Improved Wavelengths and Energy Levels of Doubly-Ionized Argon (Ar III)

New measurements of Ar III wavelengths between 508 Å and 4183 Å are combined with measurements from the literature to find improved values for the energy of most of the known levels in Ar III. Parameters derived from fitting the new level energies to an LS-coupling model are presented along with eigenvector compositions of the levels. On the basis of this analysis new designations are recommended for several levels.

In 1987 Hansen and Persson [7] published a revised analysis of the Ar III spectrum that contained all possible levels of the 3s 2 3p 4 , 3s 3p 5 , 3s 0 3p 6 , 3s 2 3p 3 (4s , 4p, and 3d ) configurations. However, they include no observational data in their paper, and their energy values were given to only one decimal place. A recent paper by Whaling et al. [8], primarily concerned with the Ar I and Ar II spectra, identified about 60 lines of Ar III in the near ultraviolet. In the present paper we present improved level energies in Ar III derived from the best wavelengths in the literature, from new wavelengths measured expressly for this work, and from some older but hitherto unpublished wavelengths. A calculation of the Ar III level system in terms of LS -coupling suggests that several levels should be renamed.

Spectra
Wavelengths longer than 2250 Å were measured on 13 spectra from the archives of the National Solar Observatory (NSO); all were recorded on the 1 m Fourier Transform Spectrometer (FTS). Wavelengths between 2800 Å and 1850 Å were measured on spectra from the vacuum FTS at Lund University, Lund, Sweden. All spectra measured on the FTS were excited in an Ar discharge in a metal hollow-cathode source operating 0.13 kPa to 0.53 kPa (1 Torr to 4 Torr) and 0.1 kW to 1.0 kW in a cathode cavity 3 mm in diameter and 25 mm long. Several different cathode metals were used, and spectra were also recorded with Ne replacing the Ar to aid in the identification of Ar lines in the crowded metal spectrum. Further details of the spectral source will be found in Ref. [8].
Wavelengths shorter than 1850 Å were measured on spectrograms recorded at the National Bureau of Standards (NBS), now NIST, in 1971. A pulsed-rf source was used with halides of Na, Li, Ge, and Si during the study [9] primarily aimed at producing the spectra of singly and doubly ionized chlorine (Cl II and III). Argon was used to assist the discharge. The spectra were recorded photographically using the 10.7 m normal incidence vacuum spectrograph. Lines of C, N, O, Si, Ge, and Cu [10] were used as reference wavelengths for the reduction of the spectrograms by polynomial interpolation.
For all FTS spectra the wavenumber scale was calibrated using internal Ar II wavenumber standards derived from heterodyne measurements of CO molecular bands [11] as described in Ref. [8]. All FTS spectra were measured with the DECOMP [12] analysis program developed at the NSO by J. W. Brault. This program fits a Voigt profile to the observed feature and records the line-center wavenumber, peak amplitude, FWHM , and other parameters of the Voigt profile. The observed line-center wavenumber in vacuum has been converted to an observed air-wavelength (for > 2000 Å) using the expression for the index of refraction developed by Peck and Reeder [13] and appears in the first column of Table 1.
As a rough indication of the relative intensity of the Ar III lines as produced in the hollow cathode source, we list in column 2 of Table 1 the logarithm of the ratio (line amplitude)/(rms noise level) for lines measured on FTS spectra. The amplitude has not been corrected for the response of the spectrometer, and a comparison of two line amplitudes is meaningful only for neighboring lines. We are unable, of course, to include the intensity of lines in Table 1 not seen in our spectra, nor do we know the intensity of the far VUV lines measured at the NIST.
We have incorporated in our linelist a few additional wavelengths from the literature that establish important links between levels or that enable us to find values for levels that do not appear in our spectra. Five magnetic dipole lines measured by Bowen [14a,14b] in astronomical spectra, and a measurement in a planetary nebula by Kelly and Lacy [15], determine the spacing between several levels of the ground configuration; we have included their results in the least-squares fit of the levels to the lines on an equal footing with our own. de Bruin [2] has published values for several transitions that join the levels we have measured with levels in the 3d" 3 D, 3d' 3 S, 3d' 3 P, and 4d' 3 S terms. We have included de Bruin's measurements in Table 1 (identified with the notation D) and used them to find the energy of these levels.
It is important to establish the uncertainty of the measured wavelengths because the uncertainties play an important role in the weighted least-squares analysis that we used to extract level energies from the measured transition energies. Of the several factors that limit the accuracy of interferometric wavenumber measurements, the important ones for the FTS spectra we used are the line-width produced in the hollow-cathode, and the noise continuum of broad-range FTS spectra. For a line well-separated from its nearest neighbor, we assign a standard uncertainty (i.e., 1 standard deviation estimate) to the measured line position of ␦WN = 0.5(FWHM )/ (S /N ), where the full width at half maximum FWHM , the peak amplitude S , and the RMS background noise level N , are parameters generated by the DECOMP linefitting program. The factor 0.5 is a convenient approximation to the more precise, but difficult to evaluate, expression given by Brault [12]. For very strong lines (S /N Ն 10 3 ) the expression above may underestimate ␦WN , as discussed in Ref. [8], and we therefore set a lower limit ␦WN min = 0.001 cm Ϫ1 . ␦WN varies from line to line and increases with wavenumber because of the increasing Doppler width; it is typically less than 0.010 cm Ϫ1 .
For lines measured with the grating spectrometer the standard uncertainty in wavelength ␦WL VUV should be the same for all wavelengths, and we have set ␦WL VUV = Ϯ 0.001 Å by analyzing the internal consistency of the network of 209 interconnected transitions used in the weighted least-squares analysis. Starting with a conservative estimate of ␦WL VUV = Ϯ 0.004 Å, and giving each observed transition energy WN Obs the weight w i = (␦WN i ) Ϫ2 , we found that the residual ⌺(w i ϫ (WN Calc Ϫ WN Obs ) 2 )/⌺w i was determined by internal consistency alone. Only when the wavelength uncertainty was reduced below 0.0009 Å did the residual show a significant increase, and we have set ␦WL VUV = Ϯ 0.001 Å for all lines measured with the grating spectrometer. Table 1. Classified Ar III lines used for determining the level energies given in Table 2. Observed wavelength in the first column is in air for 2000 Å < < 10 000 Å; otherwise in vacuum. Calculated vacuum wavenumber in the second column is followed by its standard uncertainty in parentheses. The third column displays the difference between the observed (O) and calculated (C) wavenumber; the value 0.000 means < 0.0005. The meanings of the designations KL, B, D, B2, and * are given at the end of the  Table 1. Classified Ar III lines used for determining the level energies given in Table 2.
Observed wavelength in the first column is in air for 2000 Å < < 10 000 Å; otherwise in vacuum. Calculated vacuum wavenumber in the second column is followed by its standard uncertainty in parentheses. The third column displays the difference between the observed (O) and calculated (C) wavenumber; the value 0.000 means < 0.0005. The meanings of the designations KL, B, D, B2, and * are given at the end of the  Table 1. Classified Ar III lines used for determining the level energies given in Table 2.
Observed wavelength in the first column is in air for 2000 Å < < 10 000 Å; otherwise in vacuum. Calculated vacuum wavenumber in the second column is followed by its standard uncertainty in parentheses. The third column displays the difference between the observed (O) and calculated (C) wavenumber; the value 0.000 means < 0.0005. The meanings of the designations KL, B, D, B2, and * are given at the end of the  Table 2.
Observed wavelength in the first column is in air for 2000 Å < < 10 000 Å; otherwise in vacuum. Calculated vacuum wavenumber in the second column is followed by its standard uncertainty in parentheses. The third column displays the difference between the observed (O) and calculated (C) wavenumber; the value 0.000 means < 0.0005. The meanings of the designations KL, B, D, B2, and * are given at the end of the For the wavelengths of the magnetic-dipole transitions taken from the literature we have adopted the uncertainty estimates of the original authors. The wavelengths measured by de Bruin [2] have been assigned a standard uncertainty of 0.02 Å, a value suggested by a comparison of his values with those measured on FTS spectra.

Line Identification
The hollow-cathode spectra contain Ar I, II, and III lines, plus lines from two or more stages of ionization of the cathode element. An Argon linelist was extracted from this mixture by finding lines common to spectra from two or more cathodes. Ar I and II lines, identified using the linelist published in Ref. [8], were removed and the remaining Ar lines were sufficiently sparse that the rough Ar III wavelengths compiled in Refs. [16] could be used to classify many of the remaining lines. In addition, we used transition energies computed from the Ar III level energies of Hansen and Persson [7] to identify singlet-singlet transitions not included in Refs. [16]. This initial list of classified Ar III transitions was further refined after we had obtained precise Ar III level energies and were able to calculate accurate transition energies and search our observed spectra with a small (Ϯ 0.010 cm Ϫ1 ) search window.

Level Energies
Level energies were derived from our measured transition energies with the CLEVEL least-squares code of Palmer and Engleman [17] that solves a set of overdetermined linear equations (of the form E b Ϫ E a = WN ba ) for the most probable energy values and their standard uncertainties, E i Ϯ ␦E i . It is necessary to pay careful attention to the uncertainty assigned to each measurement.
The Ar III level energy values and their uncertainties, E i Ϯ ␦E i produced by CLEVEL are listed in Table 2. For each input line, CLEVEL evaluates the calculated value of the transition energy from WN ba,Calc = E b Ϫ E a (see column 2 of Table 1) and the standard uncertainty of this calculated wavenumber which appears in parentheses following WN Calc . We list also the difference WN Obs Ϫ WN Calc in column 3 of Table 1.
Note that the standard uncertainty of the calculated wavenumber (from the appropriate element of the covariant matrix) is often very much smaller than the standard uncertainty of either level involved in the transition with respect to various other levels, including the ground level. These small uncertainties go with transitions between high levels of the same multiplicity and core configuration, and the difference in level energies depends only on the relative energy of the two levels and is independent of VUV transitions to the ground term. Any other transition between two such levels should likewise have a small standard uncertainty, and for this reason we have listed the level energies in Table 2 with more decimal places than appears to be justified by the standard uncertainty of the absolute energy of a level. For a calculated transition energy between dissimilar levels that are tied together only by transitions down to the ground term and back up again (e.g., between a quintet level and a triplet level), the standard uncertainty is much larger. For dissimilar levels the standard uncertainty should be estimated by combining in quadrature the uncertainty listed in Table 2 for the absolute energy of the initial and final level of the transition.

Theory
The ground state of doubly-ionized argon has the electron configuration 1s 2 2s 2 2p 6 3s 2 3p 4 , which gives rise to 3 P, 1 D, and 1 S terms. All of the observed excited configurations (except 3s 3p 5 and 3p 6 ) result from the excitation of a 3p electron into a higher orbital to form 3p 3 nl configurations. The parent configuration, 3p 3 , of Ar IV forms the terms 4 S o , 2 D o , and 2 P o . The arrangement of levels in all of the 3p 3 nl configurations given herein (except 3p 3 3d ) is dominated by the separation of the parent terms.
In Table 3 we give the parameter set derived from a least-squares fit of the levels of the 3s 3p 5 , 3s 2 3p 3 (3d and 4d ) configurations with the HFR Cowan code [18]. Also included are the HFR (relativistic approximations to the Hartree-Fock) values obtained and the ratio of the fitted value to that of the HFR value. Table 4 gives the eigenvector composition in the LS -coupling scheme of all of the levels of these three configurations including those for which we were unable to obtain experimental values. It is evident from the table that the 3p 3 4d configuration is only very slightly perturbed by the 3s 3p 5 and 3p 3 3d configurations; the coupling appears to be very close to LS. There is very strong parental mixing among the three 3 D terms of the 3p 3 3d configuration, as was seen by Hansen and Persson [7]. Because of the difference between their parametric fit and ours, we have labeled the 3 D terms near 156 900 and 187 800 cm Ϫ1 as having the 4 S and 2 D parents, respectively, while they did the reverse.
It should be noted that Hansen and Persson [7] did a parametric fit to the 3s 3p 5 + 3s 2 3p 3 (3d + 4s) configurations. On the basis of that fit, they named the terms at about 189 000 cm Ϫ1 and 214 000 cm Ϫ1 as 3d" 3 P and 3d' 3 P, respectively, in agreement with our designation  for these terms. However, they found such strong mixing of the 3p 3 ( 2 D) 3d 3 P and the 3p 3 ( 2 P) 4s 3 P eigenvectors in the term at 214 000 cm Ϫ1 that it may be misleading to label this term with any specific core designation. Thus, the term at 214 000 cm Ϫ1 , although labeled 3d' 3 P implying a 2 D core, takes part in 17 known optical transitions, and, in all 17 cases, the transition partner has a well-established 2 P core; no transition to a level with a 2 D core has been reported.
It was shown that in Cl II [9] the lowest odd 1 P 1 level had only 33 % of 3s 3p 5 1 P and 57 % of 3p 3 ( 2 D) 3d 1 P 1 and that level was given the latter designation. As shown in Table 4, the level at 144 022 cm Ϫ1 has only 43 % of 3s 3p 5 1 P and 50 % of 3s 2 3p 3 ( 2 D) 3d 1 P. However, because the next higher 1 P level at 219 908 cm Ϫ1 also has a larger eigenvector percentage of 1 P from the ( 2 D) 3d configuration, we have designated the lower level as 3s 3p 5 1 P.
Hansen and Persson [7] have given calculations for the 3p 4 and the 3p 3 4p configurations. With only minor exceptions, they find almost no interaction between levels of different parentage in the 3p 3 4p configuration.

Ionization Energy
In their paper on ionization energies of singly ionized rare earths, Sugar and Reader [19] showed that it is possible to use the difference in effective quantum numbers of unperturbed adjacent members of an ns series to calculate an ionization energy. Using published values of the ionization energies and 3p N 4s and 3p N 5s levels of Ca III and Sc III, we arrive at an average of ␦n = 1.0312. With this value and the experimentally determined value of ␦T = E (5s 5 S 2 ) Ϫ E (4s 5 Table 4. Percent composition of the 3s 3p 5 , 3s 2 3p 3 3d, and 3s 2 3p 3 4d levels derived from a least-squares fit of the parameters to the levels of these three configurations Table 4. Percent composition of the 3s 3p 5 , 3s 2 3p 3 3d, and 3s 2 3p 3 4d levels derived from a least-squares fit of the parameters to the levels of these three configurations-Continued