Craig J. Sansonetti, Kenneth L. Andrew, and J. Verges, "Polarization, penetration, and exchange effects in the hydrogenlike nf and ng terms of cesium," J. Opt. Soc. Am. 71, 423-433 (1981)
We have made precision measurements of the 4f–ng transitions (n = 5–11) of cesium observed in emission by using high-resolution Fourier spectroscopy. The 2G fine-structure intervals are found to have normal ordering and a slightly greater than hydrogenic splitting. Each of the 2F and 2G series of levels can be represented by a polarization formula, but the effective dipole and quadrupole polarizabilities derived from the two series differ widely. By a series of calculations using Hartree–Fock wave functions, we show that penetration and core–valence exchange effects, which are neglected in the polarization formula, contribute up to 20% of the departure from the hydrogenic nf term value. To a good approximation this explains the observed discrepancy in polarizabilities. The effective polarizabilities we obtained are compared with values measured by other experimental techniques. The role of nonadiabatic effects in limiting the accuracy and utility of polarizabilities derived from spectral data is discussed. Based on our 2G data and the best available values for the 2S and 2F levels, we find the Cs i ionization energy to be 31406.4556(20) cm−1.
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Based on 4f2F5/2 = 24472.2269 cm−1 and 4f2F7/2 = 24472.0456 cm−1 as given by Eriksson and Wenåker.9 The uncertainties reported do not include any uncertainty in the 4f levels.
See text for a discussion of the fine-structure intervals.
Δ(nl2L) = [Rα2Z4/n3l(l + 1)].
Table 3
Comparison of Polarization Fits to the n–12f2F levels (n = 4–6)
See text for discussion of the calculated and inferred corrections.
Based on uncorrected 2G series.
Based on the 2G series modified by the calculated correction.
Levels taken from Ref. 9.
Levels determined from the 6p2P–nd2D transitions measured by Kleiman10 and the 6p2P levels of Eriksson et al.24 except 5d (Ref. 9) and 6d (Ref 24).
Series limit held fixed at this value.
P. V. Bevan, “Spectroscopic observations: lithium and caesium,” Proc. R. Soc. 86, 320–329 (1912).
J. R. McNally, Jr. et al., “High members of the principal series in caesium,” J. Opt. Soc. Am. 39, 57–58 (1949).
H. R. Kratz, “The principal series of potassium, rubidium, and cesium in absorption,” Phys. Rev. 75, 1844–1850 (1949). The value 31406.71 cm−1 reported in Atomic Energy Levels and attributed to Kratz is the limit with respect to the lowest hyperfine sublevel of the Cs i 6s2S1/2 ground state. The value listed here is with respect to the center of gravity of the ground state.
I. Johansson, “Spectra of the alkali metals in the lead-sulphide region,” Ark. Fys. 20, 135–145 (1961).
Ref. 10.
Ref. 24.
Ref. 9.
Table 7
Theoretical and Empirical Values of the Cs+ Dipole and Quadrupole Polarizabilities
A. V. Vinogradov, V. V. Pustovalov, and V. P. Shevelko, “Statistical theory of atom and ion polarizability,” Zh. Eksp. Teor. Fiz. 63, 477–481 (1972).
J. Heinrichs, “Simple calculation of polarizabilities, hyperpolarizabilities, and magnetic susceptibilities of atoms and ions,” J. Chem. Phys. 52, 6316–6319 (1970).
R. M. Sternheimer, “Electronic polarizabilities of alkali atoms. II,” Phys. Rev. 183, 112–122 (1969).
R. M. Sternheimer, “Quadrupole polarizabilities of various ions and the alkali atoms,” Phys. Rev. A 1, 321–327 (1970).
G. D. Mahan, “Modified Sternheimer equation for polarizability,” Phys. Rev. A 22, 1780–1785 (1980).
L. Pauling, “The theoretical prediction of the physical properties of many-electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space,” Proc. R. Soc. London A 114, 181–211 (1927).
K. Fajans and G. Joos, “Molrefraktion von Ionen und Molekülen im Lichte der Atomstruktur,” Z. Phys. 23, 1–46 (1924).
Ref. 25.
J. Pirenne and E. Kartheuser, “On the refractivity of ionic crystals,” Physica 30, 2005–2018 (1964).
Ref. 26.
Ref. 27. These are the effective polarizabilities α′d and α′q.
This work. These are the effective polarizabilities α′d and α′q.
The 2G levels were corrected by adding the penetration and exchange corrections from Table 4.
Based on 4f2F5/2 = 24472.2269 cm−1 and 4f2F7/2 = 24472.0456 cm−1 as given by Eriksson and Wenåker.9 The uncertainties reported do not include any uncertainty in the 4f levels.
See text for a discussion of the fine-structure intervals.
Δ(nl2L) = [Rα2Z4/n3l(l + 1)].
Table 3
Comparison of Polarization Fits to the n–12f2F levels (n = 4–6)
See text for discussion of the calculated and inferred corrections.
Based on uncorrected 2G series.
Based on the 2G series modified by the calculated correction.
Levels taken from Ref. 9.
Levels determined from the 6p2P–nd2D transitions measured by Kleiman10 and the 6p2P levels of Eriksson et al.24 except 5d (Ref. 9) and 6d (Ref 24).
Series limit held fixed at this value.
P. V. Bevan, “Spectroscopic observations: lithium and caesium,” Proc. R. Soc. 86, 320–329 (1912).
J. R. McNally, Jr. et al., “High members of the principal series in caesium,” J. Opt. Soc. Am. 39, 57–58 (1949).
H. R. Kratz, “The principal series of potassium, rubidium, and cesium in absorption,” Phys. Rev. 75, 1844–1850 (1949). The value 31406.71 cm−1 reported in Atomic Energy Levels and attributed to Kratz is the limit with respect to the lowest hyperfine sublevel of the Cs i 6s2S1/2 ground state. The value listed here is with respect to the center of gravity of the ground state.
I. Johansson, “Spectra of the alkali metals in the lead-sulphide region,” Ark. Fys. 20, 135–145 (1961).
Ref. 10.
Ref. 24.
Ref. 9.
Table 7
Theoretical and Empirical Values of the Cs+ Dipole and Quadrupole Polarizabilities
A. V. Vinogradov, V. V. Pustovalov, and V. P. Shevelko, “Statistical theory of atom and ion polarizability,” Zh. Eksp. Teor. Fiz. 63, 477–481 (1972).
J. Heinrichs, “Simple calculation of polarizabilities, hyperpolarizabilities, and magnetic susceptibilities of atoms and ions,” J. Chem. Phys. 52, 6316–6319 (1970).
R. M. Sternheimer, “Electronic polarizabilities of alkali atoms. II,” Phys. Rev. 183, 112–122 (1969).
R. M. Sternheimer, “Quadrupole polarizabilities of various ions and the alkali atoms,” Phys. Rev. A 1, 321–327 (1970).
G. D. Mahan, “Modified Sternheimer equation for polarizability,” Phys. Rev. A 22, 1780–1785 (1980).
L. Pauling, “The theoretical prediction of the physical properties of many-electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space,” Proc. R. Soc. London A 114, 181–211 (1927).
K. Fajans and G. Joos, “Molrefraktion von Ionen und Molekülen im Lichte der Atomstruktur,” Z. Phys. 23, 1–46 (1924).
Ref. 25.
J. Pirenne and E. Kartheuser, “On the refractivity of ionic crystals,” Physica 30, 2005–2018 (1964).
Ref. 26.
Ref. 27. These are the effective polarizabilities α′d and α′q.
This work. These are the effective polarizabilities α′d and α′q.
The 2G levels were corrected by adding the penetration and exchange corrections from Table 4.