Vol. 1, No. 4/August 1984/J. Opt. Soc. Am. B 631

Spectrum and energy levels of eight-times ionized rubidium(Rb Ix)

Samuel Goldsmith,* Joseph Reader, and Nicolo Acquista

National Bureau of Standards, Washington, D.C. 20234

Received March 12, 1984; accepted April 13, 1984

The spectrum of the copperlike ion Rb Ix was observed with a low-inductance spark and a 10.7-m grazing-incidencespectrograph from 70 to 630 A. From the identification of 18 lines, a system of 16 energy levels of the type 3d'

0nl

was determined. The level system includes the configurations ns (n = 4-7), np (n - 4-7), nd (n = 4), nf (n = 4),and ng (n = 6). The 4f 2F term is inverted. The observed energy levels are compared with relativistic and nonrela-tivistic Hartree-Fock calculations. The ionization energy derived from the 3d'Orns and np series is 1 214 900 + 200cm- 1 (150.63 0.02 eV).

Rb ix is a member of the Cu I isoelectronic sequence. Theground configuration is 3d'0 4s. The 4s-4p resonance lineswere first observed by Mack.' Recently, Reader and Ac-quista2 observed the 4p-5s transitions of Rb Ix and remea-sured the 4s-4p transitions. In the present work we extendedthese identifications to a total of 18 lines representing tran-sitions between 16 energy levels of the type 3dlnl.

EXPERIMENT

The spectrograms were the same ones used for the results ofRef. 2. The light source was a low-inductance vacuum spark 3

operating at voltages between 1 and 12 kV. The capacitancewas 14.2 tF. The anode consisted of an aluminum rod filledwith Rb2CO3 . The cathode was a titanium rod. The spectrawere photographed on the National Bureau of Standards(NBS) 10.7-m grazing-incidence spectrograph at an angle ofincidence of 800. The grating had 1200 lines/mm, providinga plate factor of 0.25 A/mm at 300 A. The region covered was70-630 A. Wavelength calibration was obtained from sepa-rate spark spectra of yttrium 4 as well as spectra 5 of Ti, Al, C,0, and F occurring in, the Rb spark.

The ionization stages of the observed lines were distin-guished by studying the variation of relative intensity withspark voltage. The Rb IX spectrum was optimally excited ata voltage of about 4 kV. Lines of Rb ix could also be distin-guished by their relatively large width, as the observed linewidths vary directly with the stage of ionization, as noted inRef. 2. As with Sr x,6 the spectrum of Rb Ix is much weakerthan spectra obtained for other copperlike spectra excitedwith the low-inductance spark,4 7-9 and the analysis is there-fore not as complete. In particular, only one member of eachof the nd, nf, and ng series could be observed.

SPECTRUM ANALYSIS

The wavelengths, intensities, and classifications of the ob-served transitions of Rb ix are given in Table 1. The uncer-tainty of the wavelengths is ±0.005 A. The intensities arevisual estimates of plate blackening.

For most of the transitions, the identifications were carriedout by extrapolating the wave numbers from higher ions of thesequence. For these extrapolations, the wave number of wasexpressed as o- = aZ 2 + Z, + y + Z, -1, and the constantsa, , y, and were adjusted to give the best fit for the ionsSr x-Mo XIV.' Z is the effective nuclear charge; Z, = Z - N+ 1, where Z is the atomic number and N is the number ofelectrons. By using this procedure, the wavelengths forRb IX could be predicted to within about 0.2 A of their ob-served values. The relativistic Hartree-Fock (HF) calcula-tions of Cheng and Xim 10 were also of considerable help inmaking the identifications.

The energy levels are listed in Table 2. 'The level values andtheir uncertainties were determined by a least-squares opti-mization procedure." The uncertainties of the fine-structureintervals correspond to an estimated uncertainty of ±0.003A in the wavelength intervals. The fine-structure intervalsof the np and nd configurations are in good agreement withthe itervals predicted by Curtis.1 2

The observed levels and transitions are shown in Fig. 1.The wavelength given for the 4p 2

P 11 2 -6S 2S1/2 transition inthis figure is the value predicted from the optimized energylevels. This line is evidently masked by an 0 v line at 151.447A in our spectra. Similarly, the 4f-5g transitions, predictedat 459.5 A, are probably masked by strong lines of C III in thisregion. We have therefore not been able to establish the 5g2G term. Our failure to establish the 5d 2D and 5f

2F termsis probably related to a cancellation of oscillator strength ofthe 4p-5d and 4d-5f transitions caused by a change in signof the radial transition integral along the isoelectronic se-quence.13 1 4 The 4s

2S1/2-7p

2P 1 / 2 transition appears to be

masked by a line of a lower ionization stage.In Table 3 we compare the observed level values with the

relativistically calculated values of Cheng and Kim.10 Ofparticular interest is the fine-structure interval of the 4f

2Fterm. The observed interval of -38 i 3 cm-1 compares to acalculated value of -47 cm-1 . Inverted 4f

2F fine-structureintervals have also been observed in neighboring ions of thesequence.4 615 16

In Table 4 we give the nonrelativistic HF values17 of theaverage energies and spin-orbit constants of the observed

0740-3224/84/040631-04$02.00 © 1984 Optical Society of America

Goldsmith et al.

632 J. Opt. Soc. Am. B/Vol. 1, No. 4/August 1984

Table 1. Observed Lines of Rb Ix

x (A) Intensity a (cm-,) Classification

103.589 20 965 353 4s 2S1/2 -7p 2P3 /2117.106 250 853 927 4s 2 8 /2_6

p 2 P3 /2

117.436 100 851 528 4s 2 1/ 2 -6P 2P1/2127.13 10 786 600 4p 2P1/2-7S 2S1/2129.170 20 774 174 4p 2 P3/2 -7s 2S1/2154.324 200 647 987 4p 2 P3/2 -6S 2S1/2154.935 1 000 645 432 4s 2 S,/ 2 -5p 2P3 /2156.107 600 640 586 4s 2

S112 -5p 21/2

239.567 800 417 420 4p 2 PI/ 2-5S 2S1/2

246.862 2 000 405 085 4p 2 P3 /2 -5s 2S1/2306.286 200 326 492.2 4f 2F-6g 2G383.906 1 500 260 480.4 4p 2

/2-4d 2D3/2400.148 2 500 249 907.5 4p 2

P3/2-4d 2D5/2

402.992 600 248 143.9 4p 2P3/2-4d 2D3/2452.043 600 221 217.9 4d 2

D3/ 2 -4f 2

F5/2

455.752 800 219 417.6 4d 2D 5 /2-4f

2F7 /2583.399 10 000 171 409.3 4s 2

S1/2-4p 2P3 /2628.632 4 000 159 075.6 4s 2 S,/2-4p

2 P1/2

Table 2. Energy Levels of Rb Ix

Effective Fine-Energy Uncer- Quantum StructureLevel tainty Number Interval

Term J (cm-') (cm-') (n*) (cm-')

4s 2S 1/2 0 2 2.7049

4p 2 1/2 159 075 2 2.9015 12 335 23/2 171410 2 2.9186

4d 2D 3/2 419 554 3 3.3430 1 763 25/2 421 317 3 3.3467

4f 2F 7/2 640 734 4 3.9346 -38 35/2 640 772 4 3.9347

5s 2S 1/2 576 495 8 3.7314

5p 2 1/2 640 586 21 3.9341 4 846 + 103/2 645 432 21 3.9508

6s 2S 1/2 819 396 21 4.7407

6p 2P 1/2 851 528 36 4.9459 2 399 203/2 853 927 36 4.9623

6g 2G 7/2, 9/2 967 244 6 5.991

7s 2S 1/2 945 584 30 5.745

7p 2 3/2 965 353 47 5.968

Limit 1 214 900 200

configurations together with the observed values. The HFenergies represent the difference between the total energy ofa particular configuration and the total energy of the 4s con-figuration.

IONIZATION ENERGY

In Table 5 we list the values of the ionization energy obtainedfrom the observed series. We adopt for the ionization energythe value 1 214 900 cm-'. As was found for the ions Sr xthrough Mo XIV, the limit derived from the first three mem-

Table 3. Comparison of Observed Energy Levels (incm-') of Rb Ix with the Relativistically Calculated

Values of Ref. 10

Calculateda ObservedTerm J Energy Interval Energy Interval4s 2 S 1/2 0 0

4p 2p 1/2 158 254 12 026 159 075 12 3353/2 170 280 171410

4d 2D 3/2 416185 1718 4i9554 1 7635/2 417 903 421317

4f 2F 7/2 635 257 -47 640 734 -385/2 635 304 640 772

5s 2S 1/2 570 769 576 4955p 2P 1/2 634 659 4 746 640 586 4 846

3/2 639 405 645 4326s 2S 1/2 811 839 819 3966p 2P 1/2 843 969 2 385 851 528 2 399

3/2 846 354 853 9276g 2G 7/2, 9/2 958 325 967 243

a The calculated values are differences of the total energies of Ref. 10.

Table 4. Energy Parameters (in cm-') for Rb Ix

Configu- Param- Observed Observed -

ration eter HFa Observed HF HF

4s Eav 0 05s Eav 559800 576495 167006s Ea 797 400 819 396 22 0007s Eav 921400 945 584 24 200

4p Eav 154500 167 298 12800t4p 7 208 8 223 1.141

5p Eav 622 300 643 817 21 500Asp 2 839 3 231 1.138

6p Eav 828 700 853 127 24400t6p 1 429 1 599 1.119

7p Eav 939 600 9 6 4 9 0 0 b 25 300{7p 822 930c

4d Eav 398 600 420612 22000t4d 646 705 1.091

4f Eav 617 300 640750 23 400t4f 20

6g Eav 940 100 967 244 27 100t6g 2

a Calculated with the program of Ref. 17.b Calculated from observed position of 7p 2P3/ 2 level and predicted value of

{7p-c Predicted value based on estimated observed/HF ratio of 1.13.

Table 5. Values for the Ionization Energy of Rb IxDetermined from Various Series a

QuantumDefect Limit

Series Formula (cm'1)

4s-6s linear 1 214 1005s-7s linear 1 214 7204s-7s quadratic 1 214 850

4p-6p linear 1 213 8504p 2 P3 2-6P P3 /2 linear 1 213 8405p 2 P3/2-7p 2P3/2 linear 1 214 8204p 2

P3/2-7p 2P3/2 quadratic 1 215 050

a Adopted Value, 1 214 900 200 cm-1.

Goldsmith et al.

Vol. 1, No. 4/August 1984/J. Opt. Soc. Am. B 633

600/,~ ~ ~ ~ ~ ~ ~~~~~~~~ b i i.. 400 .5/

200 -3 Rb ix

0 4 1/2~4 12.

ns np nd nf ng

Fig. 1. Grotian diagram for Rb IX. Wavelengths are in A. Intensities are indicated in parentheses following the wavelengths. The wavelengthindicated for the 4p 2

PI/ 2 -6s 2

S 1 /2 transition is a predicted value.

bers of the np series is lower than that derived from the firstthree members of the ns series. From the uncertainties of thelevel values, we estimate an uncertainty for the limit of +200cm-I. The ionization energy of Rb Ix is thus 1214900 i 200cm-l (150.63 ± 0.02 eV).

ACKNOWLEDGMENTS

We would like to thank A. N. Ryabtsev of the Institute ofSpectroscopy in Moscow for sending us his measurements ofthe 4 s-6p and 4s-7p transitions. This research was sup-ported in part by the Office of Magnetic Fusion Energy of theU.S. Department of Energy.

* NBS Guest Worker, on leave from Tel-Aviv University,Tel-Aviv, Israel. Present address, Laboratory of Plasma andFusion Energy Studies, University of Maryland, College Park,Maryland 20742.

REFERENCES

1. J. E. Mack, "Excitation of high optical energy levels," Phys. Rev.38, 193-194 (1931).

2. J. Reader and N. Acquista, "4s-4p resonance transitions in highlycharged Cu- and Zn-like ions," Phys. Rev. Lett. 39, 184-187(1977).

3. U. Feldman, M. Swartz, and L. Cohen, "Vacuum ultravioletsource," Rev. Sci. Instrum. 38, 1372-1373 (1967).

4. J. Reader and N. Acquista, "Spectrum and energy levels of ten-times ionized yttrium (Y XI)," J. Opt. Soc. Am. 69, 1285-1288(1979).

5. R. L. Kelly and L. J. Palumbo, Atomic and Ionic Emission LinesBelow 2000 Angstroms, Hydrogen through Krypton, Naval Re-search Laboratory Rep. No. 7599 (U.S. Government PrintingOffice, Washington, D.C., 1973).

6. N. Acquista and J. Reader, "Spectrum and energy levels ofnine-times ionized strontium (Sr x)," J. Opt. Soc. Am. 71,569-573(1981).

7. J. Reader and N. Acquista, "Spectrum and energy levels ofeleven-times ionized zirconium (Zr XII)," J. Opt. Soc. Am. 69,1659-1662 (1979).

8. J. Reader and N. Acquista, "Spectrum and energy levels oftwelve-times ionized niobium (Nb xiii)," J. Opt. Soc. Am. 70,317-321 (1980).

9. J. Reader, G. Luther, and N. Acquista, "Spectrum and energylevels of thirteen-times ionized molybdenum (Mo XIV)," J. Opt.Soc. Am. 69, 144-149 (1979).

10. K. T. Cheng and Y.-K. Kim, "Energy levels, wavelengths, and

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634 J. Opt. Soc. Am. B/Vol. 1, No. 4/August 1984

transition probabilities for Cu-like ions," At. Data Nucl. DataTables 22, 547-563 (1978).

11. Optimization of the level values was done with the computerprogram ELCALC, written by L. J. Radziemski, Jr., Los AlamosNational Laboratory, Los Alamos, New Mexico 87544.

12. L. J. Curtis, "An explicit empirical formula for fine-structureseparations of 2Po and 2D terms for ions in the Cu isoelectronicsequence," J. Phys. B 14, 631-640 (1981).

13. L. J. Curtis and D. J. Ellis, "A formula for cancellation disap-pearances of atomic oscillator strengths," J. Phys. B 11, L543-L546 (1978).

Goldsmith et al.

14. L. J. Curtis, "Cancellations in atomic dipole transition momentsin the Cu isoelectronic sequence," J. Opt. Soc. Am. 71, 566-568(1981).

15. A. E. Livingston and S. J. Hinterlong, "Spectrum of Br VII," Phys.Rev. A 23, 758-760 (1983).

16. A. E. Livingston, L. J. Curtis, R. M. Schectman, and H. G. Berry,"Energies and lifetimes of excited states in copperlike Kr VIII,"Phys. Rev. A 21, 771-781 (1980).

17. C. Froese, "Numerical solution of the Hartree-Fock equations,"Can. J. Phys. 41, 1895-1910 (1963).