomic
units) interatomic interaction potential U(R) and the values of the local shift
δω(R) for pairs Tl–Kr, Tl–Xe.
Further in Table 4 we present our theoretical values (theory C) for the thallium
atom hyperfine line collisional shift at the temperature T = 700 K for a number of
Table 2 Local shift and
interatomic interaction
potential (in atomic units) for
the pair Tl–He
Dirac-Fock method
[25–27]
Our theory [18–21]
R δω(R) × 10
2
U(R) × 10
3
δω(R) × 10
2
U(R) × 10
3
5
4.22
7.6
3.92
6.93
6
1.34
2.0
1.21
1.76
7
0.329
0.44
0.27
0.38
8
0.0788
0.099
0.070
0.085
9
0.0032
0.024
0.0025
0.020
10 −0.0145
−0.076
−0.0131
−0.067
11
−0.0119
−0.008
Table 3 Local shift and
interatomic interaction
potential (in atomic units) for
the pair Tl–Kr, Xe (see text)
Tl–Kr (our theory)
Tl–Xe (our theory)
R δω(R) × 10
2
U(R) × 10
3
δω(R) × 10
2
U(R) × 10
3
5
−14.30
13.24
−19.05
18.31
6
−2.88
6.10
−8.22
5.95
7
−1.44
1.72
−2.67
2.04
8
−0.67
0.49
−1.52
0.65
9
−0.48
0.06
−0.74
0.01
10
−0.35
−0.03
−0.48
−0.08
11
−0.24
−0.04
−0.37
−0.09
68
O.Yu. Khetselius
data by Penkin et al., as well as experimental data (from Refs. [18–27, 30–35]).
It is noteworthy sufficiently large error for values of the van der Waals constants,
obtained during calculating on the basis of formula (11), as well as within the
standard Hartree-Fock method.
The calculation shows the importance of the quality of the atomic wave functions (using an optimization and correct account for the exchange-correlation effects
and continuum “pressure” etc.) for an adequate description of the corresponding
constants.
In Table 2 there are listed the results of our calculation of the interatomic
interaction potential U(R) and the values of the local shift δω(R) (all values are in
atomic units) of the thallium hyperfine spectral line for different values of the
internuclear distance in the system Tl–He. For comparison, similar results of the
calculation of the potential U(R) and the local shift δω(R) with using the singleconfiguration Dirac-Fock method [25–27] are presented too.
In Table 3 we list the results of our calculation (as all values are given in atomic
units) interatomic interaction potential U(R) and the values of the local shift
δω(R) for pairs Tl–Kr, Tl–Xe.
Further in Table 4 we present our theoretical values (theory C) for the thallium
atom hyperfine line collisional shift at the temperature T = 700 K for a number of
Table 2 Local shift and
interatomic interaction
potential (in atomic units) for
the pair Tl–He
Dirac-Fock method
[25–27]
Our theory [18–21]
R δω(R) × 10
2
U(R) × 10
3
δω(R) × 10
2
U(R) × 10
3
5
4.22
7.6
3.92
6.93
6
1.34
2.0
1.21
1.76
7
0.329
0.44
0.27
0.38
8
0.0788
0.099
0.070
0.085
9
0.0032
0.024
0.0025
0.020
10 −0.0145
−0.076
−0.0131
−0.067
11
−0.0119
−0.008
Table 3 Local shift and
interatomic interaction
potential (in atomic units) for
the pair Tl–Kr, Xe (see text)
Tl–Kr (our theory)
Tl–Xe (our theory)
R δω(R) × 10
2
U(R) × 10
3
δω(R) × 10
2
U(R) × 10
3
5
−14.30
13.24
−19.05
18.31
6
−2.88
6.10
−8.22
5.95
7
−1.44
1.72
−2.67
2.04
8
−0.67
0.49
−1.52
0.65
9
−0.48
0.06
−0.74
0.01
10
−0.35
−0.03
−0.48
−0.08
11
−0.24
−0.04
−0.37
−0.09
68
O.Yu. Khetselius