Craig J. Sansonetti, Kenneth L. Andrew, and J.-F. Wyart, "Spectrum and energy levels of singly ionized cesium. II. Interpretation of fine and hyperfine structures," J. Opt. Soc. Am. B 5, 2076-2086 (1988)
The theoretical interpretation of Cs ii has been extended and now includes the 5p5ns (n = 6–12), 5p5np (n = 6–8), 5p5nd (n = 5–11), 5p5nf (n = 4–8), 5p5ng (n = 5–10), and 5p5nh (n = 6–8) configurations. Most levels are well represented in the single-configuration approximation when far configuration interactions are included through effective electrostatic parameters. Explicit interactions of low-lying 5p5nd + 5p5(n + 1)s configurations have been determined. For most configurations, good jK coupling is found. Purities of the levels in jK coupling and the LS composition of the eigenvectors are given. The intermediate-coupling eigenvectors have been used to calculate magnetic-dipole hyperfine-splitting factors, and these are compared with 167 experimentally determined values from our earlier work.
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Magnetic Dipole Hyperfine-Splitting Constants A (in 10−3 cm−1) for Energy Levels of 5p5nl in Pure jK Coupling Calculated from Hyperfine-Splitting Parameters Fitted in Cs iii
j
[K]
J
p5s
p5p
p5d
p5f
p5g
p5h
3/2
[1/2]
1
29.60
−17.79
3/2
[3/2]
1
44.47
32.65
8.89
−26.68
2
26.68
19.56
5.33
−16.00
3/2
[5/2]
2
24.91
15.42
1.18
−17.79
3
17.79
11.01
0.85
−12.70
3/2
[7/2]
3
17.15
9.54
−0.64
−13.34
4
13.34
7.41
−0.50
−10.37
3/2
[9/2]
4
13.05
6.72
−1.20
5
10.67
5.50
−0.98
3/2
[11/2]
5
10.51
5.13
6
8.89
4.34
3/2
[13/2]
6
8.80
7
7.63
1/2
[1/2]
1
125.29
−41.70
1/2
[3/2]
1
104.34
−62.64
2
62.63
−37.59
1/2
[5/2]
2
58.47
−41.77
3
41.76
−31.31
1/2
[7/2]
3
41.74
−31.32
4
31.31
−24.36
1/2
[9/2]
4
30.63
−25.04
5
25.05
−20.49
1/2
[11/2]
5
24.67
6
20.86
Table 2
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5nh Configurations of Cs ii
Deviations are in inverse centimeters for energies (ΔE = Eexp − Eth) and in 10−3 cm−1 for hfs A factors. The Ath values are from Table 1.
Experimental A factor of questionable reliability.1
Table 4
Comparison between Experiment and Theory for Energy Levels and A Factors of 5p5ng Configurations in Cs iia
Deviations are in inverse centimeters for energies (ΔE = Eexp− Eth) and in 10−3 cm−1 for hfs A factors (ΔA = Aexp − Ath). The Ath values are from Table 1.
Both levels of the pair 3/2[5/2] were omitted from the least-squares fit. The deviations of the energies and A factors are consistent with a perturbation by 5p56d 1/2[5/2] levels.
Experimental A factor of questionable reliability.1
Both levels of the pair 3/2[5/2] were omitted from the least-squares fit. The deviations of the energies and A factors are consistent with a perturbation by 5p57d 1/2[5/2]levels.
Table 5
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5ng Configurations of Cs ii
The energies and deviations ΔE = Eexp − Eth are in inverse centimeters. The hfs A factors and their deviations are in 10− 3 cm−1. Ref. 1.
Energy calculated from parameters of Table 7.
Calculated from monoelectronic hyperfine-structure parameters of Table 11.
The corresponding experimental A factor was omitted from the least-squares determination of the monoelectronic hyperfine-structure parameters.
Experimental A factor of questionable reliability.1
Table 7
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5nf Configurations of Cs ii
Ratio of G4 to G2 constrained to be 1.4 on the basis of ab initio calculation using the parametric potential method.
Parameter fixed at indicated value.
Table 8
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5np Configurations of Cs ii
The energies and deviations ΔE = Eexp − Eth are in inverse centimeters. The hfs A factors and their deviations are in 10−3 cm−1. Ref. 1.
Energy calculated from parameters of Table 10.
Calculated from monoelectronic hfs parameters of Table 11.
Basis states of 5p5ns are indicated with asterisks.
The corresponding experimental energy was omitted from the least-squares analysis of the fine structure.
The corresponding experimental A factor was omitted from the least-squares determination of the monoelectronic hfs parameters.
Experimental A factor of questionable reliability.1
Table 10
Fitted Energy Parameters and Standard Errors (in cm−1) for the Configurations 5p5ns and 5p5nd of Cs ii
Parameter fixed at indicated value.
The constraint ζ5p[5p5(n + 1)s] = ζ5p(5p5nd) was imposed on the fit.
The ratio R1(pd, sp):R2(pd, ps) was constrained to the ratio obtained in a Hartree–Fock calculation.
Table 11
Monoelectronic Hyperfine-Structure Parameters Fitted for the 5p5nl Configurations of Cs iia
Except where a standard error is indicated in parentheses, the parameters are constrained for a given electron to the theoretical ratios discussed in the text. Units are 10−3 cm−1.
Parameter fixed at the indicated value.
Standard deviation of A. See text.
The standard deviation 〈ΔA〉 was calculated for the levels of 5p5nd and 5p5(n + 1)s taken together. Some experimental A factors have been omitted from the fitting and calculation of 〈ΔA〉. See Table 9.
Parameter constrained to be equal to the corresponding parameter of 5p56d.
Tables (11)
Table 1
Magnetic Dipole Hyperfine-Splitting Constants A (in 10−3 cm−1) for Energy Levels of 5p5nl in Pure jK Coupling Calculated from Hyperfine-Splitting Parameters Fitted in Cs iii
j
[K]
J
p5s
p5p
p5d
p5f
p5g
p5h
3/2
[1/2]
1
29.60
−17.79
3/2
[3/2]
1
44.47
32.65
8.89
−26.68
2
26.68
19.56
5.33
−16.00
3/2
[5/2]
2
24.91
15.42
1.18
−17.79
3
17.79
11.01
0.85
−12.70
3/2
[7/2]
3
17.15
9.54
−0.64
−13.34
4
13.34
7.41
−0.50
−10.37
3/2
[9/2]
4
13.05
6.72
−1.20
5
10.67
5.50
−0.98
3/2
[11/2]
5
10.51
5.13
6
8.89
4.34
3/2
[13/2]
6
8.80
7
7.63
1/2
[1/2]
1
125.29
−41.70
1/2
[3/2]
1
104.34
−62.64
2
62.63
−37.59
1/2
[5/2]
2
58.47
−41.77
3
41.76
−31.31
1/2
[7/2]
3
41.74
−31.32
4
31.31
−24.36
1/2
[9/2]
4
30.63
−25.04
5
25.05
−20.49
1/2
[11/2]
5
24.67
6
20.86
Table 2
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5nh Configurations of Cs ii
Deviations are in inverse centimeters for energies (ΔE = Eexp − Eth) and in 10−3 cm−1 for hfs A factors. The Ath values are from Table 1.
Experimental A factor of questionable reliability.1
Table 4
Comparison between Experiment and Theory for Energy Levels and A Factors of 5p5ng Configurations in Cs iia
Deviations are in inverse centimeters for energies (ΔE = Eexp− Eth) and in 10−3 cm−1 for hfs A factors (ΔA = Aexp − Ath). The Ath values are from Table 1.
Both levels of the pair 3/2[5/2] were omitted from the least-squares fit. The deviations of the energies and A factors are consistent with a perturbation by 5p56d 1/2[5/2] levels.
Experimental A factor of questionable reliability.1
Both levels of the pair 3/2[5/2] were omitted from the least-squares fit. The deviations of the energies and A factors are consistent with a perturbation by 5p57d 1/2[5/2]levels.
Table 5
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5ng Configurations of Cs ii
The energies and deviations ΔE = Eexp − Eth are in inverse centimeters. The hfs A factors and their deviations are in 10− 3 cm−1. Ref. 1.
Energy calculated from parameters of Table 7.
Calculated from monoelectronic hyperfine-structure parameters of Table 11.
The corresponding experimental A factor was omitted from the least-squares determination of the monoelectronic hyperfine-structure parameters.
Experimental A factor of questionable reliability.1
Table 7
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5nf Configurations of Cs ii
Ratio of G4 to G2 constrained to be 1.4 on the basis of ab initio calculation using the parametric potential method.
Parameter fixed at indicated value.
Table 8
Fitted Energy Parameters and Standard Errors (in cm−1) for 5p5np Configurations of Cs ii
The energies and deviations ΔE = Eexp − Eth are in inverse centimeters. The hfs A factors and their deviations are in 10−3 cm−1. Ref. 1.
Energy calculated from parameters of Table 10.
Calculated from monoelectronic hfs parameters of Table 11.
Basis states of 5p5ns are indicated with asterisks.
The corresponding experimental energy was omitted from the least-squares analysis of the fine structure.
The corresponding experimental A factor was omitted from the least-squares determination of the monoelectronic hfs parameters.
Experimental A factor of questionable reliability.1
Table 10
Fitted Energy Parameters and Standard Errors (in cm−1) for the Configurations 5p5ns and 5p5nd of Cs ii
Parameter fixed at indicated value.
The constraint ζ5p[5p5(n + 1)s] = ζ5p(5p5nd) was imposed on the fit.
The ratio R1(pd, sp):R2(pd, ps) was constrained to the ratio obtained in a Hartree–Fock calculation.
Table 11
Monoelectronic Hyperfine-Structure Parameters Fitted for the 5p5nl Configurations of Cs iia
Except where a standard error is indicated in parentheses, the parameters are constrained for a given electron to the theoretical ratios discussed in the text. Units are 10−3 cm−1.
Parameter fixed at the indicated value.
Standard deviation of A. See text.
The standard deviation 〈ΔA〉 was calculated for the levels of 5p5nd and 5p5(n + 1)s taken together. Some experimental A factors have been omitted from the fitting and calculation of 〈ΔA〉. See Table 9.
Parameter constrained to be equal to the corresponding parameter of 5p56d.