The Third Spectrum of Indium: In III

The present investigation reports on the extended study of the third spectrum of indium (In III). This spectrum was previously analyzed in many articles, but, nevertheless, this study represents a significant extension of the previous analyses. The main new contribution is connected to the observation of transitions involving core-excited configurations. Previous data are critically evaluated and in some cases are corrected. The spectra were recorded on 3-m as well as on 10.7-m normal incidence spectrographs using a triggered spark source. Theoretical calculations were made with Cowan’s code. The analysis results in the identifications of 70 spectral lines and determination of 24 new energy levels. In addition, the manuscript represents a compilation of all presently available data on In III.


CHAPTER-3 The Third Spectrum of Indium: In III
The third spectrum of indium (In III) belongs to Ag I isoelectronic sequence with electronic distribution [Kr] 4d 10 5s 2 S 1/2 . The outer electronic excitation gives rise to [Kr] 4d 10 nℓ (n≥5, for all ℓ except for f sub-shell) type configurations with doublet structure, while core electronic excitation involving the configurations like 4d 9 5s (5p+4f), 4d 9 5s 2 and 4d 9 5p 2 makes a three electron system that produces both doublet and quartet terms.
Out of 23 levels of 4d 9 5s5p configuration, they reported only 10 levels. Kilbane et al. [8] studied the photoabsorption spectra of In II -IV by dual laser plasma [DLP] technique. They reported the transitions from 4d 10 5s -{4d 9 5snp (n=6-11) + 4d 9 5snf (n=4-11)}. They could not observe 4d 10 5s -4d 9 5s5p transitions as they lie beyond the region of their investigation. Recently, Ryabtsev et al. [9] added new configuration 4d 9 5p 2 to In III-Te VI sequence and observed transitions from 4d 10 5p -4d 9 5p 2 39 configuration in the range 250-600 Å using a 6.65-m normal incidence spectrograph equipped with 1200 lines/mm grating giving a reciprocal linear dispersion of 1.25 Å/mm. They were able to report only 13 levels out of 28 eight levels of 4d 9 5p 2 configuration. Some spectral lines of In III-IV were also reported by Bhatia [10] in his doctoral thesis which was very useful in this analysis.
As mentioned above that a number of publications on In III appeared in the literature [1][2][3][4][5][6][7][8][9][10][11]. Among these, Bhatia's [6] analysis was more comprehensive and containing large number of one electron configurations. However, with careful insight into these results, a number of irregularities were noticed in Bhatia's results, for example several forbidden transitions were reported in this paper and many other lines classified did not match with the In III characteristics on our recorded spectra.
Moreover, the levels of 4d 9 5s5p configuration reported by Kaufamn et al. [7] and the levels of 4d 9 5p 2 configuration established by Ryabtsev et al. [7] are still incomplete.
These facts prompted us to investigate In III spectrum in detail. A Grotrian energy level diagram of In III is illustrated in Figure 3

Theoretical Calculations
The ab initio calculations were performed by the Hartree-Fock method with relativistic corrections (HFR) with the use of the RCN-RCN2-RCG chain of the Cowan code [12] with superposition of configurations including 4d 10 ns (n=5-12), 4d 10 nd (n=5-9), 4d 10 ng (n=5-9), 4d 9 (5s 2 + 5p 2 ) , 4d 9 5s(5d + 6s) configurations for even parity system and 4d 10 np (n=5-9), 4d 10 nf (n=4-7), 4d 10 nh (n=6-9), 4d 9 5snp (n=5-11) , 4d 9 5snf (n=4-12), 4d 8 5s 2 5p for odd parity matrix. There are a total of 51 configurations included in our calculations. The initial scaling of the Slater energy parameters were kept at 100% of the Hartree-Fock values for E av and ζ nl, 85% for F k , and 80% for G k as well as R k integrals. Later these parameters were more refined as soon as we started the analysis using least squares fitted levels. This program calculates the value of energy levels, wavelengths, weighted transition probability rates and weighted oscillator strengths for In III. The accuracy of Cowan's code calculations [12] for transition probability largely depends on the line strength which is greatly affected by the cancellation factor [13] which also has been calculated by the program.

Spectrum Analysis
The initial approach of the analysis is to identify the ionization character of In III lines. For the line identifications, we studied the earlier reported work of In III spectra and separate out the unclassified lines of this ion. For the verification of earlier reported work and search of new energy levels, a computer code FIND3 was used.
The analysis of In III spectra involves large number of transitions and energy levels.
All lines classified in the present scheme are given in Table 3.1 and the established enegy levels are given in Table 3.2 with the LS coupling scheme. In the present analysis, 4d 10 nℓ series and the internal excitation 4d 9 5s (5p+4f), 4d 9 5s 2 and 4d 9 5p 2 have been studied extensively.

The 4d 10 5s -[4d 10 np] Transition Array
The resonance transitions 4d 10 5s -4d 10 5p was firstly reported by Rao [1], and confirmed by all other workers [2][3][4][5]. We observed these two lines on our indium spectra with high intensity and were the main source to establish the In III ionization characteristics. Bhatia [6] reported the levels of 4d 10 np (n=5-9).We agreed with 43 Bhatia's analysis up to 4d 10 8p but 4d 10 5s -4d 10 9p transitions could not be seen on our spectra. The reported level value of 4d 10 9p 2 P 3/2,1/2 at 201180.3 cm -1 did not fit in our least squares fitted parametric calculations. Our predicted values were found to be at 203269.9 cm -1 and 203425.2 cm -1 for 2 P 3/2 and 2 P 1/2 . A plot of the energy differences between observed and Hartree Fock (HF) calculated values of 4d 10 np (n=5-9) 2 P 3/2 series is shown in Figure 3.2 and it is evident from this figure that the reported value for 4d 10 9p levels show irregular behavior. Therefore, this reported level seems to be doubtful. However, we did not get any alternative value as 4d 10 9p transitions were too weak to be observed on our plates.  The second excitation, 4d 10 5p -[4d 10 (6s + 5d) + 4d 9 5s 2 ] transitions are also observed to be quite strong. We observed transitions from 4d 10 5p -4d 10 ns (n=6-8) and 4d 10 6p -4d 10 ns (n=9-12). The 4d 10 5p -4d 10 nd transitions were considered next. Three transitions are possible between the 4d 10 np -4d 10 nd series out of which two transitions namely 2 P 1/2 -2 D 3/2 and 2 P 3/2 -2 D 5/2 were observed quite strong while the third transition 2 P 3/2 -2 D 3/2 was predicated weak in the sequence. All these three 44 transitions were observed in 4d 10 [5pnd (n=5-7)]. We therefore, confirmed the levels of 4d 10 ns (n=6-12) and 4d 10 nd (n=5-7) configurations. The transitions from 4d 10 nd (n=8, 9) to 4d 10 5p were not observed on our recorded spectra, but these transitions were reported by Bhatia [6]. However, from the least squares fitted parametric calculations, their scaling factor seems to be quite regular and a similar plot with the average energy difference between calculated and observed values in Figure 3.3 shows a regular behavior for 4d 10 ns and 4d 10 nd series. Though, we could not confirm 4d 10 nd(n=8, 9) configuration but considered these levels for the sake of completeness. The other configuration 4d 9 5s 2 in even parity system have two inverted 2 D levels having same energy range as 4d 10 5d 2 D levels. Both 2 D levels of these two configurations interact to each other, as a result of this interaction, transitions between 4d 10 5p -4d 9 5s 2 are observed. The further confirmation of these two levels was made by the observed transition from the levels of 4d 9 5s5p configuration. 45

The 4d 10 (nf + ng + nh) Configurations
The 4d 10 5d -4d 10 4f transitions lie beyond our wavelength region of investigation (above 2080Å), therefore we could not confirm experimentally in the present work.
Neither 4d 9 4f -4d 9 ng (n=5-7) nor 4d 9 5g -4d 9 nh (n=7-9) transitions lie in our wavelength region, therefore, could not be confirmed in the present work. However, we have compared with theoretical calculations for the known spectra in the isoelectronic sequence from Ag I -Sn IV [10] and they appear to be regular. The 4d 9 4f -(8g +9g) transitions do lie in our wavelength region but they are too weak to be verified. However, we have included it in our LSF calculations for the sake of completeness.

The 4d 9 5s5p Configuration
This configuration arises due to core excitation of the ground level 4d 10 5s. A number of levels from this configuration were reported by Bhatia [6]. Kaufman et al. [7] revised three levels of this configuration by observing transitions from the ground level 4d 10 5s 2 S 1/2 thus connecting only J= 1/2 and 3/2 levels. The remaining levels of Bhatia (with J=5/2, 7/2 and 9/2) remain yet to be verified. In the present investigation, we agreed with six levels of Kaufmann et al. [7] but revised four levels. The ionization separation on our recorded spectrum in this wavelength region was quite clear, thus new levels could be found with full satisfaction. The level 2 P 1/2 reported by Bhatia [6] at 199561.2 cm -1 was revised by Kaufmann et al. [7] at 197081 cm -1 . The line (507.406Å) used by Kaufman et al. [7] for this transition actually belongs to O III (507.391Å) [10] and the line used by Bhatia was not found on our spectrum. We found an unclassified In III line with moderate intensity at 504.080 Å that has been assigned to this transition which gives level value at 198382.5 cm -1 that also fitted well in the least squares calculations.
Kaufman et al. [7] revised another J=1/2 level of Bhatia [6] and re-designate it as a J=3/2 level at 170888 cm -1 based on the Bhatia's line list as this line was not seen by them. We also could not found this line on our line list, therefore, this level was rejected. According to our analysis we found the lowest J=1/2 level reported by Kaufman et al. [7] at 170812 cm -1 is in fact a J=3/2 level and the replacement of the lowest J=1/2 level is found at 171316.9 cm -1 . The lowest J=3/2 level of this configuration reported by Kaufmann et al. [7] at 167079 cm -1 is in fact based on an In IV line (598.526Å) [14,15]. However, Bhatia [6] had reported this level at 167339.1 cm -1 which is based on a correct In III line at (597.589Å) and we agree with this identification. Moreover, it also gives two transitions from the recently known 4d 9 5p 2 configuration [9] and that confirms the identification of this level.
The highest J= 3/2 level was not found by Kaufmann et al. [7] because calculations predict weak transition from the ground level. However, Bhatia [6] had reported this level at 202132.3 cm -1 . We found two strong transitions from another configuration 4d 9 5s 2 levels with right In III ionization characteristic. Thus we confirmed this level value. Table I. shows the energy values of J= 1/2 & 3/2 levels of 4d 9 5s5p configuration given by previous researchers [6,7] and present analysis. The remaining 12 levels of this configuration with higher J values (5/2-9/2) were considered next. These levels are only reported by Bhatia [6] through the transitions from 4d 9 5s 2 . We found satisfactory transitions from J=5/2 level at 194902.8 cm -1 and confirmed only this level. We were successful in locating 10 remaining levels of J=5/2 and 7/2 from 4d 9 5s 2 and 4d 9 5p 2 levels. The level with highest J value (9/2) does not connect with any other known configuration except 4d 9 5p 2 which was partially known. We extended this configuration to include J=7/2 levels. This paved the way for the establishment of J=9/2 level. We found 3 transitions to establish J=9/2 level at 168948.1 cm -1 . All 23 levels of 4d 9 5s5p configuration are now known experimentally.

The 4d 9 5s (nf + np) Configurations
These are some other configurations which arise due to the core excitation. The 4d 9 5s4f configuration has large energy spread containing 39 levels. Since ground configuration contains only 2 S 1/2 level, therefore, only J=1/2 and 3/2 levels of this configuration can be connected. Kilbane et al. [8] have studied 4d 9 5snf (n=4-12) and 4d 9 5snp (n=6-11) configurations by photoabsorption technique. They reported 10 levels of 4d 9 5s4f and 7 levels of 4d 9 5s6p belonging to J= 1/2 and 3/2. On our spectra, these transitions lie in shorter wavelength region where reflectivity of the grating falls considerably in normal incidence setting. Therefore, these transitions appeared with very weak intensity on our spectra. Secondly a large number of In V [16], In VI [17] 48 transitions overlap in this region. Therefore, it was very difficult to pick up In III line with full satisfaction for this array. Moreover, these levels lie above the ionization limit consequently, have very little population and therefore these levels could not be located in the present work. However, we performed least squares fitted parametric calculations to provide a precise prediction of the remaining levels of 4d 9 5snf (n=4-7) and 4d 9 5snp (n=6-7) configurations based on the identification made in reference [8].

The 4d 9 5p 2 Configuration
The first attempt to study the low-lying autoionizing configuration 4d 9 5p 2 in the sequence In III-Te VI was made by Ryabtsev et al. [9] connecting this configuration from 4d 10 5p. It is important to note that all the levels of this configuration lie above the ionization limit. It was difficult to find a reasonable population above the ionization limit. Certainly it was advantageous to identify the broad lines due to continuum effect but only the strongest transitions could be observed. Not many pairs connecting to both 2 P 1/2, 3/2 was found to confirm these levels. However, the lines used to locate these levels have definite In III characteristic and showing continuum broadening effect. Out of 28 levels of 4d 9 5p 2 , only 13 levels with J=1/2, 3/2 and 5/2 were reported by Ryabtsev et al. [9]. We should point out that two levels ( 1 D) 2 S 1/2 and ( 1 D) 2 P 3/2 were reported by Ryabtsev et al. [9] having same energy level values thereby based on the classification of the same pair of lines twice (555.669Å & 569.421Å). We agreed with these lines for the classification of ( 1 D) 2 P 3/2 giving level value at 237145.8 cm -1 as both transitions are predicted to be of the comparable intensity. However ( 1 D) 2 S 1/2 level predicts one strong and one weak transition and we found one unclassified lines on our plate at 555.501Å which is used to establish this level at 237201.8 cm -1 . Several levels have also been confirmed through transitions to 4d 9 5s5p configuration. The higher J values of 4d 9 5p 2 configuration (J=7/2 & 9/2) could only be established through the transitions from 4d 9 5s5p. We were successful in establishing three J=7/2 and one J=9/2 levels. Two J=7/2 and one J=9/2 levels remain unknown. The study of 4d 9 5p 2 and 4d 9 5s5p configurations together complemented each other. The other even parity configuration 4d 9 5s5d lie above the ionization limit and partially overlapped with levels of 4d 9 5p 2 configuration have also been incorporated in the least squares fitted parametric calculation to interpret the results.

Optimization of the Energy Levels
The transition wavelengths observed for this spectrum were used to derive the energy level values, for this purpose a least-squares level optimization code LOPT [18] was used. The essential factors for the level optimization procedure are the correct identification of the spectral lines and estimation of their uncertainties. The wavelength uncertainty is determined by the combined effect of the statistical deviation of the line position measured on the comparator and systematic uncertainty of reference wavelengths used in the fitting. The uncertainty of Bhatia's [6] measurements are recently estimated by Kramida [13]. He estimates the uncertainty of Bhatia lines are ±0.03Å below 1900, ±0.09 Å between 1900-2400Å and ±0.13 Å above 2440 Å. Ryabtsev et al. [9] reported the uncertainty of autoionized lines to be ±0.006 Å. Our wavelength accuracy for sharp and unblended lines is estimated to be within ±0.006Å and ±0.007Å below and above 900Å. All the lines used in the optimization of the level values were given estimated uncertainty to find the final optimized energy level values with estimated uncertainty on each level. The level uncertainties with respect to 4d 10 5p ( 1 S) 2 P 3/2 are given in Table 3.2, as this level was considered as the base level since it has the largest number of observed transitions.
All the uncertainties are taken to be at one standard deviation level.

Ionization Potential
Since more than one series with three members are known in In III therefore, its ionization potential can be determined with better accuracy. The value of ionization potential of In III given in AEL [5] at 226100 cm -1 , was derived by Catalan and Rico [19], who have derived it by comparison of the third spectra from Y to In. Bhatia [6] improved the value of ionization potential by using 4d 10 ng (n=5-9) and 4d 10 nh (n=6-9) series using polarization theory. He calculated In III limit at 226191 cm -1 and this value is listed in NIST-ASD [11]. We have calculated the ionization potential from two series, ns (n=6-12) and ng (n=5-9) series using Ritz quantum defect series extrapolation method with the aid of RITZPL code [20]. However, the non-penetrating sub-shells (4d 10 ng) series is certainly expected to give more accurate value. The IP value obtained using the three parameter extended RITZPL code [20] for the 4d 10 ns (n=6-12) series and 4d 10 ng (n=6-8) series at 226198.0 cm -1 and 226198.9 cm -1 respectively. This value is in agreement with Bhatia's value differing only by 8 cm -1 . Since Bhatia used polarization method [21] for the calculation of ionization potential on In III, we adapted his value at 226191 cm -1 .

Conclusion
A total number of 91 energy levels have been established in which 3 levels are revised and 22 are new. All these levels were based on the identification of 247 transitions, 72 being new. The results were interpreted using Cowan's code and least square fitted parametric theory. All the classified transitions are given in Table 3.1 along with their weighted transition probabilities (gA) and cancellation factor obtained by least squares fitted energy parameters. In this table, we are also providing the Ritz wavelength of each transition with their uncertainty by least-squares level optimization code (LOPT). The optimized energy levels and the least squares fitted level are given in Table 3  c Observed and Ritz wavelengths are given in standard air for wavenumber σ between 5000 cm -1 and 50000cm -1 and in vacuum outside of this range. The uncertainty (standard deviation) in the last digit is given in parentheses for both λ obs and λ Ritz , λ * stands not include in optimization. d Ritz wavelengths and their uncertainties were determined in the least-squares level optimization procedure LOPT [18]. e Difference between observed and Ritz wavelength. If this column is blank, the line was excluded from the level optimization because this line was deviate more than our given uncertainty. f The transition are classified between lower energy level and upper energy level. h Weighted transition probability values (g=2J U+1 ,is statistical weight of the upper level). If marked as # then the given gA values are too unreliable for the transitions whose cancellation factor |CF|<0.10 in the Cowan code [12]. i Reference to the source: B -Bhatia et al. [6]; B*-Previous value of [6] has been revised in this work; K*-Previous value of [7] has been revised in this work; R -Rybstev et al. [9]; TWthis work.