Analysis of the Spectrum of Doubly Ionized Molybdenum (Mo III)

The spectrum of doubly ionized molybdenum (Mo III) was produced in a sliding spark discharge and recorded photographically on the NIST 10.7-m normal incidence spectrograph in the 800-3250 Å spectral region. The analysis has led to the establishment of 76 levels of the interacting 4d4, 4d3 5s and 4d2 5s2 even configurations, 73 levels of the interacting 4d3 5d and 4d3 6s even configurations, and 181 levels of the interacting 4d3 5p and 4d2 5s5p odd configurations. Approximately 3100 lines have been classified as transitions between these experimentally determined levels. Comparison between the observed levels and those calculated from matrix diagonalizations with least-squares fitted parameters shows standard deviations of 44, 33, and 183 cm−1, respectively, for the levels of the three sets of configurations.


Introduction and Observations
In 1988 we published an analysis of the spectrum of doubly ionized molybdenum (Mo III) [1] in which a total of 679 spectral lines were classified. These were transitions between 54 levels of the 4^?" and Ad^ 5s even configurations and 65 levels of the Ad^ 5p odd configuration in that work.
We have now made additional observations in the range of 800-2100 A to supplement our earlier data which covered the region 1100-3250 A. These new observations were made under conditions similar to the previous ones but extended into the short wavelength region. The spectra were photographed on the NIST 10.7-m normal-incidence vacuum spectrograph equipped with a 1200-1/mm grating blazed at 1200 A. A sliding spark operated at various excitation conditions was used to pro- ' Retired. duce the spectra. The intensity distribution along each line and the behavior of the line intensity at 50, 80, and 150 A peak currents were used to find optimum conditions for the third spectrum. Reference wavelengths of Cu, Ge, and Si [2] were obtained with a water-cooled hollow cathode discharge. Details about the experimental methods are the same as given in reference [1]. Approximately 5000 of the observed lines had Mo iii character. The wavelength uncertainty of the observed lines is estimated to be ±0.005 A.

Analysis
The spectrum is complex due to the open 4dshell structure of the doubly ionized atom; the ground configuration is 4d*. The large number of levels in the seven lowest configurations leads to many possible transitions. With the Cowan series of atomic structure programs [3], which include Hartree-Fock calculations with relativistic corrections (HFR) and matrix diagonalizations, we were able to predict the complete electric dipole spectrum. This included both the (4d*+4d^ 5s +4d^ 5s^)-(4d^ 5p +4d^ 5s5p) and the 4d^ 5p-{4d^ 5d+4d^ 6s) transition arrays. The observed line list and the line intensities were then compared to the predictions in order to extend the earlier analysis [1]. Calculations were made for each of the following interacting configuration groups: (I) 4d^+4d''5s+4d^5s\ (2) 4d^5d + 4d^ 6s, and (3) 4d^ 5p +4d^ 5s5p. The resulting values for the radial integrals were adjusted by a least squares fit to the known levels, and improved as new levels were found.
This led to the identification of all 34 energy levels of 4d* and all 38 energy levels of 4d^ 5s. The values of four of the previously reported levels were incorrect and have been replaced. They are the ^Po2, 'l6, 'D22 and 'So2 levels of'W". We use the index numbers assigned by Nielson and Koster [4] to distinguish recurring terms in the d" configurations. These index numbers were used by Martin et al. [5] in their compilation of atomic energy levels of the rare earth elements. All other previously reported level values were adjusted with the new data. Of the nine predicted levels of 4d^ 5s^, only those of the 'F, and the 'G4 have been located. The 4d^C}i)5d ^Kg level has not been located. One strong transition is expected, but there are no appropriate lines (intensity, range,...) to establish it with certainty. For the 4d^(^¥l)5d 'K7, we have found a tentative energy value based on transitions with 4d\^U)5p % and ^Ifi at 1934.709 and 1808.672 A, respectively. Because the second transition would be coincident with a second order Mo iv line, we consider the evidence for the level questionable.
We have found 54 levels of the 4c?' 5d configuration and 19 of 4d^ 6s. With the exception of 4dXF)5d 'D, all of the levels based on the 4dXF) parent have been found. These two configurations overlap extensively and similar terms of each configuration are very close. This accounts for the strong configuration interaction (CI). This may be seen in figure 1 where the levels are connected to show the LS terms. Table 1 contains the 149 known levels of the five lowest even configurations, including for each level the configuration, term, J value, level value, difference between the observed level value and that obtained from the least-squares fits (O-C), and the leading eigenvector percentages in the Z,5-coupling scheme. The uncertainty in each level value depends on the number of combinations and on the wavelength region where the combinations appear. The uncertainties of the optimized energy-level values are generally less than ±0.10 cm"^' and no greater than ±0.20 cm~'. The average LS purities of the (4rf'*-l-4rf' 5s+4d^ 5s^) and (4rf' 5d+4d' 6s) groups of configurations are 83% and 59%, respectively. Although 15 levels of 4d^ 5d and two of 4d^ 6s have their largest eigenvector components less than 50%, only five levels of 4J' 5d have been given LS names that are not those of the largest eigenvector component. Table 2 contains the odd parity energy levels. Sixty-five levels of 4d^ 5p were included in the previous publication [1], but we have now found all 110 levels of this configuration. Seventy-one of the 90 predicted levels of 4c?^ 5s 5p were found through transitions with 4d^ 5s and 4d^ 5s^ levels in the vicinity of 1800 A. The lowest levels of 4d^ 5s 5p overlap with the highest levels of 4d^ 5p. The structure of the 4d^ 5s 5p configuration is represented in figure 2. The combined average LS purity of the levels of these two odd configurations is 63%. Only four of the levels have been given LS names that are not associated with the largest eigenvector component.
A total of about 3100 spectral lines have been classified as transitions among the 330 levels. Table  3 includes all of the spectral lines classified as Mo III, giving for each the wavelength (in air above 2000 A), intensity, wavenumber, difference between the observed wavelength and the wavelength obtained from the final level values (O-C), and its classification. The levels are denoted by their integer energy and / values. The Cowan least-squares program [3] was used to fit the radial coefficients for each of the three sets of configurations to the observed energy levels. Tables 4, 5, and 6 include the least-squares fitted (LSF) and HFR values for the parameters of the (4d'+4d^5s+4d^5s\ the (4d^ 5d+4d'6s), and the (4d^ 5p +4d^ 5s5p) configuration groups. The ratios of the LSF to HFR values are also given. The standard deviations of the fits are 44, 33, and 183 cm"', respectively.    ' The second and/or the third eigenvector component has been omitted when the first one or two components amount to 90% or greater.
'' This level is not given the LS name corresponding to the largest eigenvector component.                                  Standard deviation of the level fit = 44 cm ' " The values of j8 for Ad^ 5s and Ad^ 5s^ were held equal to each other. '' The values of the R ^ parameters were restricted to have the same LSQ/HFR ratios. "The first R\dd,ds) is the interaction parameter between Ad'' and Ad^5s. The second R\dd,ds) is for the Ad^ 5s-Ad^ 5s^ interaction. " The CI parameters were constrained to have the same LSQ/HFR ratios. -11097(520) -17820 0.623'' R'(.dp,ps) -10779(500) -17302 0.623" Standard deviation of the level fit = 183 cm-' " The values of P for the two configurations were constrained to be equal. '' The CI parameters were constrained to have the same LSF/HFR ratios.