The Fifth Spectrum of Praseodymium

Abstract

Twelve spectral lines of quadruply-ionized praseodymium in the region 840 to 2250 Å are reported. Five terms (4f²F, 5d ²D, 6s ²S, 6p ²P, and Is ²S) and the hyperfine splitting of the 6s ²S term are given. A calculation of the principal ionization energy (Pr⁴⁺ → Pr⁵⁺) leads to a value of 57.44 eV with an estimated uncertainty of ±0.05 eV.

1. Introduction

The one-electron Cs I isoelectronic sequence has been observed through Ce IV. The present work extends this to Pr V. Several orbital properties such as quantum defect, doublet splitting, and term energy intervals were found to vary in a regular way through the Cs I sequence. These regularities have been used here to verify the analysis of Pr V.

This is the first example of the structure of the fifth spectrum of a rare earth. The regularities in the level structure of the 4f period of atoms in lower stages of ionization indicate that Pr V may serve as a guide to the interpretation of the more complex fifth spectra of the rare earths.

2. Experimental Procedure

The spectrum plates obtained in the investigation of Pr IV [1]¹ were found to contain several very strong and fairly isolated lines in a 500-A spark exposure which showed no trace in the 50-A exposure. These could only be interpreted as high excitation Pr IV lines, which is unlikely because of their unusual strength, or Pr V lines. Unfortunately, the sliding-spark light source [2] used in this experiment does not suppress Pr IV relative to Pr V. Therefore, the assignment of these lines to Pr V could not be based exclusively on excitation separation.

Exposures were made in the first order of a 35-ft Eagle vacuum spectrograph at a reciprocal dispersion of 0.78 Å/mm. For further corroboration of the lines of the 6s–6p and 6p–7s transitions and for a better intensity relationship between these lines, exposures were also made in the first order of a 2.2-meter Eagle vacuum spectrograph at a reciprocal dispersion of 2.75 Å/mm. Calculated and measured wavelengths of C, N, O, Si, Ge, and Cu in various stages of ionization were used as standards of calibration [3–7]. The estimated wavelength uncertainty for all lines, except those at 1958 Å, is ±0.005 Å. Those at 1958 Å have an estimated uncertainty of ±0.003 Å.

3. Wavelengths and Energy Levels

A list of the classified lines of Pr V, including visual estimates of their relative intensities, wavenumbers, and classifications is given in table 1. The list of energy levels of Pr V derived therefrom is given in table 2. It includes the level designation, the observed position with estimated uncertainty, the fine structure splitting where appropriate, and the hyperfine structure splitting for the 6s ²S term. The hyperfine splitting of the 7s level is calculated to be about 1. cm⁻¹. Because the width of the 6p–7s lines is about 2. cm⁻¹, this splitting could not be observed.

Table 1.

Observed spectral lines of Pr V

Wavelength (Å)	Intensity	Wavenumber (cm−1)	Classification
843.783	200	118 513.9	$4f{}^2{\text{F}}_{5/2}^{\circ }-5d{}^2{\text{D}}_{5/2}$
865.902	7000	115 486.5	$4f{}^2{\text{F}}_{7/2}^{\circ }-5d{}^2{\text{D}}_{5/2}$
869.170	5000	115 052.3	$4f{}^2{\text{F}}_{5/2}^{\circ }-5d{}^2{\text{D}}_{3/2}$
869.662	80	114 987.2	$5d{}^2{\text{D}}_{3/2}-6p{}^2{\text{P}}_{3/2}^{\circ }$
896.654	1000	111525.7	$5d{}^2{\text{D}}_{5/2}-6p{}^2{\text{P}}_{3/2}^{\circ }$
922.290	750	108 425.8	$5d{}^2{\text{D}}_{3/2}-6p{}^2{\text{P}}_{1/2}^{\circ }$
1234.070	250	81 032.7	$6p{}^2{\text{P}}_{1/2}^{\circ }-7s{}^2{\text{S}}_{1/2}$
1342.775	250	74 472.6	$6p{}^2{\text{P}}_{3/2}^{\circ }-7s{}^2{\text{S}}_{1/2}$
1958.088	200	51 070.23	$6s{}^2{\text{S}}_{1/2}\left(\text{F}=2\right)-6p{}^2{\text{P}}_{3/2}^{\circ }$
1958.201	400	51 067.28	$6s{}^2{\text{S}}_{1/2}\left(\text{F}=3\right)-6p{}^2{\text{P}}_{3/2}^{\circ }$
2246.759	300	44 508.56	$6s{}^2{\text{S}}_{1/2}\left(\text{F}=2\right)-6p{}^2{\text{P}}_{1/2}^{\circ }$
2246.900	300	44 505.76	$6s{}^2{\text{S}}_{1/2}\left(\text{F}=3\right)-6p{}^2{\text{P}}_{1/2}^{\circ }$

Table 2.

Energy levels of Pr V

Designation	J	Energy (cm−1)	Uncertainty (cm−1)	Splitting (cm−1)
4f2F°	2½	0.0		3027.4
	3½	3 027.4	± 1.0
5d 2D	1½	115 052.3	1.0	3461.5
	2½	118 513.8	1.0
6s 2S (F = 2)	½	178 969.4	1.5	2.95
(F=3)	½	178 972.3	1.5
6p 2P°	½	223 478.1	1.5	6561.4
	1½	230 039.5	1.5
7s 2S	½	304 511.5	2.0

The interpretation of the observed spectral lines was begun with an accurate estimate of ζ4f obtained from the 4f6s configuration of Pr³⁺. This value allowed an unambiguous interpretation of the intense 4f – 5d lines. Using this 5d doublet splitting, we were able to interpret the almost-equally prominent 5d–6p lines. In figure 1, the ratios of the spin-orbit splitting, ΔT to Z_a are plotted against Z_a in the Cs I isoelectronic sequence. The spin-orbit splittings are those of the 4f²F, 5d²D, and 6p²P terms, and Z_(l is the positive charge on the ion remaining after the removal of the outer electron. The values for Pr V provide smooth extensions of the curves drawn through the previously known points.

Figure 1. Variation of $\frac{\mathrm{\Delta }\text{T}}{{\text{Z}}_{\text{a}}}$ along the Cs I isoelectronic sequence where ΔT equals spin-orbit splittings of the 4f ²F, 5d ²D, and 6p ²P terms.

Note the anomalous position of the Ba II 4f²F point. References for the plotted values are Cs I; H. Kleiman, J. Opt. Soc. Am. 52, 441 (1962), Ba II; E. Rasmussen, Zeit. f. Phys. 83, 404 (1933), La III; see ref. [10]. Ce IV; see ref. [8].

The combinations of the 6p ²P term with the 6s and 7s ²S levels were not so easily distinguished because of the comparable strength of numerous Pr IV lines in the same spectral region. Evidence for our interpretation of these lines in terms of the behavior of the 6s – 7s energy interval is presented in figure 2 where the observed value for Pr V follows the smooth variation of this interval in the Cs I isoelectronic sequence.

Figure 2. Variation of the ratio of separation of the 6s ²S and 7s ²S terms to Z_a along the isoelectronic sequence.

For references for the plotted values see the caption of figure 1.

In figure 3 we present the sequential behavior of the quantum defect, n – n_a, for each of the observed terms. These points are interrelated since the quantum defects depend on the positions of the terms relative to the ionization limit which in turn is determined by the positions of the ns ²S terms. Therefore the agreement of the Pr V experimental values with the isoelectronic sequence is a strong confirmation of the analysis of this spectrum.

Figure 3. Variation of quantum defect of the center of gravity of the 4f, 5d, 6p, 6s, and 7s terms along the Cs I isoelectronic sequence.

Note the anomalous position of the Ba II 4f point. The error bar on the 7s ²S Pr V point indicates the variation in the quantum defect for a change in the ionization energy of ±400 cm⁻¹. For references for the plotted values see the caption of figure 1.

Because of the noticeable departure of the Ba II 4f²F points in figures 1 and 3, we have examined the nf series of Ba II in detail and found that the behavior of (n – n_a) versus $1/n_a^2$ is quite different from that of the same series in Cs I and La III. It is our impression that this part of the Ba II analysis bears reexamination.

The value of the spin-orbit parameter, ζ_4f, derived from the 4f²F term of Pr V equals 865.0±0.3 cm⁻¹. From the 4f6s configuration of Pr IV, one finds [1] ζ_4f= 860.8 ±0.2 cm⁻¹. The difference is due to a slight shielding of the 4f electron by the 65 electron in Pr IV. The same order of magnitude of this effect can be found in the comparison of the same configurations of Ce IV and Ce III [8, 9]. However, the value of ζ_4f from La III [10] is slightly smaller than that obtained from 4f6s of La II [11]. This is probably due to a small perturbation in La II where configurations of the same parity are very close.

4. Ionization Potential

In table 2 of the recent paper of Sugar and Reader [12] values of Δn_a = n_a(7s) − n_a(6s) derived from several 4f^Nns series in the region of the rare earths are given which show that a value of Δn_a= 1.050±0.005 cm⁻¹ can be used with confidence to compute the ionization energies of rare earths. The values listed are for singly, doubly and triply ionized species. With this value and the experimentally determined value of ΔT= E(7s)−E(6s) =125540.4 cm⁻¹, the equation

$$\mathrm{\Delta }T=\frac{Z_a^{2}R}{{\left[n_a\left(6s\right)\right]}^2}-\frac{Z_a^{2}R}{{\left[n_a\left(6s\right)+\mathrm{\Delta }{n}_a\right]}^2},$$

where Z_n = 5, was solved for n_a(6s). The corresponding value of $T\left(6s\right)=Z_a^{2}R/{\left[n_a\left(6s\right)\right]}^2,$ when added to the level value of 6s ²S gives the ionization potential as 463 350 cm⁻¹. On the basis of the uncertainty in the value of Δn_a, the value of the ionization potential is given as 463 400 ±400 cm⁻¹ (57.44 ±0.05 eV).

In figure 3, the error bar on the 7s ²S, Pr V point shows the extent of the possible change in the position of that point for a change in the ionization energy of the stated uncertainty. This gives us confidence that the value of Δn_a used is valid for highly ionized rare earths.

5. Hyperfine Splitting of the 6s Term

The hyperfine splitting of the 6s ²S term of 2.95 ± 0.05 cm⁻¹ leads to a value for the splitting factor of the 65 electron (a6s) of 0.98₃±0.01₇ cm⁻¹. It is of interest to compare this value with a_6s = 0.639 ± 0.007 cm⁻¹ for Prill given by Reader and Sugar [13]. Relating these splittings according to the Goudsmit-Fermir-Segré formula, we get

$${\left[\frac{a_{6s}}{Z_a^2}\cdot \frac{n_a^3}{d{n}_a/dn}\right]}_{ Pr \text{v}}={\left[\frac{a_{6s}}{Z_a^2}\cdot \frac{n_a^3}{d{n}_a/dn}\right]}_{\text{Pr III}}$$

Insertion of the experimental values in the above equation gives a_6s (Pr V)= 1.03s ±0.032 cm⁻¹, which leads to an expected splitting of 3.11 ±0.10 cm⁻¹. This compares quite well with the experimentally determined value listed above.