Resonance Transitions in the Spectra of the Ag 6 + – Ag 8 + Ions

The spectrum of silver, excited in a vacuum spark, was recorded in the region 150–350 Å on a 3-m grazing incidence spectrograph. The resonance 4dk–(4dk−15p + 4dk−14f + 4p54dk+1) was studied in the Ag6+–Ag8+ spectra (Ag VII–Ag IX) with k = 5–3, respectively. Several hundred lines were identified with the aid of the Cowan code and orthogonal operator technique calculations. The energy levels were found and the transition probabilities were calculated.


Introduction
Six-through eight-times ionized silver atoms are the members of the isonuclear sequence of the silver ions with the unfilled 4d k (k = 5-3) ground-state configuration.The spectra of these ions have not been investigated previously.The excitation of the 4d electron leads to the lowest odd configurations 4d k−1 5p and 4d k−1 4f.The third odd configuration 4p 5 4d k+1 is formed by the excitation of the inner shell 4p electron.The resonance transitions are represented by the transitions from these odd configurations to the ground-state configuration.Out of all resonance transitions only the 4d k -4d k−1 4p (k = 9-6) ones were previously studied in the silver spectra of the lower ionization stages: Ag III [1], Ag IV [2], Ag V [3] and Ag VI [4].On the other hand, all three resonance transition arrays were investigated in rather simple spectra of ions having 4d and 4d 2 ground-state configurations: Ag XI [5,6] and Ag X [7].In this article we report the results of the study of the Ag VII, Ag VIII and Ag IX to fill the gap between the Ag VI and Ag X isonuclear spectra.
This study is part of a project to get atomic data for the ions of lighter than tin chemical elements isoelectronic with Sn IX-Sn XIV which are relevant to a development of bright source for projection lithography at the 135 Å wavelength.The results for the palladium isonuclear spectra were recently published (see [8] and references therein).Such isoelectronic data are necessary for validation of previously reported analyses of the corresponding tin ion spectra [9,10].Research on these spectra is also of general interest to atomic physics for improving of theoretical methods of calculations of multi-electron heavy atom spectra.

Experiment
The experimental technique and the theoretical approaches for spectrum calculations were the same as in our previous publications [7,8].Briefly, the light source was a low-inductance vacuum spark operated with an additional inductance up to 2.5 µH.A 150 or 12 µF capacitor was charged up to 4.5 kV resulting in the spark peak current in a range of ~10-20 kA.Ionization stages were distinguished by comparing the intensities of the lines at various peak currents.A 3 m grazing incidence spectrograph (85 • angle of incidence) equipped with a gold coated holographic grating having 3600 lines/mm was used for taking the spectra.A plate factor of the spectrograph in the region 160-350 Å was 0.32-0.46Å mm −1 respectively.The spectra were recorded on Kodak SWR photographic plates (Eastman Kodak Company, Rochester, NY, USA) and measured on an EPSON EXPRESSION 10000XL scanner (Seiko Epson Corporation, Suwa, Japan).Wavelengths were calibrated using titanium ion lines [11] as the standards.The titanium spectrum was superimposed on some silver exposures.The measured wavelength uncertainty is estimated as ±0.005Å for the unperturbed lines of moderate intensity.General view of the silver spectrum in the region 150-350 Å is shown in Figure 1, where the lines identified in this work, previously identified, and remaining unidentified are marked by different colours depending on particular spectrum.
Atoms 2016, 4, x 2 of 5 having 3600 lines/mm was used for taking the spectra.A plate factor of the spectrograph in the region 160-350 Å was 0.32-0.46Å mm −1 respectively.The spectra were recorded on Kodak SWR photographic plates (Eastman Kodak Company, Rochester, NY, USA) and measured on an EPSON EXPRESSION 10000XL scanner (Seiko Epson Corporation, Suwa, Japan).Wavelengths were calibrated using titanium ion lines [11] as the standards.The titanium spectrum was superimposed on some silver exposures.The measured wavelength uncertainty is estimated as ±0.005Å for the unperturbed lines of moderate intensity.General view of the silver spectrum in the region 150-350 Å is shown in Figure 1, where the lines identified in this work, previously identified, and remaining unidentified are marked by different colours depending on particular spectrum.The relative line intensities were obtained as described in our previous article [8] "from the measured optical densities using an approximate photoplate response curve estimated from different experiments.They should be considered mostly as qualitative ones because of some uncertainty of used photoplate response curve and neglect of the wavelength dependence of the spectrograph efficiency and photoplate sensitivity.Also the saturation effects resulting from the photoplate response nonlinearity can significantly influence the intensity ratios of the weak to strong lines."The intensity I = 1000 was attributed to the strongest line of the 4d k − 4d k−1 5p transition array in each ion spectrum.
The program IDEN [12] was used for the spectrum identification.As in [8], ab initio calculations were performed with the use of the Dirac-Fock (DF) code of Parpia et al [13], or by the Hartree-Fock method with relativistic corrections (HF) with the use of the Cowan code (Cowan programs RCN, RCN2, RCG, and RCE) [14].Semiempirical correction of ab initio values of Slater parameters was made with the RCE Cowan code or by using a technique of orthogonal operators [15][16][17][18].
The energies derived after the identification of spectral lines were optimized using the program LOPT [19]."

Results
In the following, the results of the analyses of silver ions in the charge states Ag 6+ , Ag 7+ and Ag 8+ are presented.Line identifications are summarized in Tables A1-A4 (see Appendix A at the end of the document) and energy levels are collected in Tables A5-A11.The data were interpreted using semi-empirical orthogonal parameters and Cowan code calculations resulting in calculated values for the energy levels, wave-function composition, transition probabilities and energy parameters.The The relative line intensities were obtained as described in our previous article [8] "from the measured optical densities using an approximate photoplate response curve estimated from different experiments.They should be considered mostly as qualitative ones because of some uncertainty of used photoplate response curve and neglect of the wavelength dependence of the spectrograph efficiency and photoplate sensitivity.Also the saturation effects resulting from the photoplate response nonlinearity can significantly influence the intensity ratios of the weak to strong lines."The intensity I = 1000 was attributed to the strongest line of the 4d k -4d k−1 5p transition array in each ion spectrum.
The program IDEN [12] was used for the spectrum identification.As in [8], ab initio calculations were performed with the use of the Dirac-Fock (DF) code of Parpia et al. [13], or by the Hartree-Fock method with relativistic corrections (HF) with the use of the Cowan code (Cowan programs RCN, RCN2, RCG, and RCE) [14].Semiempirical correction of ab initio values of Slater parameters was made with the RCE Cowan code or by using a technique of orthogonal operators [15][16][17][18].
The energies derived after the identification of spectral lines were optimized using the program LOPT [19].

Results
In the following, the results of the analyses of silver ions in the charge states Ag 6+ , Ag 7+ and Ag 8+ are presented.Line identifications are summarized in Tables A1-A4 (see Appendix A at the end of the document) and energy levels are collected in Tables A5-A11.The data were interpreted using semi-empirical orthogonal parameters and Cowan code calculations resulting in calculated values for the energy levels, wave-function composition, transition probabilities and energy parameters.The semi-empirical energy parameters and their comparison with the corresponding ab initio values are shown in Tables A12-A14.

Ag VII
A diagram of the low lying configurations of Ag VII with the ground-state configuration 4d 5 is shown in Figure 2. As in the case of silver ions in lower stages of ionization (Ag III-Ag VI) we were able to make the analysis of only the 4d 5 -4d 4 5p transition array (Table A1).The lines of these transitions are represented by a compact group in the region 271-343 Å mostly isolated from the other transitions in Ag VII as well as in the neighboring ions (see Figure 1).Three hundred and seventy-eight lines were identified in this transition array, 47 of them were doubly and one trebly identified.Eight lines are probably blended with previously identified Ag VI transitions.Thirty-four levels out of 37 possible 4d 5 ones were found (Table A5) and 142 levels of the 4d 4 5p configurations were located out of 180 possible levels (Table A6).The relative uncertainty of the level energies given by least-squares optimization [19] ranges from 1 to 4 cm −1 for 4d 5 levels and from 3 to 8 cm −1 for 4d 4 5p depending on the number of lines used for the level optimization and on their wavelength uncertainties.Identification was performed with the help of the semi-empirical calculations based on the orthogonal operators.The initial orthogonal energy parameters were extrapolated along the sequence Ag IV-Ag V. Final energy parameters of Ag VII after a fitting of the calculated levels to the found levels are listed in Tables A12 and A13.They are compared with the values from the Parpia et al. code [13].Only the parameters of the 4d 5 and 4d 4 5p configurations are listed in the tables although the matrixes of the interacting 4d 5 + 4d 4 5s + 4d 3 5s 2 (even) and 4d 4 5p + 4d 3 5s5p + 4d 2 5s 2 5p (odd) configurations were used in the fittings.The parameters of the unknown configurations were fixed on extrapolated values; the interaction parameters were fixed on values obtained with scaling by 0.85 of the ab initio integrals.
Atoms 2016, 4, x 3 of 5 semi-empirical energy parameters and their comparison with the corresponding ab initio values are shown in Tables A12-A14.

Ag VII
A diagram of the low lying configurations of Ag VII with the ground-state configuration 4d 5 is shown in Figure 2. As in the case of silver ions in lower stages of ionization (Ag III-Ag VI) we were able to make the analysis of only the 4d 5 -4d 4 5p transition array (Table A1).The lines of these transitions are represented by a compact group in the region 271-343 Å mostly isolated from the other transitions in Ag VII as well as in the neighboring ions (see Figure 1).Three hundred and seventy-eight lines were identified in this transition array, 47 of them were doubly and one trebly identified.Eight lines are probably blended with previously identified Ag VI transitions.Thirty-four levels out of 37 possible 4d 5 ones were found (Table A5) and 142 levels of the 4d 4 5p configurations were located out of 180 possible levels (Table A6).The relative uncertainty of the level energies given by least-squares optimization [19] ranges from 1 to 4 cm −1 for 4d 5 levels and from 3 to 8 cm −1 for 4d 4 5p depending on the number of lines used for the level optimization and on their wavelength uncertainties.Identification was performed with the help of the semi-empirical calculations based on the orthogonal operators.The initial orthogonal energy parameters were extrapolated along the sequence Ag IV-Ag V. Final energy parameters of Ag VII after a fitting of the calculated levels to the found levels are listed in Tables A12 and A13.They are compared with the values from the Parpia et al. code [13].Only the parameters of the 4d 5 and 4d 4 5p configurations are listed in the tables although the matrixes of the interacting 4d 5 + 4d 4 5s + 4d 3 5s 2 (even) and 4d 4 5p + 4d 3 5s5p + 4d 2 5s 2 5p (odd) configurations were used in the fittings.The parameters of the unknown configurations were fixed on extrapolated values; the interaction parameters were fixed on values obtained with scaling by 0.85 of the ab initio integrals.Sd.Lp…SS(dp)20 are magnetic 2-body dp-parameters [15], and T16 to T35 are the electrostatic 3-body ddp-parameters.In case of Ag VII 2-body magnetic parameters were varied at the fitting on one In a treatment of the 4d 5 shell (as well as of the other 4d k shells) by the orthogonal parameter technique O2, O2 , Ea and Eb are the orthogonal counterparts of the traditional parameters F 2 (4d,4d,), F 4 (4d,4d), α and β.The one-electron magnetic (spin-orbit) operator ζ(4d) and the effective 3-particle electrostatic operators T1 and T2 are the same as in Cowan code and (Ac...A0) are additional 2-body magnetic parameters.The 4d 4 5p configuration and the other 4d k−1 5p configurations contain additional parameters: C1dp-C3pd are the orthogonal counterparts of the Slater exchange integrals G 1 (4d,5p)-G 3 (4d,5p); S1dp, S2dp are the effective electrostatic 2-body dp-parameters; Sd.Lp . . .SS(dp)20 are magnetic 2-body dp-parameters [15], and T16 to T35 are the electrostatic 3-body ddp-parameters.In case of Ag VII 2-body magnetic parameters were varied at the fitting on one bunch keeping the ratios of the corresponding ab initio values.Root mean square deviations of the fitting σ were 14 and 19 cm −1 in even and odd configurations, respectively.
Almost all levels of the 4d 5 configuration can be well designated with the leading member of their eigenvector composition.Only 48,086 cm −1 (J = 3/2) and 47119 cm −1 (J = 5/2) were designated with the second term.For 4d 4 5p configuration, in many cases two wave functions have the same first component leading to non-unique labels for the energy levels.Therefore, the level energies are listed in Table A6 along with the level designations to avoid the ambiguities.
According to our predictions the most intense lines of the 4d 5 -(4d 4 4f + 4p 5 4d 6 ) transitions are expected in the 170-240 Å wavelength range.As it is seen in Figure 1 there are many unknown lines in this region but we were not able to make reliable identification of these lines.

Ag VIII
The low lying configurations of Ag VIII are shown in Figure 3.The transitions from all low odd configurations decaying to the ground-state 4d 4 configuration are identified in this spectrum.The 4d 4 -4d 3 5p transitions are overlapped with some unknown lines of moderate intensity.But nevertheless, 118 lines were identified in this transition array (Table A2).Twenty-one lines were doubly and two lines trebly identified.Twenty-nine (out of 34 possible) 4d 4 levels were found with the relative uncertainty from 3 to 7 cm −1 and collected in Table A7.The levels of the 4d 3 5p configurations are contained in Table A8.It was possible to locate 83 out of 110 possible levels of this configuration.Their uncertainties are from 4 to 14 cm −1 .As in Ag VII the identification of the 4d 4 4d 3 5p transitions was performed with by means of the semi-empirical calculations based on the orthogonal operators.
Atoms 2016, 4, x 4 of 5 bunch keeping the ratios of the corresponding ab initio values.Root mean square deviations of the fitting σ were 14 and 19 cm −1 in even and odd configurations, respectively.
Almost all levels of the 4d 5 configuration can be well designated with the leading member of their eigenvector composition.Only 48,086 cm −1 (J = 3/2) and 47119 cm −1 (J = 5/2) were designated with the second term.For 4d 4 5p configuration, in many cases two wave functions have the same first component leading to non-unique labels for the energy levels.Therefore, the level energies are listed in Table A6 along with the level designations to avoid the ambiguities.
According to our predictions the most intense lines of the 4d 5 − (4d 4 4f + 4p 5 4d 6 ) transitions are expected in the 170-240 Å wavelength range.As it is seen in Figure 1 there are many unknown lines in this region but we were not able to make reliable identification of these lines.

Ag VIII
The low lying configurations of Ag VIII are shown in Figure 3.The transitions from all low odd configurations decaying to the ground-state 4d 4 configuration are identified in this spectrum.The 4d 4 -4d 3 5p transitions are overlapped with some unknown lines of moderate intensity.But nevertheless, 118 lines were identified in this transition array (Table A2).Twenty-one lines were doubly and two lines trebly identified.Twenty-nine (out of 34 possible) 4d 4 levels were found with the relative uncertainty from 3 to 7 cm −1 and collected in Table A7.The levels of the 4d 3 5p configurations are contained in Table A8.It was possible to locate 83 out of 110 possible levels of this configuration.Their uncertainties are from 4 to 14 cm −1 .As in Ag VII the identification of the 4d 4 4d 3 5p transitions was performed with by means of the semi-empirical calculations based on the orthogonal operators.The energy parameters obtained in the final fitting are collected in Table A12 for 4d 4 and Table A13 for 4d 3 5p.For the meaning of the energy parameters and the procedure of the calculations see Section 3.1.Root mean square deviations of the fitting were 26 and 47 cm −1 in the 4d 4 and 4d 3 5p configurations, respectively.In case of the 4d 3 5p configuration the fitting is affected by the interaction with the levels of the 4p 5 4d 5 configuration.The 4d 3 5p levels above ~424,000 cm −1 overlap with the low lying 4p 5 4d 5 levels.Their interaction cannot be taken into account in the orthogonal operator code.
The LS-coupling scheme is good approximation for the 4d 4 levels.The value of the first component of the eigenvector composition for all levels is not less than 50%, thus a unique label by the name of the first component can be assigned to all energy levels.To differentiate 4d 4 terms with the same LS values (recurring terms) the seniority numbers are used in the orthogonal operator code, whereas the Nielson and Koster sequential indices [20] are employed in the Cowan code [14].Both labels are retained in Table A7 for the 4d 4 levels because the 4d 4 − (4d 3 5p + 4d 3 4f + 4p 5 4d 5 ) transitions were The energy parameters obtained in the final fitting are collected in Table A12 for 4d 4 and Table A13 for 4d 3 5p.For the meaning of the energy parameters and the procedure of the calculations see Section 3.1.Root mean square deviations of the fitting were 26 and 47 cm −1 in the 4d 4 and 4d 3 5p configurations, respectively.In case of the 4d 3 5p configuration the fitting is affected by the interaction with the levels of the 4p 5 4d 5 configuration.The 4d 3 5p levels above ~424,000 cm −1 overlap with the low lying 4p 5 4d 5 levels.Their interaction cannot be taken into account in the orthogonal operator code.The LS-coupling scheme is good approximation for the 4d 4 levels.The value of the first component of the eigenvector composition for all levels is not less than 50%, thus a unique label by the name of the first component can be assigned to all energy levels.To differentiate 4d 4 terms with the same LS values (recurring terms) the seniority numbers are used in the orthogonal operator code, whereas the Nielson and Koster sequential indices [20] are employed in the Cowan code [14].Both labels are retained in Table A7 for the 4d 4 levels because the 4d 4 -(4d 3 5p + 4d 3 4f + 4p 5 4d 5 ) transitions were analyzed with the aid of the Cowan code as described below.Contrary to 4d 4 , the percentage of the first component of the eigenvector composition is less than 50% for many of the 4d 3 5p levels.It goes down to 16%.It makes LS-labeling of many levels meaningless in many cases.Therefore, the energy level values are listed in Table A2 along with the LSJ labels for the wavelength identification.
The identification of the 4d 4 -(4d 3 5p + 4d 3 4f + 4p 5 4d 5 ) transitions using the Cowan code resulted in 118 classified lines in the region 162-189 Å (Table A3).Seventeen lines were doubly classified.The wavelengths and intensities of 10 lines are affected by blending with the Ag IX lines.Table A9 contains the (4d 3 4f + 4p 5 4d 5 ) levels above 556,000 cm −1 .It was possible to find 58 levels of these configurations with the uncertainties from 7 to 19 cm −1 .Cowan's calculations of the odd level system were performed for a matrix of interacting configurations 4d 3 5p + 4d 3 6p + 4d 2 5s5p + 4d5s 2 5p + 4d 3 (4f-6f) + 4p 5 4d 5 + 4p 5 4d 4 5s.Starting energy parameters for the 4d 3 5p, 4d 3 4f and 4p 5 4d 5 configurations in Ag VIII were estimated by extrapolation of the scaling factors (the ratios of the fitted to the corresponding Hartree -Fock energy parameters) from Pd VII [21] and Pd VIII [8].The ab initio electrostatic parameters in the unknown configurations were multiplied by 0.85 scaling factor.The configuration interaction parameters were scaled by 0.8 and the average energies along with the spin-orbit parameters were fixed at the corresponding HF values.Final energy parameters for the 4d 3 5p, 4d 3 4f and 4p 5 4d 5 configurations obtained in the fitting of the calculated energy levels to the experimental ones using the Cowan code are presented in Table A14.Standard deviation of the fitting σ was 213 cm −1 .It should be noted, that for the 4d 3 levels alone, the fitting by the Cowan code results in σ = 129 cm −1 what is 2.7 times larger than at the fitting using the orthogonal parameter code (see Table A13).
All found levels belong to the upper part of configurations ("emissive zone" [22]) from 557,000 to 669,000 cm −1 .Only the levels for this energy range are listed in Table A9.According to our calculations full spread of the 4d 3 4f + 4p 5 4d 5 levels cover the range up to 424,000 cm −1 overlapping with the 4d 3 5p levels.Because of significant uncertainty in prediction of the low lying 4d 3 4f + 4p 5 4d 5 levels they are omitted from Table A9.
Examination of Table A9 shows that the percentage contribution of the leading eigenvector component never exceeds 41% and can be as low as 9%.Moreover, the 4d 3 4f wave function can be found as the leading component only at 13 levels with the largest contribution 31%, second component being mostly 4p 5 4d 5 .Therefore, not only LS-assignment of many levels in Table A3, but also configuration attributions are arbitrary in many cases.Therefore, in Table A9, the upper levels of the transitions are designated by their energies and J values, whereas for convenience, a configuration name and LS-label are given according to the output files from the Cowan code in spite of possible ambiguity in many cases.

Ag IX
The scheme of the 4d 3 , 4d 2 5p, 4d 2 4f and 4p 5 4d 4 levels for Ag IX is shown in Figure 4.It shows that in comparison with Ag VII and Ag VIII the 4d 2 5p levels are almost fully imbedded within the widely spread 4d 2 4f + 4p 5 4d 4 levels.The levels of all odd configurations strongly interact.Their initial prediction in the framework of the Cowan code was performed by cross-extrapolation of the scaling factors and effective parameters from isonuclear Ag VIII (this work) and isoelectronic Pd VIII [8].The 4d 3 energies were calculated in the framework of the orthogonal parameters by extrapolation from Ag VII and Ag VIII (Table A12) and used as an input to Cowan's calculations of the 4d 3 -(4d 2 5p + 4d 2 4f + 4p 5 4d 4 ) transition probabilities.Thus predicted energy levels and transition probabilities were then used for the spectrum analysis by the IDEN code [12].As a result, 132 lines were identified in the 4d 3 -(4d 2 5p + 4d 2 4f + 4p 5 4d 4 ) transition array (Table A4).Nine lines were doubly classified and one line was trebly classified.The 4d 3 -4d 2 5p part of this transition array lying in the 221-244 Å region is overlapped by unidentified lines (see Figure 1) discussed in Section 3.1.Nevertheless, it was possible to select the majority of the Ag IX lines by observation of their intensities with the change of the vacuum spark excitation conditions.The other 4d 3 − (4d 2 4f + 4p 5 4d 4 ) part falls in the middle of the region where the spectrum consists of many overlapping lines in Ag VIII-Ag XII.Therefore 10 lines of Ag IX are found to be blended with Ag VIII and 8 with Ag X.In total, 17 levels of the 4d 3 configuration and 78 levels of the 4d 2 5p + 4d 2 4f + 4p 5 4d 4 configurations were established and collected in Tables 10 and 11, respectively.The uncertainty of relative positions of the levels after optimization by LOPT [19] ranges from 4 to 17 cm −1 for the ground-state configuration and from 6 to 19 cm −1 for the excited configurations.
As was mentioned above the energy levels of the 4d 3 configuration were treated by orthogonal operator technique.As in Ag VII and Ag VIII calculated matrix consisted of three interacting configurations: 4d 3 + 4d 2 5s + 4d5s 2 with similar scaling of the energy parameters for unknown configurations.The levels of the 4d 3 configuration are presented in Table A10 along with the eigenvector compositions and deviations from the orthogonal parameter calculations.Standard deviation of the fitting was 27 cm −1 .The resulting energy parameters of this configuration are collected in Table A12 in comparison with those of 4d 4 (Ag VIII) and 4d 5 (Ag VII).Table A12 shows regular behavior of the parameters and scaling factors along this part of the isonuclear sequence of silver ions.The labeling of the 4d 3 energy levels by the fist component of their eigenvectors is unambiguous.
Table A11 contains all 306 levels of the 4d 2 5p + 4d 2 4f + 4p 5 4d 4 configurations.Because of the numerous blends only 78 levels were found.Similar to Ag VIII, a set of the interacting configurations (4d 2 5p + 4d 2 6p + 4d5s5p + 5s 2 5p + 4d 2 (4f − 6f) + 4p 5 4d 4 + 4p 5 5d 3 5s) with the same treatment of the unknown configurations was used in the Cowan code calculations.The energy parameters for these configurations in Ag IX are listed in Table A14.The standard deviation of the fitting σ was 327 cm −1 , to be compared with σ = 213 cm −1 in Ag VIII.It should be noted that in Ag IX more energy parameters than in Ag VIII were fixed on the estimated values for stability of the fitting.Similar considerations are applied to the eigenvector composition of the Ag IX odd levels.There are ambiguities in the LSlabeling and configuration assignment of the levels.Only the level energy and J value can serve as unique label, what is used in the list of the identified lines in Table A4.As a result, 132 lines were identified in the 4d 3 -(4d 2 5p + 4d 2 4f + 4p 5 4d 4 ) transition array (Table A4).Nine lines were doubly classified and one line was trebly classified.The 4d 3 -4d 2 5p part of this transition array lying in the 221-244 Å region is overlapped by unidentified lines (see Figure 1) discussed in Section 3.1.Nevertheless, it was possible to select the majority of the Ag IX lines by observation of their intensities with the change of the vacuum spark excitation conditions.The other 4d 3 -(4d 2 4f + 4p 5 4d 4 ) part falls in the middle of the region where the spectrum consists of many overlapping lines in Ag VIII-Ag XII.Therefore 10 lines of Ag IX are found to be blended with Ag VIII and 8 with Ag X.In total, 17 levels of the 4d 3 configuration and 78 levels of the 4d 2 5p + 4d 2 4f + 4p 5 4d 4 configurations were established and collected in Tables A10 and A11, respectively.The uncertainty of relative positions of the levels after optimization by LOPT [19] ranges from 4 to 17 cm −1 for the ground-state configuration and from 6 to 19 cm −1 for the excited configurations.

Discussion
As was mentioned above the energy levels of the 4d 3 configuration were treated by orthogonal operator technique.As in Ag VII and Ag VIII calculated matrix consisted of three interacting configurations: 4d 3 + 4d 2 5s + 4d5s 2 with similar scaling of the energy parameters for unknown configurations.The levels of the 4d 3 configuration are presented in Table A10 along with the eigenvector compositions and deviations from the orthogonal parameter calculations.Standard deviation of the fitting was 27 cm −1 .The resulting energy parameters of this configuration are collected in Table A12 in comparison with those of 4d 4 (Ag VIII) and 4d 5 (Ag VII).Table A12 shows regular behavior of the parameters and scaling factors along this part of the isonuclear sequence of silver ions.The labeling of the 4d 3 energy levels by the fist component of their eigenvectors is unambiguous.
Table A11 contains all 306 levels of the 4d 2 5p + 4d 2 4f + 4p 5 4d 4 configurations.Because of the numerous blends only 78 levels were found.Similar to Ag VIII, a set of the interacting configurations (4d 2 5p + 4d 2 6p + 4d5s5p + 5s 2 5p + 4d 2 (4f − 6f) + 4p 5 4d 4 + 4p 5 5d 3 5s) with the same treatment of the unknown configurations was used in the Cowan code calculations.The energy parameters for these configurations in Ag IX are listed in Table A14.The standard deviation of the fitting σ was 327 cm −1 , to be compared with σ = 213 cm −1 in Ag VIII.It should be noted that in Ag IX more energy parameters than in Ag VIII were fixed on the estimated values for stability of the fitting.Similar considerations are applied to the eigenvector composition of the Ag IX odd levels.There are ambiguities in the LSlabeling and configuration assignment of the levels.Only the level energy and J value can serve as unique label, what is used in the list of the identified lines in Table A4.

Discussion
The spectra reported in this article are relevant to the verification of the identifications of the EUV spectra of Sn ions [9,10] which are used as a "fuel" in the radiation sources for the projection lithography at the 135 Å wavelength.The previous analyses in [9,10] were performed without any isoelectronic or isoionic support.The isoelectronic sequence Rh VIII-Cd XI was recently studied in [7].It was found by extrapolation to Sn XIII that the identification of this spectrum should be revised.Similar conclusion was made after the identification of the M1 transitions between the levels of ground-state configurations in Sn XIII and other ions with open 4d-shell [23].More data on the VUV spectra of the neighboring to Sn elements are needed.The analyses of Ag VII, Ag VIII and Ag IX were performed in this work for the first time and all Ag ion spectra with the 4d k (k = 1-10) ground-state configuration now became known.After the studies of spectra of the 4d-palladium ions ( [8] and references therein) the present work on Ag ion spectra is the next step in the study of the ion spectra isoelectronic with Sn IX-Sn XIII.The work on Cd-and In-ion spectra is in progress at this laboratory.
Author Contributions: A.R. recorded the spectra, performed their analyses and wrote the paper; E.K. made spectrum measurements and wrote the paper.

Conflicts of Interest:
The authors declare no conflict of interest.a The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number preceding the terms is the seniority number.The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number preceding the terms is the seniority number.The number following the terms displays Nielson and Koster sequential indices [20].Table A14.Fitted (FIT) with their uncertainties (Unc.) and Hartree -Fock (HF) energy parameters in cm −1 of the odd 4d 3 5p, 4d 3 4f, and 4p 5 4d 4 configurations in Ag VIII and 4d 2 5p, 4d 2 4f and 4p

Figure 1 .
Figure 1.Spectrum of silver in the region 150-350 Å excited in a vacuum spark.Lines of different ion spectra are marked by different colours: Ag VI-royal blue, Ag VII-wine, Ag VIII-magenta, Ag IX-green, Ag X-blue, Ag XI-red, Ag XII-black and unidentified lines-gray.

Figure 1 .
Figure 1.Spectrum of silver in the region 150-350 Å excited in a vacuum spark.Lines of different ion spectra are marked by different colours: Ag VI-royal blue, Ag VII-wine, Ag VIII-magenta, Ag IX-green, Ag X-blue, Ag XI-red, Ag XII-black and unidentified lines-gray.

Figure 2 .
Figure 2. Energy levels of Ag VII.The arrows show electric dipole transitions.The levels found in this work and studied transitions are marked by red color.Black color indicates unknown levels and transitions.

Figure 2 .
Figure 2. Energy levels of Ag VII.The arrows show electric dipole transitions.The levels found in this work and studied transitions are marked by red color.Black color indicates unknown levels and transitions.

Figure 3 .
Figure 3. Energy levels of Ag VIII.The arrows show electric dipole transitions studied in this article.The levels found in this work are marked by red color.Black color indicates unknown levels.

Figure 3 .
Figure 3. Energy levels of Ag VIII.The arrows show electric dipole transitions studied in this article.The levels found in this work are marked by red color.Black color indicates unknown levels.

Figure 4 .
Figure 4. Energy levels of Ag IX.The arrows show electric dipole transitions studied in this article.The levels found in this work are marked by red color.Black color indicates calculated positions of unknown levels.

Figure 4 .
Figure 4. Energy levels of Ag IX.The arrows show electric dipole transitions studied in this article.The levels found in this work are marked by red color.Black color indicates calculated positions of unknown levels.

a
The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c Configuration attribution is arbitrary in a few cases (see text); d For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number following the terms of the 4d 4 configuration displays Nielson and Koster sequential indices[20].
a Observed wavelengths, d-doubly identified, t-trebly identified; b 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 only from that line; c Relative intensity; VI-line is also identified as Ag VI; e The number preceding the terms is seniority number.

Table A2 .
Cont.Observed wavelengths, d-doubly identified, t-trebly identified; b 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 only from that line; c Relative intensity; e The number preceding the terms is seniority number; f Term attribution is arbitrary in a few cases (see text) for the level composition, see TableA8.The number preceding the terms of the 5d 3 configuration is seniority number. a
[20]served wavelengths: d-doubly identified, w-wide; b 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 only from that line; c Relative intensity; IX-line is also identified as Ag IX; e Numbers following the term values display Nielson and Koster sequential indices[20]; f Designation and configuration attribution is arbitrary in a few cases (see text), for the level composition, see TableA9.Numbers following the term values of the 4d 5 configuration display Nielson and Koster sequential indices[20].

Table A4 .
[20].Observed wavelengths: d-doubly identified, t-trebly identified; b 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 only from that line; c Relative intensity: X, VIII-line is also identified as respectively Ag X or Ag VIII; m masked by O IV; e Numbers following the term values display Nielson and Koster sequential indices[20]; f Designation and configuration attribution is arbitrary in a few cases (see text), for the level composition, see TableA11.Numbers following the term values of the 4d 4 configuration display Nielson and Koster sequential indices[20]. a

Table A5 .
Energies (in cm −1 ) of the 4d 5 configuration of Ag VII.

Table A5 .
Cont.The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number preceding the terms is the seniority number. a

Table A7 .
Energies (in cm −1 ) of the 4d 4 configuration of Ag VIII.

Table A8 .
Cont.The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number preceding the terms is the seniority number. a

Table A9 .
[20].The star * indicates a calculated value for the level; b The difference between the observed and the calculated energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number following the terms displays Nielson and Koster sequential indices[20]. a

Table A10 .
[20]gies (in cm −1 ) of the 4d 3 configuration of Ag IX.The star * indicates a calculated value for the level; b The difference between the observed and the calculated by orthogonal parameter technique energies; c For the eigenvector composition, up to three components with the largest percentages in the LS-coupling scheme are listed.The number following the terms displays Nielson and Koster sequential indices[20]. a

Table A13 .
Cont. r1-parameters are fixed at DF ratio to Ac, r1 parameters are fixed at DF ratio to Sd.Lp; b f-parameter is fixed on predetermined value. a

Table A14 .
5 4d 3 configurations in Ag IX calculated with the Cowan code.Cont.E av (5p), E av (4f) and E av (pd) stand for E av (4d k−1 5p), E av (4d k−1 4f) and E av (4p 5 4d k+1 ) for Ag VIII and Ag IX where k = 4 and 3, respectively; b f-parameter is fixed on predetermined value; c For E av the FIT-HF difference is listed; a d Adjacent pairs of parameters are linked at their HF ratios.