The Spectrum of Doubly Ionized Tungsten (W III)

The spectrum of doubly ionized tungsten (W III) was produced in a sliding-spark discharge and recorded photographically on the NIST 10.7-m normal-incidence vacuum spectrograph in the 600–2680 Å spectral region. The analysis has led to the establishment of 71 levels of the interacting 5d4, 5d3 6s and 5d2 6s2 even configurations and 164 levels of the interacting 5d3 6p and 5d2 6s 6p odd ones. A total of 2636 lines have been classified as transitions between the 235 experimentally determined levels. Comparison between the observed levels and those calculated from matrix diagonalizations with least-squares fitted parameters shows an rms deviation of ±87 cm−1 for the even configurations and ±450 cm−1 for the odd ones.


Introduction
There are almost no experimental data on spectra or energy level analyses of ions that are isoionic or isoelectronic with W iii. Of all the third spectra of the 5</-group, only Lu m [1] with one 5d electron and Au in [2] with nine 5d electrons have been studied. The isoelectronic Ta ii has been analyzed [3] and a study of the (Srf-l-fo)* configurations in the second spectra [4] was done. However, no systematic studies of electronic configurations for the third spectra of this group of elements have been reported.
This is the furst analysis of the spectrum of doubly-ionized tungsten (W in) to be pubhshed. It is a four-electron spectrum and belongs to the third transition group of elements with 5d, 6s, and 6p electrons in the lowest configurations. The even configurations discussed below are 5d*, 5d^ 6s and 5d^ 6s^, and the odd configurations are 5d^ 6p and 5d^6s6p. The ground term is the ^D of the 5d* configuration. It is the only term of this configuration that does not overlap with the next even configuration, 5d^ 6s. The overlap of the configurations causes very strong configuration interaction (CI), especially between the odd ones. The level eigenvectors include different terms and configurations and produce a large number of transitions. Thus, W III is quite a complex spectrum.

Observations
The spectra were photographed in the region 600-2680 A with the National Institute of Standards and Technology (NIST) 10.7-m normal-incidence vacuum spectrograph equipped with a 1200-grooves/mm grating and having a plate factor of 0.77 A/mm. A sliding-spark light source with a quartz spacer was used. Peak currents of approximately 50, 200, and 500 A gave excellent separation of W ii, W iii, and W iv lines. In order to maintain the discharge, it was necessary to introduce helium at approximately 20 Torr. A watercooled copper hollow-cathode containing small pieces of germanium and silicon was operated at 500 mA with helium at 2 Torr to produce spectral lines of Cu, Ge, and Si at different ionization stages [5] which were used as reference lines. Part of one of the plates is presented in figure 1. Some of the spectrograms were measured at NIST and the remainder at the Instituto de Optica. The estimated uncertainty in the measurements is ±0.005 A.
Approximately 3700 lines were identified as belonging to Will, over 1000 lines to Wiv [they were the basis of the report entitled "Analysis of the Fourth Spectrum of Tungsten (W iv)"] [6], and about 3500 lines to W ii [7]. The analysis of W m has allowed us to classify 2636 lines (73% of the observed lines) as transitions between 71 even levels and 164 odd levels. The unclassified lines in the shorter wavelength region probably correspond to transitions of the 5d^ Ip and 5d^ 5/electron configurations, and the longer wavelength unclassified lines are probably 5d^ Is and 5d^ 6d transitions. Table 1 includes all of the W iii classified spectral lines, giving for each of them: wavelength (expressed in air above 2000 A), intensity, wavenumber, difference between the observed wavelength and the wavelength obtained from the final level values, and classification. The classification includes the integer portion of the energy level value and the / value for each of the two levels. Table 2 contains the wavelength, intensity and wavenumber for each of 953 unclassified lines identified as W in. We have omitted lines with intensities estimated at "1".

Analysis
In order to give some idea of the complexity of the electronic structure and the nimiber and the type of levels in the £5-coupling scheme, the predicted quintets, triplets, and singlets for the above mentioned configurations are presented in table 3. One should be aware that the coupling is far from pure LS. Most of the experimentally determined levels are characterized by a large number of observed transitions. This indicated a strong mixing between different terms and configurations which was later confirmed by the theoretical calculations.
The first goal of the analysis was the determination of the levels corresponding to the 'D ground term of the 5d'* lowest configuration. Then the energy levels of the other configurations could be established relative to the ground state fDo=0.00 cm~'). The 5d* ^D ground term is the only one that does not overlap the next even configuration, and it is one of the few terms whose designation in Z,5'-coupling is possible. The observed transitions to the even levels with predominantly quintet characteristics, 5d* 'D and 5d^CF)6s 'F, assisted in the determination of the 5d\'^F)6p 'G term and the 'Gf, (97039.60 cm-') and 'G5 (89630.99 cm"') of the 5d^ 6s 6p configuration. The rest of the levels have no good LS-coupling names. The energy range of these configurations is shown in figure 2. Tables 4 and 5 give the relevant information about the even and odd levels, respectively. The uncertainties of the optimized energylevel values are generally less than ±0.10 cm~' and no greater than ±0.20 cm~'. Included for each level in table 4 are the configuration and term (whenever possible), J value, level value, uncertainty, number of observed transitions to or from the level, difference between the observed and calculated energy level, and leading eigenvector percentages in LS coupling. Percentages less than 5% have been omitted. Table 5 differs from table 4 in that the first two columns (configuration and term) have been omitted. Only the three first leading percentages, when they are larger than 5%, have been included.
The present situation in the energy-level analysis of W III is shown in table 6. It gives a resume of the total number of observed and predicted levels, by J value, for the even and odd groups of configurations.

Theoretical Calculations
The low excitation stages of W ill correspond to configurations with 'id, 65', and dp electrons, giving rise to large numbers of levels. Calculations for several even and odd configurations were carried out using Cowan's Hartree-Fock program that includes relativistic corrections (HFR) [8]. When the analysis had provided a reasonable number of experimentally derived levels (more than 60%) we were able to try the parametric calculations (leastsquares fitting). Several coupling schemes were considered for the even and odd level systems. The average purities obtained in the most representative schemes are: Even Odd LS 53% 36% 51% 35% indicating that no coupling scheme is appropriate to name the levels. Nevertheless, parametric calculations were performed with the use of the L5-coupling scheme for both even and odd configurations. As expected, CI plays an important role for the structure of this spectrum.

Even Configurations
The Sc?* and 'Sd^ 6s configurations overlap over a wide energy range and, as a consequence, their levels interact very strongly. We first set up one Hamiltonian matrix for these two configurations, including the corresponding CI parameter. The fitting was not at all satisfactory, the mean deviation being greater than ±300 cm~'. Because of the unsatisfactory results and with the knowledge that the lowest levels of the next even configuration, 5d^ 6s^, appear at about 40000 cm""' overlapping the highest levels of 5d^ 6s, a Hamiltonian matrix including all three even configurations was used. A least-squares fit (LSF), including all of the known 71 even levels resulted in a mean deviation of ±87 cm~' between the observed and calculated values. The resulting LSF parameter values are presented in table 7, in which we also include the HFR values and the LSF/HFR ratios. The /3 parameter of 5d^ 6s^ was fixed at zero because the levels that help to determine its value are not known.
The resulting Z,5-percentage compositions of the levels are listed in table 4. More than half of these even levels have been designated in the LScoupling scheme. The remainder have compositions which do not allow us to make any assignments of term or configuration.

Odd Configurations
For the odd configurations, the situation is considerably more complicated. Most of the levels of 5d^ 6p and 5d^ 6s 6p are so mixed that there is no way of naming the levels. This is especially true for the intermediate and low /-valued levels. The matrix for the two configurations included, of course, the corresponding CI parameters. Many attempts were made in order to get a reasonable fit of the parameter values which could provide moderate differences between the observed and calculated energy levels. Although we have used the 164 experimentally determined levels (more than 80% of those predicted for the two odd configurations), the fitting has been almost impossible. This was especially true for the G\dp) parameters. They were, therefore, fixed at their respective HFR values for the final LSF. Table 8 contains the resulting LSF parameter values, those obtained from the HFR calculations, and the LSF/HFR ratios.
The L5-percentage compositions of the levels have been included in table 5. As can be observed for most of the levels, the leading percentages are less than 30, and there are no meaningful configuration assignments. For this reason, we have designated the levels by the energy value expressed in units of cm~'.
A mean deviation of ±450 cm~' between the observed and calculated levels was obtained. Some calculated levels differ from the observed ones by about 1000 cm-'. We included them in the LSF because they are real energy levels; the large number of observed transitions and the small level uncertainties confirm this.
The question arises whether there are any other odd configurations, e.g., 5d6s^6p, 5d^lp and/or 5d^ 5f, interacting with the two that we have identified. A study and discussion of the structure of the spectra of the third transition group, especially of configurations involving 5d, 6s, and 6p electrons, by theoreticians would be very helpful for future studies of spectra of the Pt group.