Spectrum of Sn 5 + in the Region 500 – 1300 Å

The spectrum of tin, excited in a vacuum spark, was recorded in the region 500–1131 Å on a 6.65-m normal incidence spectrograph. The transitions between 4d85s, 4d86s, 4d85p and 4d85d excited configurations in Sn VI were studied. More than 500 lines of the 4d85p–4d85d and 4d85p–4d86s were identified with the aid of the Cowan code calculations. 67 energy levels (out of 70 possible levels of the 4d85d configuration) and all but two 4d86s levels were found. The wavelength of the 4d85s–4d85p transitions in the region 839–1131 Å were re-measured and supplemented by Sn VI lines in the region 1131–1300 Å measured previously by Srivastava et al. (1977) for optimisation of the energy level values. The SnVI line list in the region 500–1300 Å contains now 741 lines with calculated transition probabilities.


Experimental Details
The spectrum of tin was recorded on the SWR plates using the 6.65-m normal incidence spectrograph of the Institute of Spectroscopy.With 1200 L/mm grating it has plate factor 1.25 Å/mm.The spectrum was excited in a vacuum spark discharge with electric parameters of the circuit: C = 7500 µF, U = 220 V and L = 8 and 25 µH.The plates were measured on an Epson Expression 10000XL scanner (Seiko Epson Corporation, Suwa, Japan).It was found [5], that a flatbed scanner, in their case Epson Expression XL11000, can have periodic errors with an amplitude up to 0.05 mm in the direction perpendicular to the linear detector in scanner (horizontally on the scanner bed) and almost no errors in the direction parallel to the detector.Therefore, our plates were scanned in a position vertically on the scanner bed.
The wavelengths were calculated using the impurity lines of aluminum, oxygen, silicon and carbon of different stages of the ionization [6] as the references.One standard deviation of the reference lines 0.006 Å was adopted as the measurement uncertainty for sharp unblended lines.Relative intensity of the lines is affected by wavelength dependence of the spectrograph effectivity and Atoms 2017, 5, 47 2 of 33 photoplate sensitivity, which were not taken into account.The saturation effects strongly influenced the intensities of strong lines.Thus, the measured intensities have mostly qualitative character.

Results
The analysis was guided by the Cowan code [7] calculations of the energy levels and transition probabilities.The matrices of the 4d 9 + 4d 8 (5s-7s) + 4d 8 (5d-7d) + 4d 7 5s 2 and 4d 8 5p + 4d 8 6p + 4d 8 4f + 4d 8 5f + 4p 5 d 10 configurations were used respectively for the even and odd levels.The energy parameters for the 4d 8 5s and 4d 8 5p configurations were obtained by a fitting of the calculated energy levels to the levels known from [2].Initial energy parameters in the 4d 8 5d and 4d 8 6s configurations for the 4d-4d and 4d-6s interactions were obtained by a scaling of the corresponding ab initio Hartree-Fock integrals on the ratios of fitted to Hartree-Fock parameters (scaling factors) obtained for the Sn VI 4d 8 5s configuration.The scaling factors for the 4d-5d interaction parameters were taken from In V [8].The levels of the 4d 8 4f + 4d 8 6p configurations were predicted with the energy parameters from [3].All parameters of the other unknown configurations were kept at the Hartree-Fock values.Thus, the predicted spectrum was used for the identification of the Sn VI lines with the aid of the IDEN code [9].
Identified lines of the 4d 8 5p-4d 8 5d and 4d 8 5p-4d 8 6s transitions in the region 510-1052 Å with calculated transition probabilities are presented in Table A1 (see Appendix A at the end of the document).It contains 518 newly identified lines, 24 of which are doubly identified.Previously identified lines of the 4d 8 5s-4d 8 5p transitions [2] falling in our region (up to 1131 Å) were re-measured and listed in Table A1 in comparison with previous measurements.They are supplemented by sixty lines from 1137 Å through 1276 Å from [2] for completeness of the 4d 8 5s-4d 8 5p transition array.
The energy levels of the 4d 8 5d and 4d 8 6s configurations found from the identified lines are given in Table A2.Kramida's code LOPT [10] was used for the optimization of the level energies.In the optimization procedure, doubly classified, masked, blended, wide and weak lines were given a reduced weight.The uncertainties of the levels relative to each other given by LOPT are also listed.For consistency with our wavelength measurements, previously known 4d 8 5s and 4d 8 5p levels were also optimized and are given in Tables A2 and A3.A difference with previous values for the 4d 8 5p level energies is shown in Figure 1.
influenced the intensities of strong lines.Thus, the measured intensities have mostly qualitative character.

Results
The analysis was guided by the Cowan code [7] calculations of the energy levels and transition probabilities.The matrices of the 4d 9 + 4d 8 (5s-7s)+ 4d 8 (5d-7d) + 4d 7 5s 2 and 4d85p + 4d 8 6p + 4d 8 4f + 4d 8 5f + 4p 5 d 1 ° configurations were used respectively for the even and odd levels.The energy parameters for the 4d 8 5s and 4d 8 5p configurations were obtained by a fitting of the calculated energy levels to the levels known from [2].Initial energy parameters in the 4d 8 5d and 4d 8 6s configurations for the 4d-4d and 4d-6s interactions were obtained by a scaling of the corresponding ab initio Hartree-Fock integrals on the ratios of fitted to Hartree-Fock parameters (scaling factors) obtained for the Sn VI 4d 8 5s configuration.The scaling factors for the 4d-5d interaction parameters were taken from In V [8].The levels of the 4d 8 4f+4d 8 6p configurations were predicted with the energy parameters from [3].All parameters of the other unknown configurations were kept at the Hartree-Fock values.Thus, the predicted spectrum was used for the identification of the Sn VI lines with the aid of the IDEN code [9].
Identified lines of the 4d 8 5p-4d 8 5d and 4d 8 5p-4d 8 6s transitions in the region 510-1052 Å with calculated transition probabilities are presented in Table A1 (see Appendix A at the end of the document).It contains 518 newly identified lines, 24 of which are doubly identified.Previously identified lines of the 4d 8 5s-4d 8 5p transitions [2] falling in our region (up to 1131 Å ) were re-measured and listed in Table A1 in comparison with previous measurements.They are supplemented by sixty lines from 1137 Å through 1276 Å from [2] for completeness of the 4d 8 5s-4d 8 5p transition array.
The energy levels of the 4d 8 5d and 4d 8 6s configurations found from the identified lines are given in Table A2.Kramida's code LOPT [10] was used for the optimization of the level energies.In the optimization procedure, doubly classified, masked, blended, wide and weak lines were given a reduced weight.The uncertainties of the levels relative to each other given by LOPT are also listed.For consistency with our wavelength measurements, previously known 4d 8 5s and 4d 8 5p levels were also optimized and are given in Tables A2 and A3.A difference with previous values for the 4d 8 5p level energies is shown in Figure 1.Although our wavelengths for the 4d 8 5s-4d 8 5p transitions generally agree with previous measurements [2] within mutual measurement uncertainties, linear systematic shift exists up to 0.015 Å in going from longer to shorter wavelengths.It is reflected in a trend of the difference for the level energies visible in Figure 1.The 311.827 Å line of the 4d 9 2 D 5/2 -4d 8 5p ( 3 F 2 )D 5/2 transition [1] was used for a connection of the levels of the excited configurations to the ground level.With estimated 0.005 Å uncertainty of this line [1] it gives 5 cm −1 for the uncertainties of excited levels relative to the ground level.
As it is often the case for the ions with the 4d k ground state configuration, the designation of a level by the first component of its eigenvector is sometimes ambiguous (see, for example, 237,695.74 and 242,240.86 cm −1 levels having first component respectively 52% and 47% from the same 5s( 3 P) 4 P 3/2 level).For this reason, the energy level value is given in Table A1 in addition to the designation by the first eigenvector component.
The configuration interaction within the low lying excited configurations included in the calculation is seen in the eigenvector composition limited to three components only for two levels.The 5d( 1 G) 2 H 9/2 at 475,041.6 cm −1 has 25% contribution from the levels of the 4d 7 5s 2 configuration and the 6s( 1 D) 2 D 5/2 level at 509,540.7 cm −1 is mixed with the 5d( 1 S) 2 D 5/2 level.
The energy parameters and rms level deviations obtained after final fitting of the known levels are given in Table A4.As in preliminary calculations, the matrices of the 4d 9 + 4d 8 (5s-7s) + 4d 8 (5d-7d) + 4d 7 5s 2 and 4d 8 5p + 4d 8 6p + 4d 8 4f + 4d 8 5f + 4p 5 d 10 configurations were used.Only parameters of known configurations are listed in Table A4.The parameters of unknown 4d 8 nl configurations were tied at the Hartree-Fock ratios with the corresponding parameters of these configurations.Their average energies E av were shifted with respect to the Hartree-Fockenergies on the values obtained for 4d 8 5p and 4d 8 6s configurations.Hartree-Fock average energies are defined such that the ground level energy of the 4d 9 + 4d 8 (5s-7s) + 4d 8 (5d-7d) + 4d 7 5s 2 configurations is equal to zero.Ab initio E av for the ground level configuration 4d 9 in this case appears to be equal to 5338 cm −1 .The average energy of the 4d 7 5s 2 configuration was taken lower by 6500 cm −1 than the one given by the ab initio calculation.This value was estimated from the shift of the 4d 8 5s 2 configuration in SnV [11] calculated with similar set of the configurations as in Sn VI.All configuration interaction parameters were fixed on values obtained with scaling by 0.85 of the Hartree-Fock integrals.
Good consistency of all relevant energy parameters for all studied configurations within the limit of their uncertainties should be noted.Due to extended set of interacting odd configurations rms deviation of the fitting for the 4d 8 5p levels 61 cm −1 is 2.5 times smaller than in the one configuration approximation (151 cm −1 ) in the work by Srivastava et al. [2].Notes: a The star * indicates a calculated value for the level.Tentative value of the level is listed with the question mark; b The energy uncertainty relative to any other level of the 4d 8 5s, 4d 8 5s and 4d 8 5s configurations.The energy uncertainty relative to ground level 4d 9 2 D 5/2 is 5 cm −1 ; c The number of spectral lines used for the determination of each level energy; d The difference between the observed and the calculated energies; e For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.Notes: a The energy uncertainty relative to any other level of the 4d 8 5p, 4d 8 5s and 4d 8 5s configuration.The energy uncertainty relative to ground level 4d 9 2 D 5/2 is 5 cm −1 ; b The number of spectral lines used for the determination of each level energy; c The difference between the observed and the calculated energies; d For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.

Figure 1 .
Figure 1.Difference between the level energies of the 4d 8 5p configuration measured in this work (ETW) and the energies ESr published by Srivastava at al. [2].

Figure 1 .
Figure 1.Difference between the level energies of the 4d 8 5p configuration measured in this work (E TW ) and the energies E Sr published by Srivastava at al. [2].

Table A1 .
[2]].Relative intensity; b Observed wavelengths: ?-questionable line; db-doubly identified; m-masked by close lying strong line; w-wide line; mR-masked by close lying strong line, calculated Ritz value is listed; m2-blended by second order line; m3 and m5-blended respectively by the Sn III[12]and Sn V[11]lines.Above1131 Å the measurements by Srivastava et al.[2]were used; c Difference between the observed wavelength and the wavelength derived from the final level energies (Ritz wavelength).A blank value indicates that the upper level is derived from that line only; d Previous measurements by Srivastava at al.[2].
85p and 4d 8 5d configurations in Sn VI calculated with the Cowan code.