Energy Levels of Singly-Ionized Platinum

The analysis of Pt II is extended by using accurate wavelength measurements by Sansonetti et al. Forty-three new even and 104 new odd levels have been found. The Slater-Condon parametric method is used for the interpretation of the 5d9, 5d86s, and 5d76s2 low even configurations and the 5d8(7s+6d) high even configurations with root mean square deviations smaller than 80 cm−1. The importance of the 5d8–5d76s core interaction in interpreting the even-parity levels is stressed.


Introduction
The spectrum of platinum emitted by a hollow cathode lamp has been recently observed and measured [1]. The improved wavelengths of the classified lines led Reader et al. [2] to determine accurate energies for the known levels. The extensive line list comprised many unclassified lines. Their interpretation has been undertaken at Laboratoire Aime Cotton in order to improve the knowledge of excited levels at the end of the 5dperiod.
The strong unclassified lines have been interpreted in the present work with the support of theoretical energy level predictions and a computer program to search for recurring energy differences in the list of observed wave numbers. The measured wave numbers of classified lines deviate from the differences between their initial and final levels by less than 0.050 cm~* if the lines are not blended with other transitions. The energy levels are reported in Tables 2, 3, and 5, in which the 3-digit ' In association with Universitd Paris-Sud. values are taken from Ref. [2]. The /-values of some levels have been changed and the newly classified lines led to slight modifications of their energies. The uncertainty of the levels depends on the intensities and spectral regions of their transitions. It ranges from 0.050 to 0.100 cm''. The classified lines are reported in Ref. [1].
5d'^~^6s^. In Pt II, all 21 levels found by Shenstone [4] were supported by the theoretical calculation, but six of his empirical LS designations did not correspond to the leading component of the eigenfunction. The 5d^6y^-configuration was limited to four known levels and the relevant energy parameters needed to be fixed or constrained. The present analysis was guided by the results of [3] and the number of levels of the (5d+6sy group has been brought from 21 to 33. The present interpretation of the three configurations 5d', 5d^6s and 5d''6s^ leads to improved parameter values, a number of constraints in the least-squares fitting process being now removed. The present set of parameters includes: a constant energy for all three configurations, A, the energy differences between configurations, Sid^^'s^) and S(d's-d''s% all Slater integrals describing the electrostatic interactions within the studied group, the effective electrostatic parameters oso and /3o as defined in the formalism of orthogonal operators [5], and finally, the usual spin-orbit parameters. These 18 parameters have been reduced to 13 adjustable ones by means of constraints detailed in Table 1. These constraints were derived from earlier studies of {5d + 6sY groups. The root mean square deviation is 73 cm"^ The comparison of experimental and theoretical energies is given in Table 2. The theoretical data are limited to the theoretical energy Eth, the first component of the eigenfunction and the percentage of the components of the 3 configurations (squared amplitudes) in the eigenfunctions. The coefficients of the interaction parameter R\5d^,5d6s) in intermediate coupling show that 5d^6s^?ia and 5d'6is"Pi/2 which are distant by 33700 cm"' have a mutual repulsion of 7000 cm"' and that four other levels of 5d^6s are shifted to lower energies by more than 2000 cm"'. " Parameters constrained to be equal in 5rf'6r^ and Sd^Ss. '■ The parameter R^(5d^,6s^) of the 5d^6s'^-5d^ interaction is held in a constant ratio with the G^{5d,6s) of 5^*65. ' Slater parameters R^^\5d\5d6s) for 5d"6s-5d^ and Si"ds-Srf'Ss^ interactions are held in a constant ratio. ■• f(5i'6r^) + r(5d')=2f(5rf"65).

The Predicted Low Configurations of Ptm
The spectrum of Pt rii is still unknown but, for application to Pt ii, its low energy levels can be predicted by means of the Slater-Condon method. By comparing the lowest energy levels of 5d'^, 5d'^~^6s and 5d^-^6s^ in Hf iii (N =2) [6], W m (JV = 4) [7], Auiir (N = 9) [8] and Hgiii {N = 10) [9], one can reasonably assume that the excitation energies of 5d''6s ^Fs and 5d'6s^ 'Fs and 5d'6s^ 'D^ levels above the ground level 5d^ ^FA are about 20000 and 60000 cm~S respectively. All other parameters needed for describing (5^+6?)^ in Pt iii may be obtained from regular trends investigated in second spectra [3] and in third spectra. The results of this preliminary study are summarized below.
For all /-values, the configuration 5d' does not overlap the energy range of the 5d^6s and 5d^6s^ configurations, but this does not prevent configuration mixing. The effect of 5d^6s^ is a constant shift of about -800 cm"' for all levels of 5d^ except ^Po and ^So, both shifted by -1400 cm"^ The effect of the 5d^6s-5d^ mbdng is more selective and is reported in the last column of Table 3. These shifts mean that the 5d^ parameters would certainly differ if fitted in the approximation of isolated configurations or in mixed groups (5d+6sY. The LS names are well defined except for the / = 2 levels, for which ^P2 is nowhere the leading component of the eigenfunction. Since the second and third 7 = 2 levels have respectively dominant ^Fj and 'D2 characters, the lowest / = 2 level has been given the designation ^P2 for identification purposes in the next step of the work.

Interpretation of the Upper Even Configurations
Nine high even levels were identified by Shenstone [4] as 5d^s and 5d^6d. One of these levels has now been rejected and the /-values of two revised. The three levels ofSd^&s and 5dVd have not been confirmed. Thirty-two levels have been found between 101500 and 121700 cm"'. The intensity of their transitions and some relatively large deviations Eeyp-Etb in the separate studies of these configurations led us to evaluate their mixing. The 21 integrals needed to describe the levels of 5d^7s+5d^6d were reduced to 15 adjustable parameters by means of constraints given in Table  1. The mixing of the lowest / = 1/2 levels leads to a well-defined value for the interaction parameter R\5dls,5d6d) and the final rms deviation is 79 cm"'. As shown in Table 1, the values of the parameters F\5d,5d) and a for 5d%6d +7s) differ significantly from those for 5d^6s^ and 5d^6s; however, the parameters are well-defined in the leastsquares fit. We consider this to be an effect of truncation problems discussed in Sec. 3. It seems likely that these inconsistencies would be corrected if all six configurations (5d + 6s)^s+(5d + 6sf6d were studied together. This extended parametric study has not been undertaken because 5d^6s^7s, 5d^6s^6d and 5d^6s6d are totally unknown and only two levels of5d''6s7s are located so far. The predictions of our restricted study might well be unreliable and the theoretical energies of unknown levels have therefore not been reported here.

Odd Levels of Pt ii
The lowest odd levels were attributed to 5d%p by Shenstone [4]. This configuration is also known in other ions of the isoelectronic sequence through Bivii [9][10][11]. The approximation of an isolated 5d%p configuration, if valid, has been used for the theoretical study of Auiii-Bivii spectra. It does not hold for Pt 11. In second spectra, the overlap of 5d"6p, 5d"~^6s6p and 5d'^~^6s'^6p requires a multiconfigurational treatment. In Hfii, Tail, Wii, Au II and Hg II [12], these low odd configurations had been interpreted with rms deviations smaller than 200 cm"'. For unclear reasons, the rms deviation for Pt II is larger than 500 cm"' and the designations reported in Table 4 are carefully limited to the lowest levels. Some of them might well be revised with further advances in the parametric interpretation. The 5d''6s6p configuration starts with the 62820 level, for which we explain the absence of decay to 5d''6s^ ''F9/2 by the selection rule on the strongly forbidden transition 6iy6p ^Po-fo^'So. Most of the levels without designation belong to 5d^6s6p with some admbcture of 5d^6s^6p for the highest energies.

Conclusion
The strongest unclassified lines of Ptii have been interpreted by extending the early analysis of Shenstone with the help of accurate wavelength measurements and parametric calculations of the main configurations. The number of levels has been brought from 29 to 72 in the even parity and from 71 to 174 in the odd parity. The theoretical study stresses the importance of the 5d^-5d^6s interaction and, although somewhat preliminary, the parametric interpretation of the low odd levels indicates that all levels with 7=3/2 through 11/2 below 79000 cm"' have been found. 220 Table 4. Upper even levels of Pt ii. The theoretical energies E,h are from the parametric study of 5d*6d + 5d"7*. The core term of Sd" is indicated in parenthesis for 5rf"6rf only