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Spectrum and energy levels of five-times ionized zirconium (Zr VI)

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Published 5 January 2016 • © 2016 Not subject to copyright in the USA/Contribution of National Institute of Standards and Technology
, , Citation Joseph Reader and Mark D Lindsay 2016 Phys. Scr. 91 025401 DOI 10.1088/0031-8949/91/2/025401

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joseph.reader@nist.gov

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1 National Institute of Standards and Technology, Gaithersburg, MD 20899-8422, USA

Dates

  1. Received 19 August 2015
  2. Revised 4 November 2015
  3. Accepted 2 December 2015
  4. Published

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1402-4896/91/2/025401

Abstract

We carried out a new analysis of the spectrum of five-times-ionized zirconium Zr VI. For this we used sliding-spark discharges together with normal- and grazing-incidence spectrographs to observe the spectrum from 160 to 2000 Å. These observations showed that the analysis of this spectrum by Khan et al (1985 Phys. Scr. 31 837) contained a significant number of incorrect energy levels. We have now classified ∼420 lines as transitions between 23 even-parity levels 73 odd-parity levels. The 4s24p5, 4s4p6, 4s24p44d, 5s, 5d, 6s configurations are now complete, although a few levels of 4s24p45d are tentative. We determined Ritz-type wavelengths for ∼135 lines from the optimized energy levels. The uncertainties range from 0.0003 to 0.0020 Å. Hartree–Fock calculations and least-squares fits of the energy parameters to the observed levels were used to interpret the observed configurations. Oscillator strengths for all classified lines were calculated with the fitted parameters. The results are compared with values for the level energies, percentage compositions, and transition probabilities from recent ab initio theoretical calculations. The ionization energy was revised to 777 380 ± 300 cm−1 (96.38 ± 0.04 eV).

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1. Introduction

The zirconium atom has atomic number Z = 40. Five-times-ionized zirconium, Zr VI, is isoelectronic with neutral Br. The ground state is 4s24p5 2P, and excited states are mainly of the type 4s24p4nl. The first work on this spectrum was done by Paul and Rense [1]. From their observation of transitions to the ground term, they determined the 4p5 2P interval as well as the first excited state 4s4p6 2S1/2 and several levels of the 4p44d and 4p45s configurations. Subsequently, Chaghtai [2, 3] re-observed the resonance transitions and found that nearly all of Paul and Rense's excited levels were in error. Chaghtai gave values for 16 new levels in these configurations. Subsequently, Ekberg et al [4] re-investigated the spectrum and gave improved values for nearly all levels of the 4p44d and 5s configurations. Seven of Chaghtai's levels were found to be spurious. Chaghtai et al [5] later extended the resonance lines to the 4p45d, 6s, 6d, and 7s configurations. Khan et al [6] determined the levels of the 4p45p configuration by using longer wavelength transitions from the above configurations to levels of 4p45p.

In the present work we re-observed the spectrum of Zr VI in the vacuum ultraviolet and revised the analysis considerably. In particular, 13 of the 21 levels of 4p45p reported by Khan et al [6] were found to be spurious. Several new levels of 4p44d, 5s, 5d, and 6s reported in [6] were also found to be spurious.

2. Experiment

The observations used for this work were the same as used for earlier work in our laboratory on zirconium [7]. The main light source was a low-voltage sliding-spark with metallic Zr electrodes. The source was operated as described by Reader et al [8]. From 500 to 2000 Å the spectra were recorded on our 10.7 m normal-incidence vacuum spectrograph. From 160 to 500 Å the spectra were recorded on our 10.7 m grazing incidence spectrograph. Both instruments had gratings with 1200 lines/mm. The plate factor for the normal-incidence spectrograph was about 0.78 Å mm−1. The plate factor for the grazing-incidence spectrograph at 350 Å was 0.25 Å mm−1. From 600 to 2000 Å the spectra were calibrated by spectra of Cu II excited in a hollow cathode discharge. Below 600 Å calibration was obtained from lines of Y in various stages of ionization. Shifts between the positions of the reference spectra and those of the unknown spectra due to differing illumination of the spectrograph were removed by use of impurity lines of oxygen, nitrogen, carbon, and silicon. Complete references for the calibration spectra are given in [7].

Ionization stages were distinguished by comparing the intensities of the lines at various peak currents in the spark. The spectra of Zr VI were relatively enhanced at a peak current of about 2000 A.

The wavelengths, intensities, and classifications of the observed lines of Zr VI are given in table 1. The intensities are estimates of photographic plate blackening. No effort was made to harmonize the intensities through the complete region of observation. The general uncertainty of the wavelengths is ±0.005 Å. Hazy lines (h) were given an uncertainty of ±0.010 Å; perturbed (p), or asymmetric lines (s, l) an uncertainty of ±0.020; unresolved (u) or doubly classified (dc) lines an uncertainty of ±0.030 Å. By perturbed we mean that the measured position may possibly be affected by the presence of a close line. The line at 1749.353 Å could not be measured in the original observations because of a local defect in the emulsion of one of the photographic plates. It was later recorded with an image plate [9, 10] on the normal-incidence spectrograph. Its wavelength uncertainty was also taken as ±0.005 Å. All uncertainties are reported at the level of one standard deviation.

Table 1.  Observed spectral lines of Zr VI. Wavelengths and wave numbers are in vacuum. Wavelength values in parentheses are Ritz values. General uncertainty of the observed wavelengths is ±0.005 Å. Uncertainties for less certain wavelengths are given in section 2 of text. Acc. is the accuracy estimate.

λobs(Å) Intensity   σobs(cm−1) Even Odd λRitz(Å) Unc(λRitz-Å) gUA(s−1) $\mathrm{log}({g}_{L}f)$ |CF| Acc.
        levela levela            
165.930 5   602 664 6s31 p5 3 165.9308 0.0011 2.28E + 09 −2.03 0.15 D+
170.342 6   587 054 6s31 p5 1 170.3408 0.0012 6.37E + 09 −1.56 0.60 D+
174.066 6   574 495 5d85 p5 3 174.0660 0.0003 2.46E + 09 1.95 0.30 D+
174.489 70   573 102 6s25 p5 3 174.4891 0.0003 2.27E + 10 0.99 0.65 D+
178.236 50   561 054 6s21 p5 3 178.2371 0.0003 9.00E + 09 1.37 0.54 D+
178.776 60   559 359 6s23 p5 3 178.7769 0.0003 8.48E + 09 1.39 0.55 D+
178.794 30   559 303 5d83 p5 1 178.7993 0.0004 6.19E + 09 1.53 0.26 D+
179.144 10   558 210 6s11 p5 3 179.1445 0.0003 1.17E + 09 2.25 0.51 E
179.308 70   557 700 6s33 p5 1 179.3084 0.0003 2.14E + 10 0.99 0.70 D+
182.213 30   548 808 5d73 p5 3 182.2139 0.0003 3.07E + 09 1.82 0.16 D+
182.550 20   547 795 5d51 p5 3     4.24E + 09 1.67 0.14 D+
182.657 90   547 474 6s13 p5 3 182.6578 0.0003 1.86E + 10 1.03 0.25 D+
182.744 80   547 214 5d75 p5 3 182.7439 0.0003 1.34E + 10 1.18 0.45 D+
183.262 70   545 667 5d65 p5 3 183.2623 0.0003 9.69E + 09 1.31 0.35 D+
183.336 60 dc 545 447 6s15 p5 3 183.3357 0.0004 2.33E + 09 1.93 0.67 D+
183.336 60 dc 545 447 6s21 p5 1 183.3471 0.0003 1.07E + 10 1.27 0.40 D+
183.680 90   544 425 5d63 p5 3     3.65E + 10 0.73 0.50 D+
183.908 5   543 750 6s23 p5 1 183.9068 0.0004 1.19E + 09 2.22 0.35 E
184.063 60   543 292 5d41 p5 3 184.0618 0.0003 6.50E + 09 1.48 0.17 D+
187.075 20   534 545 5d53 p5 3 187.0723 0.0003 2.64E + 09 1.86 0.06 D+
187.361 100   533 729 5d55 p5 3 187.3582 0.0003 2.74E + 10 0.84 0.41 D+
187.549 80   533 194 5d73 p5 1 187.5459 0.0004 2.50E + 10 0.88 0.42 D+
187.830 5 ${\mathcal{l}}$ 532 396 5d45 p5 3 187.8277 0.0003 1.04E + 09 2.26 0.25 E
187.905 60   532 184 5d51 p5 1     1.67E + 10 1.05 0.44 D+
188.490 20   530 532 5d43 p5 3 188.4876 0.0003 2.23E + 09 1.93 0.20 D+
188.912 2 x 529 347 5d35 p5 3 188.9103 0.0003 1.89E + 08 3.00 0.05 E
189.046 3   528 972 5d33 p5 3 189.0444 0.0003 7.85E + 08 2.38 0.31 E
189.101 30   528 818 5d63 p5 1     6.39E + 09 1.47 0.29 D+
189.267 2   528 354 5d31 p5 3 189.2658 0.0003 3.84E + 08 2.69 0.11 E
189.506 5   527 688 5d41 p5 1 189.5041 0.0004 4.92E + 08 2.58 0.02 E
191.557 90   522 038 5d25 p5 3 191.5577 0.0003 2.73E + 10 0.82 0.43 D+
191.666 80   521 741 5d23 p5 3 191.6663 0.0004 1.43E + 10 1.10 0.42 D+
192.182 20 u, J 520 340 5d21 p5 3 192.1679 0.0004 2.51E + 09 1.86 0.20 D+
192.696 60   518 952 5d53 p5 1 192.6968 0.0004 7.84E + 09 1.36 0.23 D+
194.108 1   515 177 5d13 p5 3 194.1104 0.0003 5.39E + 07 3.52 0.01 E
194.197 20 p, x 514 941 5d43 p5 1 194.1988 0.0004 2.32E + 09 1.88 0.12 D+
195.024 2 x 512 757 5d31 p5 1 195.0250 0.0004 4.35E + 08 2.61 0.08 E
197.575 80   506 137 5d23 p5 1 197.5749 0.0005 1.90E + 09 1.95 0.05 D+
236.281 100   423 225 5s31 p5 3 236.2818 0.0005 3.14E + 09 1.58 0.06 D+
245.327 90 u 407 619 5s31 p5 1 245.3261 0.0006 1.62E + 10 0.84 0.47 D+
253.678 80   394 201 5s33 p5 3 253.6812 0.0005 2.26E + 09 1.66 0.04 D+
254.092 400   393 558 5s25 p5 3 254.0939 0.0005 6.20E + 10 0.22 0.65 C
259.888 200   384 781 5s21 p5 3 259.8878 0.0006 2.91E + 10 0.53 0.67 D+
263.310 500   379 780 5s23 p5 3 263.3127 0.0006 4.96E + 10 0.29 0.83 C
264.142 90 p 378 584 5s33 p5 1 264.1361 0.0007 4.67E + 10 0.31 0.61 C
264.940 100   377 444 5s11 p5 3 264.9343 0.0006 6.57E + 08 2.16 0.15 D+
270.480 200   369 713 5s13 p5 3 270.4811 0.0006 6.60E + 10 0.14 0.74 C
270.872 200   369 178 5s21 p5 1 270.8716 0.0007 3.75E + 10 0.39 0.61 C
274.105 200   364 824 5s15 p5 3 274.1024 0.0006 2.76E + 09 1.51 0.33 D+
274.598 100   364 169 5s23 p5 1 274.5941 0.0007 4.14E + 09 1.33 0.24 D+
276.364 80   361 842 5s11 p5 1 276.3582 0.0007 2.53E + 07 3.54 0.01 E
279.198 90 p 358 169 4d83 p5 3 279.1985 0.0007 1.78E + 10 0.68 0.05 D+
282.400 90   354 108 5s13 p5 1 282.3990 0.0008 3.56E + 09 1.37 0.10 D+
288.730 200   346 344 4d51 p5 3 288.7290 0.0008 2.75E + 10 0.46 0.11 D+
290.949 500   343 703 4d85 p5 3 290.9433 0.0007 1.05E + 12 1.12 0.85 C
291.920 500 p 342 560 4d83 p5 1 291.9151 0.0009 6.60E + 11 0.93 0.85 C
294.395 500   339 680 4d73 p5 3 294.3923 0.0007 5.84E + 11 0.88 0.90 C
298.779 300   334 696 4d41 p5 3 298.7796 0.0008 2.81E + 11 0.58 0.71 C
302.351 300   330 741.4 4d51 p5 1 302.3498 0.0010 2.56E + 11 0.55 0.87 C
307.148 30   325 575.9 4d75 p5 3 307.1472 0.0010 3.16E + 06 4.35 0.00 E
308.569 100   324 076.6 4d73 p5 1 308.5658 0.0009 4.65E + 09 1.18 0.02 D+
313.150 300   319 335.8 4d63 p5 3 313.1496 0.0010 1.27E + 10 0.73 0.11 D+
313.389 300   319 092.2 4d41 p5 1 313.3891 0.0010 2.55E + 10 0.43 0.11 C
329.242 300   303 728.0 4d63 p5 1 329.2361 0.0012 1.31E + 10 0.67 0.06 D+
333.768 400   299 609.3 4d65 p5 3 333.7687 0.0010 2.97E + 09 1.31 0.10 D+
340.915 30   293 328.2 4p61 5p83 340.9169 0.0011 1.38E + 09 1.62 0.02 E
343.493 10   291 126.7 4p61 5p61 343.4908 0.0011 2.34E + 07 3.38 0.02 E
348.262 200 p 287 140.1 4d55 p5 3 348.2592 0.0012 9.38E + 08 1.77 0.01 D+
353.221 250   283 108.9 4d45 p5 3 353.2171 0.0011 2.40E + 09 1.35 0.01 D+
357.837 30   279 456.8 4d53 p5 3 357.8365 0.0012 2.21E + 08 2.37 0.00 D+
358.755 300   278 741.8 4d35 p5 3 358.7544 0.0012 1.71E + 09 1.48 0.02 D+
364.080 300   274 664.9 4d43 p5 3 364.0791 0.0013 1.52E + 09 1.52 0.01 D+
366.095 60 p 273 153.1 4p61 5p51 366.0947 0.0012 9.72E + 08 1.71 0.18 D+
366.522 200   272 834.9 4d33 p5 3 366.5226 0.0014 2.11E + 09 1.37 0.02 D+
367.523 300   272 091.8 4d31 p5 3 367.5238 0.0015 1.72E + 09 1.46 0.15 D+
368.494 300   271 374.8 4d25 p5 3 368.4947 0.0015 1.28E + 09 1.58 0.61 D+
368.600 250   271 296.8 4d23 p5 3 368.6010 0.0013 8.52E + 08 1.76 0.01 D+
375.546 30   266 279.0 4d21 p5 3 375.5467 0.0015 2.99E + 07 3.20 0.00 E
378.342 60   264 311.1 4p61 5p63 378.3472 0.0013 1.61E + 09 1.46 0.27 D+
378.992 80   263 857.8 4d53 p5 1 378.9969 0.0015 6.03E + 07 2.89 0.00 E
386.007 250   259 062.7 4d43 p5 1 386.0068 0.0016 1.55E + 09 1.46 0.01 D+
388.754 20   257 232.1 4d33 p5 1 388.7546 0.0018 3.39E + 07 3.12 0.00 E
389.881 100 p 256 488.5 4d31 p5 1 389.8811 0.0019 1.43E + 08 2.49 0.01 E
391.094 100 p 255 693.0 4d23 p5 1 391.0936 0.0017 3.67E + 07 3.07 0.00 E
397.112 30   251 818.1 4d11 p5 3     2.79E + 07 3.18 0.01 E
398.588 2   250 885.6 4p61 5p43 398.5922 0.0014 2.20E + 08 2.28 0.15 D+
398.919 80   250 677.5 4d21 p5 1 398.9218 0.0019 1.53E + 08 2.44 0.00 E
399.967 80   250 020.6 4d13 p5 3 399.9718 0.0018 4.90E + 07 2.93 0.00 E
401.701 80   248 941.4 4d15 p5 3 401.7031 0.0019 5.69E + 07 2.86 0.00 E
411.136 4   243 228.5 4p61 5p21 411.1384 0.0016 7.96E + 07 2.70 0.08 E
423.344 5   236 214.5 4d11 p5 1     1.93E + 07 3.29 0.00 E
514.611 1 x 194 321.5 4d13 5p41     2.32E + 08 2.04 0.07 D+
516.763 10   193 512.3 4d15 5p43     7.64E + 08 1.52 0.06 D+
516.970 10 x 193 434.8 4d27 5p55 516.9686 0.0014 3.09E + 08 1.91 0.06 E
522.000 2000   191 570.9 4p61 p5 3     2.62E + 09 0.97 0.04 D+
522.929 20   191 230.5 4d17 5p35     1.95E + 09 1.10 0.08 D+
524.835 5   190 536.1 4d13 5p35     2.97E + 08 1.91 0.06 D+
530.404 5 x 188 535.5 4d15 5p33     1.43E + 08 2.22 0.01 D+
532.528 10 s 187 783.6 4d23 5p73 532.5335 0.0017 6.94E + 08 1.53 0.11 D+
533.450 30   187 459.0 4d13 5p33     7.08E + 08 1.52 0.10 D+
535.216 80   186 840.5 4d13 5p31     1.16E + 09 1.30 0.12 D+
538.618 5   185 660.3 4d11 5p33     3.24E + 08 1.85 0.12 D+
539.350 70 ${\mathcal{l}}$, x 185 408.4 4d13 5p23     3.38E + 07 2.83 0.00 E
539.765 10 ${\mathcal{l}}$, x 185 265.8 4d53 5p51 539.7620 0.0014 1.46E + 08 2.20 0.02 D+
540.791 40   184 914.3 4d43 5p55 540.7885 0.0015 1.06E + 09 1.33 0.24 E
541.756 10 x 184 584.9 4d23 5p63 541.7643 0.0017 1.56E + 08 2.16 0.02 D+
542.264 60   184 412.0 4d43 5p73 542.2639 0.0015 1.15E + 09 1.30 0.08 D+
544.117 10   183 784.0 4d31 5p63     2.25E + 08 2.00 0.09 D+
546.182 80   183 089.2 4d37 5p55     1.27E + 09 1.24 0.10 D+
546.508 50 p, x 182 979 .9 4d11 5p21     1.59E + 09 1.15 0.19 D+
556.729 80   179 620.6 4d53 5p73 556.7295 0.0013 5.98E + 08 1.55 0.07 D+
559.569 200   178 709.0 4d15 5p17     1.54E + 09 1.14 0.55 D+
560.428 2 x 178 435.1 4d23 5p45 560.4292 0.0018 2.26E + 08 1.97 0.14 D+
560.769 300   178 326.5 4d17 5p17     9.64E + 09 0.34 0.71 C
561.601 10 x 178 062.4 4d21 5p41     1.88E + 08 2.05 0.03 D+
562.444 300   177 795.5 4d17 5p25     4.34E + 09 0.69 0.33 C
564.537 200   177 136.3 4d35 5p63 564.5382 0.0015 1.19E + 09 1.25 0.16 D+
565.300 5 x 176 897.2 4d33 5p45     6.70E + 07 2.49 0.10 D+
566.546 20 ${\mathcal{l}}$ 176 508.2 4d37 5p27     1.65E + 08 2.10 0.03 D+
566.670 300 p 176 469.6 4d45 5p55 566.6725 0.0013 5.13E + 09 0.61 0.34 C
566.819 300   176 423.2 4d53 5p63 566.8261 0.0014 2.37E + 09 0.94 0.18 D+
567.620 80 h 176 174.2 4d21 5p43     4.59E + 08 1.65 0.14 D+
568.284 2000   175 968.4 4p61 p5 1     1.19E + 09 1.24 0.05 D+
569.281 300   175 660.2 4d13 5p11     2.08E + 09 1.00 0.27 D+
573.360 300   174 410.5 4d27 5p35     5.60E + 09 0.56 0.17 C
575.179 500   173 858.9 4d11 5p11     3.29E + 09 0.79 0.58 D+
576.090 10   173 584.0 4d23 5p53 576.0923 0.0019 5.03E + 07 2.60 0.01 E
577.233 20   173 240.3 4d37 5p45     2.04E + 09 0.99 0.09 D+
577.863 500   173 051.4 4d15 5p15     1.10E + 10 0.26 0.69 C
578.737 100   172 790.1 4d31 5p53     9.14E + 08 1.34 0.18 D+
578.811 80   172 768.0 4d45 5p63 578.8171 0.0014 8.03E + 08 1.40 0.05 D+
579.142 400 ${\mathcal{l}}$ 172 669.2 4d17 5p15     1.47E + 10 0.13 0.43 C
579.913 200   172 439.7 4d55 5p55 579.9174 0.0018 1.38E + 09 1.15 0.22 D+
580.321 300 ${\mathcal{l}}$ 172 318.4 4d15 5p13     7.13E + 09 0.45 0.36 C
581.236 200   172 047.2 4d33 5p53     1.44E + 09 1.14 0.26 D+
581.480 300   171 975.0 4d13 5p15     2.49E + 09 0.90 0.66 D+
581.610 200   171 936.5 4d55 5p73 581.6144 0.0018 1.34E + 09 1.16 0.18 D+
583.063 200   171 508 .1 4d33 5p41     1.59E + 09 1.09 0.33 D+
583.970 400   171 241.7 4d13 5p13     7.86E + 09 0.40 0.68 C
584.111 150   171 200.3 4d21 5p33     9.04E + 08 1.33 0.34 D+
584.251 250   171 159.3 4d23 5p43 584.2568 0.0020 1.67E + 09 1.07 0.25 D+
584.517 200 x 171 081.4 4d25 5p43     9.33E + 08 1.32 0.27 D+
586.229 100   170 581.8 4d21 5p31     8.86E + 08 1.34 0.26 D+
588.625 200   169 887.4 4d45 5p27 588.6235 0.0015 1.42E + 09 1.13 0.36 D+
589.367 5 x 169 673.6 4d43 5p41 589.3639 0.0019 1.98E + 08 1.99 0.03 D+
(590.182)   A (169 439.3) 4d11 5p13     2.20E + 09 0.94 0.71 D+
591.079 100   169 182.1 4d25 5p35     2.29E + 09 0.92 0.35 D+
593.405 200   168 519.0 4d21 5p21     3.21E + 09 0.77 0.66 D+
595.987 5 x 167 788.9 4d43 5p43 595.9900 0.0019 4.71E + 08 1.60 0.07 D+
596.236 5   167 718.8 4d33 5p35     3.91E + 08 1.68 0.12 D+
598.686 400   167 032.5 4d47 5p27     3.31E + 09 0.75 0.65 D+
600.282 1000   166 588.4 4d29 5p27     3.30E + 10 0.25 0.73 C
601.759 2   166 179.5 4d23 5p33     1.23E + 09 1.18 0.15 D+
601.914 50   166 136.7 4d35 5p53 601.9125 0.0017 3.33E + 09 0.74 0.21 C
602.040 100   166 101.9 4d25 5p33     7.35E + 09 0.40 0.59 C
602.387 2000   166 006.2 4d19 5p17     3.36E + 10 0.26 0.80 C
602.932 5   165 856.2 4d55 5p27     5.55E + 08 1.52 0.46 D+
604.002 100   165 562.4 4d23 5p31     4.62E + 09 0.60 0.44 C
604.515 50   165 421.9 4d53 5p53 604.5140 0.0016 1.93E + 09 0.97 0.29 D+
606.493 50   164 882.4 4d53 5p41 606.4912 0.0016 4.18E + 09 0.64 0.71 C
607.378 100   164 642.1 4d33 5p33     2.27E + 09 0.90 0.28 D+
609.525 100 p 164 062.2 4d37 5p35     1.82E + 10 0.01 0.78 C
609.552 90 u 164 054.9 4d25 5p23     7.55E + 09 0.38 0.76 C
610.639 500   163 762.9 4d47 5p45     2.09E + 10 0.07 0.65 C
610.834 1000   163 710.6 4d35 5p43 610.8309 0.0018 6.00E + 09 0.48 0.36 C
611.614 10   163 501.8 4d23 5p21     2.05E + 09 0.94 0.22 D+
612.145 200   163 360.0 4d63 5p61     5.37E + 09 0.52 0.48 C
612.234 50   163 336.2 4d31 5p23     1.49E + 09 1.07 0.40 D+
614.207 5   162 811.6 4d43 5p33 614.2076 0.0020 1.51E + 09 1.07 0.18 D+
615.047 200   162 589.2 4d55 5p45 615.0504 0.0020 2.12E + 09 0.92 0.40 D+
616.547 100   162 193.6 4d43 5p31 616.5475 0.0020 2.95E + 09 0.77 0.41 D+
617.422 200   161 963.8 4d33 5p21     2.16E + 09 0.91 0.29 D+
617.999 5   161 812.6 4d35 5p35 617.9987 0.0019 2.77E + 08 1.80 0.06 D+
618.172 200   161 767.3 4d45 5p53 618.1718 0.0016 2.80E + 09 0.80 0.25 D+
619.181 50   161 503.7 4d27 5p17     1.22E + 09 1.15 0.23 D+
620.741 2   161 097.8 4d53 5p35 620.7415 0.0017 1.53E + 08 2.05 0.05 D+
621.223 800   160 972.8 4d27 5p25     1.55E + 10 0.05 0.80 C
622.037 100   160 762.1 4d43 5p23 622.0372 0.0020 3.26E + 09 0.72 0.42 C
627.081 200   159 469.0 4d65 5p73 627.0812 0.0019 6.98E + 09 0.38 0.57 C
627.358 10   159 398.6 4d21 5p11     4.46E + 08 1.58 0.09 D+
627.583 50   159 341.5 4d45 5p43 627.5823 0.0017 2.84E + 09 0.78 0.18 D+
627.667 100   159 320.1 4d75 5p83     1.54E + 10 0.04 0.68 C
629.982 20   158 734.7 4d35 5p33 629.9817 0.0019 1.61E + 09 1.02 0.33 D+
632.835 5   158 019.1 4d53 5p33 632.8321 0.0017 8.15E + 08 1.31 0.11 D+
633.968 200   157 736.7 4d55 5p53     7.53E + 09 0.34 0.68 C
635.151 50   157 442.9 4d45 5p35 635.1510 0.0017 1.27E + 09 1.12 0.24 D+
635.318 5   157 401.5 4d53 5p31 635.3164 0.0018 4.21E + 08 1.59 0.10 D+
638.222 5   156 685.3 4d35 5p23 638.2213 0.0020 1.29E + 09 1.10 0.14 D+
639.920 200   156 269.5 4d65 5p63 639.9202 0.0019 4.09E + 09 0.60 0.63 C
640.764 500   156 063.7 4d57 5p55     1.65E + 10 0.01 0.85 D
641.147 5   155 970.5 4d53 5p23 641.1470 0.0018 4.45E + 08 1.56 0.07 D+
641.661 500   155 845.5 4d27 5p15     3.05E + 09 0.73 0.26 C
642.080 40   155 743.8 4d25 5p25     8.32E + 08 1.29 0.48 D+
643.746 50   155 340.8 4d53 5p21 643.7469 0.0019 1.13E + 09 1.15 0.20 D+
643.869 400   155 311.1 4d55 5p43     4.62E + 09 0.54 0.50 C
645.249 2   154 978.9 4d21 5p13     3.77E + 08 1.62 0.17 D+
646.881 2   154 587.9 4d47 5p35     6.90E + 08 1.37 0.13 D+
647.745 100 p 154 381.7 4d23 5p11     1.52E + 09 1.02 0.38 D+
647.816 100   154 364.8 4d45 5p33 647.8152 0.0017 2.33E + 09 0.84 0.26 D+
651.100 30   153 586.2 4d31 5p11     9.61E + 08 1.22 0.78 D+
654.264 2   152 843.5 4d33 5p11     1.02E + 09 1.19 0.31 D+
655.940 10   152 453.0 4d43 5p25     2.88E + 08 1.73 0.17 D+
656.533 20   152 315.3 4d45 5p23 656.5312 0.0018 1.52E + 09 1.01 0.15 D+
661.560 4   151 157.9 4d37 5p17     2.67E + 08 1.75 0.08 D+
662.196 100   151 012.7 4d43 5p11     9.46E + 08 1.21 0.15 D+
663.593 5   150 694.8 4d23 5p15     3.43E + 08 1.65 0.23 D+
663.892 100   150 626.9 4d37 5p25     3.94E + 09 0.58 0.18 C
663.935 5 u, x 150 617.2 4d25 5p15     3.00E + 08 1.70 0.12 D+
665.185 1   150 334.1 4d55 5p33     2.80E + 07 2.73 0.01 E
666.124 100   150 122.2 4d65 5p45     3.19E + 09 0.67 0.40 C
666.835 50   149 962.1 4d23 5p13     3.73E + 08 1.61 0.10 D+
667.185 10   149 883.5 4d25 5p13     2.76E + 08 1.74 0.10 D+
668.970 500   149 483.5 4d57 5p27     4.62E + 09 0.51 0.55 C
670.392 700   149 166.5 4d31 5p13     2.13E + 09 0.84 0.47 D+
673.754 50   148 422.1 4d33 5p13     5.75E + 08 1.41 0.11 D+
673.961 100   148 376.5 4d35 5p25     1.96E + 09 0.88 0.52 D+
674.378 5   148 284.8 4d55 5p23     5.80E + 08 1.40 0.08 D+
683.926 3   146 214.6 4d57 5p45     4.04E + 08 1.55 0.07 D+
687.812 50   145 388.6 4d63 5p51     2.24E + 09 0.80 0.63 C
688.367 5   145 271.3 4d65 5p53     7.18E + 08 1.29 0.24 D+
694.411 2   144 006.9 4d45 5p25     1.44E + 08 1.99 0.03 D+
698.082 100 u 143 249.6 4d35 5p15     1.45E + 09 0.98 0.27 D+
700.055 5   142 845.9 4d65 5p43     4.85E + 08 1.45 0.18 D+
701.587 10   142 534.0 4d53 5p15     3.91E + 08 1.54 0.17 D+
701.674 20   142 516.3 4d35 5p13     8.50E + 08 1.20 0.11 D+
705.214 2   141 800.9 4d53 5p13     9.27E + 07 2.16 0.02 D+
708.275 2   141 188.1 4d85 5p83 708.2769 0.0020 6.05E + 08 1.34 0.10 D+
708.456 5   141 152.0 4d47 5p25     5.80E + 08 1.36 0.05 D+
709.488 2   140 946.7 4d65 5p35     2.36E + 08 1.75 0.30 D+
715.604 10   139 742.1 4d63 5p73     9.63E + 08 1.13 0.27 D+
720.052 10   138 878.9 4d45 5p15     4.34E + 08 1.47 0.09 D+
723.873 2   138 145.8 4d45 5p13     1.22E + 08 2.02 0.02 D+
729.724 10   137 038.1 4d57 5p35     5.03E + 08 1.39 0.15 D+
732.372 5   136 542.6 4d63 5p63     7.52E + 08 1.22 0.23 D+
736.276 10   135 818.6 4d65 5p23     7.16E + 08 1.23 0.23 D+
746.246 20   134 004.1 4d75 5p55     1.24E + 09 0.98 0.55 D+
784.259 50   127 508.9 4d65 5p25     3.45E + 08 1.50 0.21 D+
789.090 50 x 126 728.3 4d83 5p83     6.11E + 08 1.24 0.38 D+
792.305 1   126 214.0 6s13 5p13     1.55E + 09 0.84 0.20 C
796.541 10   125 542.8 4d63 5p53     1.14E + 08 1.97 0.29 D+
802.832 1   124 559.1 6s23 5p21     3.50E + 09 0.47 0.90 C
803.010 500   124 531.5 4d83 5p61     2.80E + 09 0.57 0.64 C
803.806 20   124 408.1 5d65 5p13     1.45E + 08 1.85 0.01 D+
803.974 20   124 382.1 4d41 5p73     6.16E + 08 1.22 0.64 D+
805.445 10   124 155.0 4d75 5p45     7.02E + 07 2.16 0.13 D+
808.568 200 D, x 123 675.4 5d65 5p15     9.03E + 07 2.05 0.01 D+
809.056 100   123 600.8 4d57 5p25     3.76E + 08 1.43 0.08 D+
809.255 50   123 570.4 6s33 5p45     9.49E + 09 0.03 0.72 C
810.226 200   123 422.4 6s15 5p15     1.26E + 10 0.09 0.92 C
810.562 1   123 371.2 6s25 5p45     2.76E + 09 0.57 0.98 C
812.226 1 x 123 118.4 4d63 5p43     5.80E + 07 2.24 0.05 D+
820.482 5   121 879.6 6s23 5p33     3.80E + 09 0.42 0.60 C
821.060 10   121 793.8 6s13 5p11     3.04E + 09 0.51 0.47 C
824.069 20   121 349.1 6s11 5p31     3.31E + 09 0.47 0.90 C
825.195 1000 p 121 183.5 4d41 5p63     1.62E + 09 0.78 0.57 C
828.279 1   120 732.3 6s11 5p33     1.61E + 09 0.78 0.45 C
830.886 1000   120 353.5 6s13 5p25     1.03E + 10 0.03 0.75 C
832.618 1000   120 103.1 6s25 5p27     1.53E + 10 0.20 0.98 C
834.044 5000   119 897.8 4d73 5p55 834.0424 0.0018 8.56E + 08 1.05 0.43 E
837.561 2000   119 394.3 4d73 5p73 837.5570 0.0018 1.52E + 09 0.80 0.35 C
841.738 500   118 801.8 6s23 5p35     1.12E + 10 0.07 0.95 C
843.194 1   118 596.7 6s21 5p43     1.65E + 09 0.75 0.35 C
844.072 2   118 473.3 4d57 5p15     9.53E + 07 1.99 0.06 D+
844.754 500 x 118 377.7 4d51 5p51     2.32E + 09 0.61 0.72 C
847.336 500 D, x 118 016.9 5d65 5p17     1.18E + 08 1.90 0.01 E
849.157 500 dc 117 763.9 6s15 5p17     1.50E + 10 0.21 0.96 C
849.157 500 dc 117 763.9 6s31 5p83     6.86E + 09 0.13 0.97 C
851.623 1   117 422.9 6s33 5p63     2.66E + 09 0.54 0.52 C
853.072 2 p, x 117 223.4 6s25 5p63     2.54E + 09 0.56 0.40 C
856.823 2   116 710.2 6s21 5p41     2.72E + 09 0.52 0.80 C
860.618 5000   116 195.6 4d73 5p63 860.6195 0.0018 2.28E + 09 0.60 0.44 C
860.800 5   116 171.0 6s21 5p53     3.66E + 09 0.39 0.75 C
863.029 20   115 871.0 4d85 5p55 863.0271 0.0019 5.95E + 08 1.17 0.18 D+
863.893 50   115 755.1 6s11 5p43     3.78E + 09 0.37 0.94 C
866.786 5000   115 368.7 4d85 5p73 866.7907 0.0019 1.90E + 09 0.66 0.39 C
873.541 2   114 476.6 6s23 5p53     1.88E + 09 0.67 0.49 C
875.480 10   114 223.1 6s33 5p73     4.39E + 09 0.30 0.60 C
877.011 1   114 023.7 6s25 5p73     1.77E + 09 0.69 0.80 C
879.351 1   113 720.2 6s33 5p55     1.99E + 09 0.64 0.80 D
880.897 200   113 520.6 6s25 5p55     7.80E + 09 0.04 0.79 D
887.057 500   112 732.3 4d51 5p73     6.69E + 08 1.11 0.46 D+
891.516 5000   112 168.5 4d85 5p63 891.5150 0.0020 3.05E + 09 0.44 0.63 C
892.506 5   112 044.1 6s13 5p23     3.83E + 09 0.34 0.49 C
914.995 20   109 290.2 4d85 5p27     3.91E + 08 1.30 0.47 D+
921.000 2   108 577.6 6s33 5p51     1.79E + 09 0.64 0.60 C
925.122 1 x 108 093.9 5d35 5p13     5.65E + 08 1.14 0.03 D+
928.000 1   107 758.6 4d41 5p43     1.24E + 08 1.80 0.15 D+
938.478 5000   106 555.5 4d83 5p51     2.04E + 09 0.57 0.49 C
943.213 100   106 020.6 4d85 5p45     3.05E + 08 1.38 0.30 D+
945.016 150   105 818.3 5d41 5p33     2.19E + 09 0.53 0.74 C
(955.500)   A (104 657.28) 4d73 5p41     1.05E + 09 0.85 0.32 C
972.924 5000 p 102 783.0 4d41 5p33     2.28E + 08 1.49 0.33 D+
973.902 5   102 679.7 5d31 5p11     1.21E + 08 1.76 0.01 D+
983.256 50 x 101 702.9 5d35 5p17     7.73E + 07 1.95 0.04 D+
988.431 5000   101 170.4 4d85 5p53     5.81E + 08 1.07 0.57 D+
990.984 1000   100 909.8 4d83 5p73     4.24E + 08 1.20 0.19 D+
991.356 50   100 871 .9 4d73 5p35     4.03E + 07 2.23 0.14 D+
992.272 2000   100 778.8 5d25 5p13     1.82E + 09 0.57 0.11 C
1009.339 200   99 074.74 5d73 5p45     2.04E + 09 0.51 0.64 C
1012.720 1000   98 743.98 4d85 5p43     4.34E + 08 1.17 0.19 D+
1017.202 500   98 308.89 5d55 5p23     8.45E + 08 0.89 0.03 D
1020.467 1000   97 994.35 4d51 5p41     4.49E + 08 1.17 0.28 D+
1021.266 200   97 917.68 5s21 5p61     7.83E + 07 1.91 0.03 D+
1022.554 200   97 794.35 4d73 5p33     9.17E + 07 1.85 0.05 D+
1023.436 2   97 710.07 4d83 5p63     1.96E + 07 2.51 0.01 D+
1025.821 5000   97 482.89 5d75 5p45     1.07E + 10 0.23 0.73 C
1029.063 500   97 175.78 4d73 5p31     2.53E + 08 1.40 0.35 D+
1030.122 500   97 075.88 5d53 5p33     1.48E + 09 0.63 0.16 C
1032.576 1000   96 845.17 4d85 5p35     4.39E + 08 1.15 0.55 D+
1038.852 5000   96 260.10 5d55 5p33     2.90E + 09 0.33 0.20 C
1040.906 2000   96 070.15 5d27 5p15     3.87E + 09 0.20 0.36 C
1041.006 2000   96 060.93 5d23 5p11     6.16E + 09 0.00 0.60 C
1044.492 2000   95 740.32 5d43 5p21     7.26E + 09 0.08 0.47 C
1050.577 2000   95 185.79 5d11 5p13     6.10E + 09 0.00 0.91 C
1051.358 2000   95 115.08 4d73 5p21     8.84E + 07 1.84 0.09 D+
1052.487 100 D, x 95 013.05 5s13 5p51     5.10E + 07 2.07 0.02 D+
1053.458 500   94 925.47 5d45 5p33     2.32E + 09 0.41 0.24 D
1053.556 2000   94 916.64 5d25 5p25     8.76E + 09 0.16 0.72 C
1055.367 200   94 753.77 5s15 5p55     5.68E + 07 2.02 0.01 D+
1055.966 200 J 94 700.02 5d21 5p11     3.98E + 09 0.17 0.89 C
1059.473 2000   94 386.55 5d25 5p17     1.03E + 08 1.76 0.12 D+
1061.816 1000 dc 94 178.28 5d33 5p21     1.79E + 09 0.52 0.17 C
1061.816 1000 dc, J 94 178.28 5d57 5p27     1.13E + 10 0.28 0.78 C
1064.694 1000   93 923.70 5d35 5p23     4.46E + 09 0.12 0.22 C
1064.821 5000   93 912.50 5d13 5p13     1.28E + 10 0.34 0.88 C
1068.842 2000   93 559.20 5d31 5p21     6.85E + 09 0.07 0.93 C
1068.964 200   93 548.52 5d33 5p23     1.05E + 09 0.75 0.17 C
1072.874 5000   93 207.59 5d15 5p13     1.02E + 10 0.25 0.43 C
1073.192 2000   93 179.97 5d13 5p15     4.58E + 09 0.10 0.88 C
1074.556 1000 p 93 061.69 5d43 5p33     5.19E + 09 0.05 0.55 C
1081.130 1000 dc 92 495.81 5d17 5p15     2.21E + 10 0.59 0.61 C
1081.130 1000 dc 92 495.81 5d47 5p45     3.61E + 10 0.80 0.95 C
1081.395 5000   92 473.15 5d15 5p15     1.65E + 10 0.46 0.90 C
1084.707 500   92 190.79 5d83 5p61     1.48E + 10 0.42 0.94 C
1085.589 2000 p 92 115.89 5d33 5p31     1.32E + 10 0.37 0.92 C
1085.784 90   92 099.35 5d53 5p43     8.62E + 08 0.82 0.15 C
1088.440 2000   91 874.61 5d35 5p33     1.32E + 10 0.37 0.74 C
1088.758 1000   91 847.78 5d45 5p35     5.43E + 09 0.02 0.59 C
1090.297 500   91 718.13 4d85 5p23     3.06E + 08 1.26 0.18 D+
1092.917 500   91 498.26 5d31 5p31     7.50E + 08 0.87 0.14 C
1094.784 500   91 342.22 5s25 5p83     2.89E + 08 1.29 0.30 D+
1095.491 2000   91 283.27 5d55 5p43     1.30E + 10 0.37 0.76 C
1097.314 5   91 131.62 4d51 5p33     2.98E + 07 2.28 0.06 D+
1099.589 5000   90 943.07 5d27 5p25     3.23E + 10 0.77 0.98 C
1100.351 1000   90 880.09 5d31 5p33     9.06E + 08 0.79 0.37 C
1101.745 2000   90 765.10 5d11 5p11     2.82E + 09 0.29 0.49 C
1104.807 200 x 90 513.55 4d51 5p31     5.83E + 07 1.98 0.16 D+
(1108.491)   B (90 215.17) 5d53 5p41     1.16E + 10 0.34 0.90 C
1111.222 200   89 991.02 5d83 5p83     2.82E + 09 0.28 0.78 C
1111.745 200   89 948.68 5d45 5p43     1.34E + 09 0.60 0.07 D
(1113.735)   E (89 787.93) 5d65 5p63     1.13E + 10 0.32 0.79 C
1114.480 2000   89 727.94 5d73 5p73   ` 7.73E + 09 0.16 0.70 C
1114.688 10 000 J 89 711.20 5d19 5p17     4.43E + 10 0.92 0.99 C
1115.161 1000   89 673.15 5d53 5p53     1.16E + 09 0.67 0.32 C
1115.532 2000   89 643.33 5d29 5p27     4.44E + 10 0.92 1.00 C
1116.101 1000   89 597.63 5d85 5p83     2.49E + 10 0.67 0.98 C
1117.413 1000   89 492.43 5d13 5p11     1.66E + 09 0.51 0.20 C
1118.689 2000   89 390.35 5d37 5p35     3.49E + 10 0.82 0.99 C
1118.987 500 D, x 89 366.54 5s13 5p73     6.71E + 07 1.90 0.01 D+
1125.394 2000   88 857.77 5d55 5p53     5.54E + 09 0.02 0.36 D+
1126.166 500   88 796.86 5d35 5p35     1.19E + 09 0.65 0.11 C
(1127.231)   G (88 712.97) 5d51 5p73     2.14E + 09 0.39 0.57 C
(1129.374)   C (88 544.61) 5d63 5p63     7.98E + 09 0.18 0.62 C
1134.603 2000   88 136.56 5d75 5p73     1.17E + 10 0.35 0.65 C
1135.257 500   88 085.78 5d43 5p43     9.15E + 08 0.75 0.10 C
1141.121 1000   87 633.13 5d75 5p55     3.11E + 09 0.22 0.33 D
1142.544 5000   87 523.98 5d45 5p53     1.45E + 10 0.46 0.73 C
1143.696 1000   87 435.82 4d73 5p25     1.58E + 07 2.51 0.04 D+
1143.930 2000   87 417.94 5d41 5p63     3.49E + 09 0.16 0.57 C
1144.579 5000   87 368.37 5d17 5p25     3.33E + 09 0.18 0.25 C
1150.770 2000   86 898.34 5d35 5p43     7.27E + 09 0.16 0.67 C
1151.571 2000   86 837.89 5d17 5p17     1.13E + 10 0.35 0.99 C
1151.851 1000   86 816.78 5d15 5p17     1.81E + 09 0.45 0.83 C
1154.620 2000   86 608.58 5d25 5p23     1.26E + 10 0.40 0.59 C
1154.902 1000   86 587.43 5d65 5p73     2.10E + 09 0.38 0.21 C
1155.225 1000   86 563.22 4d41 5p13     6.92E + 07 1.86 0.23 D+
1158.574 2000   86 313.00 5d23 5p23     6.05E + 09 0.08 0.76 C
(1161.638)   F (86 085.32) 5d65 5p55     8.72E + 09 0.24 0.53 D+
1162.848 1000   85 995.76 4d73 5p11     9.04E + 07 1.75 0.08 D+
1164.083 500   85 904.53 5d31 5p43     2.39E + 08 1.32 0.10 D+
1167.411 2000   85 659.63 5d43 5p53     2.74E + 09 0.25 0.39 C
1187.404 50 x 84 217.33 5d41 5p73     1.15E + 09 0.61 0.81 C
(1189.322)   I (84 081.49) 5d73 5p51     4.76E + 09 0.04 0.74 C
1204.078 150 H, x 83 051.10 5d51 5p51     4.76E + 09 0.00 0.86 C
1314.039 10   76 101.24 5s23 5p63     1.45E + 09 0.43 0.68 C
1330.353 1 x 75 168.02 5s13 5p53     7.65E + 08 0.69 0.18 C
1406.536 10   71 096.65 5s21 5p63     2.55E + 08 1.12 0.65 D+
1411.561 5   70 843.56 5s13 5p35     1.64E + 08 1.31 0.02 D+
1416.418 500   70 600.63 5s15 5p23     4.67E + 08 0.85 0.20 C
1417.866 2000   70 528.53 5s33 5p51     2.39E + 09 0.14 0.84 C
1483.078 500   67 427.34 5s11 5p53     4.13E + 08 0.87 0.27 C
1489.263 100   67147.31 5s13 5p31     2.61E + 08 1.06 0.15 C
1495.035 50   66 888.07 5s11 5p41     1.55E + 08 1.29 0.35 D+
1514.569 50 000   66 025.38 5s25 5p55     5.87E + 09 0.31 0.74 D+
1521.702 10 000   65 715.89 5s13 5p23     2.94E + 09 0.01 0.63 C
1526.201 5000   65 522.17 5s25 5p73     1.39E + 09 0.31 0.84 C
1529.397 5000   65 385.25 5s33 5p55     1.53E + 09 0.27 0.87 D
1536.037 2000   65 102.60 5s23 5p53     1.04E + 09 0.44 0.36 C
1538.423 5000   65 001.63 5s11 5p43     2.19E + 09 0.11 0.91 C
1541.255 10 000   64 882.19 5s33 5p73     3.10E + 09 0.05 0.62 C
1548.859 2000   64 563.66 5s23 5p41     1.73E + 08 1.21 0.12 D+
1591.797 50000   62 822.08 5s15 5p17     8.70E + 09 0.52 0.97 C
1595.481 50   62 677.02 5s23 5p43     2.75E + 08 0.98 0.10 C
1604.549 20 000   62 322.81 5s25 5p63     1.63E + 09 0.20 0.42 C
1605.358 10   62 291.40 5s15 5p25     1.29E + 08 1.30 0.06 D+
1621.198 20 000   61 682.78 5s33 5p63     1.28E + 09 0.30 0.49 C
1621.441 20000   61 673.54 5s31 5p83     3.96E + 09 0.19 0.96 C
1645.331 50 000   60 778.04 5s23 5p35     5.80E + 09 0.37 0.97 C
1663.953 50 000   60 097.85 5s21 5p53     2.02E + 09 0.08 0.93 C
1665.978 20000   60 024.80 5s11 5p33     8.35E + 08 0.46 0.54 C
1679.024 20 000   59 558.41 5s21 5p41     1.35E + 09 0.25 0.94 C
1681.349 10000   59 476.05 5s31 5p61     1.84E + 09 0.11 0.97 C
1682.238 50 000   59 444.62 5s25 5p27     7.47E + 09 0.50 0.98 C
1683.307 20 000   59 406.87 5s11 5p31     1.48E + 09 0.20 0.94 C
1724.855 1000   57 975.89 5s11 5p23     6.61E + 08 0.53 0.36 C
1733.090 50 000   57 700.41 5s23 5p33     1.77E + 09 0.10 0.65 C
1733.928 50000   57 672.52 5s21 5p43     1.09E + 09 0.31 0.65 C
1741.944 100 000   57407.13 5s13 5p25     5.00E + 09 0.36 0.98 C
1749.353 50 000   57 163.99 5s15 5p15     4.87E + 09 0.35 0.96 C
1751.844 50   57 082.71 5s23 5p31     1.76E + 08 1.09 0.16 C
1772.078 50 000   56 430.92 5s15 5p13     2.43E + 09 0.06 0.92 C
1780.139 2000   56 175.39 5s25 5p45     9.92E + 08 0.32 0.95 C
1786.788 20000   55 966.35 5s13 5p11     1.38E + 09 0.19 0.95 C
1800.659 50 000   55 535.22 5s33 5p45     3.62E + 09 0.25 0.78 C
1817.490 5000   55 020.94 5s23 5p21     1.22E + 09 0.22 0.96 C
1940.003 10 000   51 546.31 5s13 5p13     4.54E + 08 0.59 0.35 C
1974.492 3 h 50 645.94 5s21 5p23     2.04E + 08 0.92 0.19 C

aLevel codes are explained in table 2. Symbols: dc, doubly classified; p, perturbed; u, unresolved from close line; s, shaded to shorter wavelength; ${\mathcal{l}}$, shaded to longer wavelength; x, not included in level optimization; h, hazy.A, not observed due to break in spectrum—Ritz value.B, greatly perturbed by Si III line—Ritz value.C, covered by ghost of Si IV line—Ritz value.D, intensity much higher than expected, not used in level optimization.E, covered by ghost of Zr V line—Ritz value.F, covered by Si III line—Ritz value.G, covered by ghost of Si IV line—Ritz value.H, uncertain classification, not included in level optimization.I, covered by neighboring strong lines—Ritz value.J, even level for this line not included in least-squares fit.

3. Spectrum analysis and level value determination

The analysis was carried out in a manner similar to that used for the recent analysis of Mo V [11]. As described there 'Interpretation of the spectrum was guided by calculations of the level structures and transition probabilities with the Hartree–Fock code of Cowan [12]. Further guidance was provided by construction of two-dimensional transition arrays with the computer spreadsheet method described by Reader [13]'.

The odd parity energy levels are given in table 2, the even levels in table 3. In addition to the usual spectroscopic designations in either LS or jl (pair) coupling, the levels are given shorthand designations that are used in the classification of the spectral lines. The shorthand designations are explained in the footnotes to tables 2 and 3. As described in [11] 'the values of the energy levels were optimized with the computer program ELCALC [14], an iterative procedure in which the observed wave numbers are weighted according to the inverse square of their uncertainties. The uncertainties of the level values given by this procedure are also listed'. For the level optimization only the most reliably classified lines were used. That is, lines that were very weak or that appeared with suspiciously high intensities were excluded.

Table 2.  Odd parity energy levels (cm−1) of Zr VI.

Configuration Term J Desig.a Energy Uncert. No. trans.b
4s24p5 2P 3/2 p5 3 0.00 0.80 55
    1/2 p5 1 15 602.78 0.97 32
4s24p45p (3P2)[1] 3/2 5p13 421 257.96 0.12 20
  (3P2)[2] 5/2 5p15 421 991.19 0.19 17
  (3P2)[1] 1/2 5p11 425 678.16 0.18 15
  (3P2)[3] 5/2 5p25 427 118.65 0.14 17
  (3P2)[3] 7/2 5p17 427 649.11 0.20 13
  (3P1)[0] 1/2 5p21 434 797.76 0.21 12
  (3P2)[2] 3/2 5p23 435 427.69 0.15 20
  (3P0)[1] 1/2 5p31 436 859.11 0.16 13
  (3P1)[2] 3/2 5p33 437 477.01 0.13 26
  (3P1)[2] 5/2 5p35 440 554.88 0.17 20
  (3P0)[1] 3/2 5p43 442 453.66 0.15 24
  (3P1)[1] 1/2 5p41 444 340.07 0.17 10
  (3P1)[1] 3/2 5p53 444 879.34 0.13 20
  (1D2)[3] 5/2 5p45 449 730.72 0.12 16
  (1D2)[3] 7/2 5p27 452 999.87 0.21 11
  (1D2)[1] 3/2 5p63 455 878.16 0.12 19
  (1D2)[2] 3/2 5p73 459 077.64 0.15 20
  (1D2)[2] 5/2 5p55 459 580.77 0.14 15
  (1D2)[1] 1/2 5p51 464 724.05 0.25 9
  (1S0)[1] 1/2 5p61 482 699.28 0.36 6
  (1S0)[1] 3/2 5p83 484 897.26 0.33 9

aDesignations are given with a short form of the configuration (two places) followed by the ordinal number of the calculated J value for the configuration (one place) and the J value (one place). For example 5p73 indicates the seventh level with J = 3/2 for the 4p45p configuration. p5 3 and p5 1 indicate the J = 3/2 and 1/2 levels of the 4p5 configuration, respectively. bTotal number of transitions for each level, including those omitted from the level optimization procedure.

Table 3.  Even parity energy levels (cm−1) of Zr VI.

Configuration Term J Desig. Energy Notea Uncert. No. trans.b
4s4p6 2S 1/2 4p61 191 570.67   0.89 8
4s24p44d (3P)4D 5/2 4d15 248 940.11   0.85 6
  (3P)4D 7/2 4d17 249 322.89   0.90 4
  (3P)4D 3/2 4d13 250 017.63   0.79 9
  (3P)4D 1/2 4d11 251818.7   1.3 5
  (3P)4F 9/2 4d19 261 642.9   1.4 1
  (3P)4F 7/2 4d27 266 145.41   0.71 5
  (1D)2P 1/2 4d21 266 278.49   0.73 9
  (3P)4F 3/2 4d23 271 296.05   0.57 13
  (3P)4F 5/2 4d25 271 374.36   0.72 8
  (3P)4P 1/2 4d31 272 091.26   0.73 7
  (3P)4P 3/2 4d33 272 834.44   0.69 10
  (1D)2D 3/2 4d43 274 665.60   0.50 11
  (3P)2F 7/2 4d37 276 491.34   0.69 6
  (3P)4P 5/2 4d35 278 742.23   0.47 10
  (1D)2P 3/2 4d53 279 457.21   0.41 14
  (1D)2D 5/2 4d45 283 112.00   0.39 12
  (1D)2G 7/2 4d47 285 967.09   0.65 4
  (1D)2G 9/2 4d29 286 411.5   1.4 1
  (3P)2F 5/2 4d55 287 142.42   0.52 9
  (1D)2F 5/2 4d65 299 608.66   0.45 9
  (1D)2F 7/2 4d57 303 517.22   0.48 6
  (1S)2D 3/2 4d63 319 336.18   0.60 8
  (1S)2D 5/2 4d75 325 576.82   0.75 4
  (1D)2S 1/2 4d41 334 694.92   0.33 7
  (3P)2P 3/2 4d73 339 682.78   0.21 11
  (3P)2D 5/2 4d85 343 709.55   0.22 11
  (3P)2P 1/2 4d51 346 345.56   0.42 7
  (3P)2D 3/2 4d83 358 168.09   0.32 7
4s24p45s (3P2)[2] 5/2 5s15 364 827.11   0.12 7
  (3P2)[2] 3/2 5s13 369 711.65   0.11 11
  (3P0)[0] 1/2 5s11 377 452.05   0.12 8
  (3P1)[1] 3/2 5s23 379 776.65   0.11 10
  (3P1)[1] 1/2 5s21 384 781.44   0.16 8
  (1D2)[2] 5/2 5s25 393 555.34   0.11 7
  (1D2)[2] 3/2 5s33 394 195.47   0.11 7
  (1S0)[0] 1/2 5s31 423 223.46   0.33 4
4s24p45d (3P2)[2] 5/2 5d15 514 465.31   0.46 3
  (3P2)[3] 7/2 5d17 514 487.01   0.30 3
  (3P2)[2] 3/2 5d13 515 170.73   0.31 4
  (3P2)[1] 1/2 5d11 516 443.48   0.37 2
  (3P2)[4] 9/2 5d19 517 360.31 * 0.45 1
        517 292.44 # 0.45 1
  (3P2)[4] 7/2 5d27 518 061.55   0.35 2
  (3P2)[0] 1/2 5d21 520 378.18 * 0.48 2
  (3P2)[1] 3/2 5d23 521 740.06   0.63 4
  (3P2)[3] 5/2 5d25 522 035.99   0.34 5
  (3P1)[1] 1/2 5d31 528 357.52   0.31 7
  (3P0)[2] 3/2 5d33 528 976.13   0.44 4
  (3P0)[2] 5/2 5d35 529 351.71   0.24 7
  (3P1)[3] 7/2 5d37 529 945.22   0.43 1
  (3P1)[1] 3/2 5d43 530 538.91   0.37 6
  (3P1)[2] 5/2 5d45 532 402.86   0.34 5
  (3P1)[3] 5/2 5d55 533 736.95   0.25 5
  (3P1)[2] 3/2 5d53 534 552.78   0.29 5
  (1D2)[4] 7/2 5d47 542 226.54 * 0.45 1
  (1D2)[4] 9/2 5d29 542 643.20 * 0.45 1
        542 711.07 # 0.45 1
  (1D2)[0] 1/2 5d41 543 295.84   0.41 5
  (1D2)[1] 3/2 5d63 544 423   10 2
  (1D2)[2] 5/2 5d65 545 666.07   0.78 5
  (1D2)[3] 7/2 5d57 547 178.00 * 0.50 1
  (1D2)[3] 5/2 5d75 547 213.94   0.28 4
  (1D2)[1] 1/2 5d51 547 791   11 3
  (1D2)[2] 3/2 5d73 548 805.54   0.33 4
  (1S0)[2] 5/2 5d85 574 494.88   0.52 2
  (1S0)[2] 3/2 5d83 574 889.14   0.74 3
4s24p46s (3P2)[2] 5/2 6s15 545 413.52   0.77 3
  (3P2)[2] 3/2 6s13 547 471.92   0.42 5
  (3P0)[0] 1/2 6s11 558 208.73   0.48 4
  (3P1)[1] 3/2 6s23 559 356.47   0.41 6
  (3P1)[1] 1/2 6s21 561 050.32   0.41 5
  (1D2)[2] 5/2 6s25 573 101.84   0.48 6
  (1D2)[2] 3/2 6s33 573 301.14   0.35 6
  (1S0)[0] 1/2 6s31 602 661.0   4.0 3

aDesignations are explained in table 2; 4p61 indicates the 2S1/2 level of 4s4p6. bTotal number of transitions for each level, including those omitted from the level optimization procedure. Notes:*Tentative value; not included in least-squares fit.#Alternate value for interchange of classifications of λ1114.688 and 1115.532 Å.

Figure 1 shows a schematic overview of the positions of the 4s24p5, 4s4p6, 4s24p44d, 5s, 5p, 5d, and 6s, configurations. It also shows the calculated positions of the 4s24p44f and 4s4p54d configurations, although no levels have as yet been established for them.

Figure 1.

Figure 1. Schematic overview of the configurations of Zr VI. The calculated positions of the 4s24p44f and 4s4p54d configurations, for which no levels are known, are also shown.

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3.1. 4s24p44d levels

Nearly all levels of this configuration that could combine with the ground state were present in [4]. Remaining as unknown were (3P)4D1/2,7/2, (1S)2D5/2, (3P)4F7/2/9/2, (3P)2F7/2, (1D)2G7/2,9/2, and (1D)2F7/2. Values for these 9 levels were given in [6]. Our present work shows that 6 of the 9 were spurious. Details of these 9 levels are:

  • (1)  
    (3P)4D1/2—new level; two new resonance lines (397.112 and 423.344 Å) and three transitions to levels of 4p45p
  • (2)  
    (3P)4D7/2—new level; four strong transitions to levels of 4p45p
  • (3)  
    (1S)2D5/2—new level; one new resonance line (307.148 Å) and three transitions to levels of 4p45p
  • (4)  
    (3P)4F7/2—present in [6]; five transitions to levels of 4p45p
  • (5)  
    (3P)4F9/2—new level; single line at 602.387 Å, places (3P)4F9/2 close to prediction
  • (6)  
    (3P)2F7/2—new level; six transitions to levels of 4p45p
  • (7)  
    (1D)2G7/2—new level; four transitions to levels of 4p45p
  • (8)  
    (1D)2G9/2—present in [6]; single line at 600.282 Å; places (1D)2G9/2 close to prediction
  • (9)  
    (1D)2F7/2—present in [6]; six transitions to levels of 4p45p.

We note that the two J = 9/2 levels of 4p44d are established by single transitions that are close in wavelength, 600.282 Å and 602.387 Å. Thus, one could consider interchanging their classifications without changing the level values very much. Our present classifications were chosen to provide the best match with the level values given by the least-squares fit (LSF) with the Cowan code, described in section 4 below.

The structure of the 4p44d configuration is shown in figure 2. This is similar to figure 1 of [4], except that we show here the observed positions of levels that were previously unknown.

Figure 2.

Figure 2. Structure of the 4s24p44d configurations of Zr VI.

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3.2. 4s24p45s levels

The 4s24p45s levels [1, 2, 4] have improved values due to their combinations with 4s24p45p. For completeness, in figure 3 we give the structure of the 4p45s configuration. This is the same as figure 2 of [4], except that here we designate the levels in jl coupling, rather than J1j. This coupling scheme is more now more commonly used for np4ns configurations.

Figure 3.

Figure 3. Structure of the 4s24p45s configurations of Zr VI. The levels are designated in jl-coupling.

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3.3. 4s24p45p levels

As already mentioned, all levels of this configuration were given in [6]. However, we find that 13 of the 21 levels of this configuration given in [6] were spurious. The following levels from [6] have been replaced by new levels in table 2. (We use here the LS designations from [6], although for this coupling scheme, it is not possible to specify the J-value of the core term.):

  • (1)  
    (3P2)4P3/2 at 423 114; now 5p13 at 421 257.96 cm−1
  • (2)  
    (3P2)4P5/2 at 424 592; now 5p15 at 421 991.19 cm−1
  • (3)  
    (3P1)2P1/2 at 436 172; now 5p21 at 434 797.76 cm−1
  • (4)  
    (3P2)4D3/2 at 437 474; now 5p23 at 435 427.69 cm−11
  • (5)  
    (3P0)4D1/2 at 438 427; now 5p31 at 436 859.11 cm−1
  • (6)  
    (3P2)2P3/2 at 440 224; now 5p33 at 437 477.01 cm−1
  • (7)  
    (3P0)4S3/2 at 444 078; now 5p43 at 442 453.66 cm−1
  • (8)  
    (3P1)2D3/2 at 445 849; now 5p53 at 444 879.34 cm−1
  • (9)  
    (3P1)2S1/2 at 447 709; now 5p41 at 444 340.07 cm−1
  • (10)  
    (1D2)2F7/2 at 452 408; now 5p27 at 452 999.87 cm−1
  • (11)  
    (1D2)2P3/2 at 472 926; now 5p73 at 459 077.64 cm−1
  • (12)  
    (1S0)2P3/2 at 483 178; now 5p83 at 484 897.26 cm−1
  • (13)  
    (1S0)2P1/2 at 487 131; now 5p61 at 482 699.28 cm−1

The structure of the 4p45p levels is shown in figure 4. The levels are designated in jl-coupling.

Figure 4.

Figure 4. Structure of the 4s24p45p configuration of Zr VI. The levels are designated in jl-coupling.

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3.4. 4s24p45d and 4s24p46s levels

The structures of the 4p45d and 4p46s configurations are shown in figure 5. As these configurations lie very close in energy, we treat them together.

Figure 5.

Figure 5. Structures of the 4s24p45d and 4s24p46s configurations of Zr VI. The levels are designated in jl-coupling. The 4s24p46s levels are shown as dashed. Levels noted by open circles are tentative.

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A number of 4p45d and 4p46s levels were established by Chaghtai et al [5], based on their observation of resonance lines in the 174–200 Å region. They reported almost all of the levels that could make transitions to the ground term, that is levels with J = 1/2, 3/2 or 5/2. Only 4p4(3P)5d 4D5/2 was missing. These levels were given again in [6], some with improved accuracy. Our present work confirms most of these levels, improves their accuracies, and provides values for the J = 7/2, 9/2 levels, which cannot radiate to the ground term. Five of the levels of [5, 6] were found to be spurious, and several J-values were revised. The spurious levels were 4p4(3P)5d 4P1/2, 4p4(1S)5d 2D3/2, 4p46s (3P2)5/2, 4p46s (3P0)1/2, and 4p46s (1S0)1/2 (designations from [6]). We confirm the level 4p46s(1D2)5/2 given in [5] (573 105 cm−1), but reject the revised value given in [6] (573 135 cm−1). Our present value is 573 101.84 cm−1.

Our results for the 4p45d and 4p46s levels are given in table 3. Although this is a complete set, for some levels only tentative values can be given:

  • (1)  
    The 4p45d (3P2)[0]1/2 level (5d21) is established by two lines: 192.182 Å to p5 3 and 1055.966 Å to 5p11. However, the 192.182 Å line is largely obscured by a strong line of O IV and so was given a large uncertainty in the level optimization. The value of 4p45d (3P2)[0]1/2 is thus based almost entirely on 1055.966 Å, 5d21–5p11. A possible confirming transition predicted at 1008.876 Å, 5d21–5p13, was not observed. This could occur because of our use of a filter to eliminate higher order lines that has low-wavelength cutoff near 1000 Å. The level is thus uncertain and was not included in the LSF.
  • (2)  
    The 4p45d (1D2)[4]7/2 level (5d47) is established by a single line, 1081.130 Å, 5d47–5p45. This transition is predicted to be extremely strong, so this is likely correct. However, 1081.130 Å is also classified as 5d17–5p15. We thus consider 4p45d (1D2)[4]7/2 to be tentative and exclude it from the LSF.
  • (3)  
    The 4p45d (1D2)[3]7/2 level (5d57) is established by a single line, 1061.816 Å, 5d57–5p27. This transition is predicted to be strong, so this is likely correct. A possible confirming transition 5d55–5d57 cannot be observed due to the presence of a strong line of Si III. Unfortunately, 1061.816 Å is also classified as 5d33–5p21, which makes our value for 5d57 tentative at best. It was not included in the LSF.
  • (4)  
    The 4p45d (3P2)[4]9/2 level (5d19) is established by a single line, 1114.688 Å, 5d19–5p17. This transition is predicted to be strong, so this is likely correct. However, since there are no confirming transitions, we consider the level to be tentative.
  • (5)  
    The 4p45d (1D2)[4]9/2 level (5d29) is established by a single line, 1115.532 Å, 5d29–5p27. This transition is predicted to be strong, so this is likely correct. However, since there are no confirming transitions, we consider the level to be tentative.

As can be seen, the lines that establish 5d19 and 5d29, 1114.688 Å and 1115.532 Å, have nearly the same wavelength. The matching of these two lines with the 5d19 and 5d29 levels was done so as to produce the best agreement with the LSF predictions. An effort was made to resolve the question by an isoelectronic comparison. However, the lines were again predicted to be so close that a clear resolution was not possible. In table 3, we list alternative values for the 5d19 and 5d29 levels that would apply if the designations were interchanged.

3.5. Higher 4p4nd and 4p4ns levels

In [5] some levels of these configurations were located on the basis of resonance lines in the region around 159 Å. In [6] a number of these levels were reported to make transitions to levels of 4p45p. In our present observations many of these lines do not appear as belonging to Zr VI, and we thus conclude that the results for these configurations in [5, 6] cannot be accepted without further confirmation.

4. Theoretical Interpretation

4.1. Odd parity configurations

As in [11] 'the observed configurations were interpreted theoretically by making LSFs of the energy parameters to the observed levels with the Cowan suite of codes, RCN (Hartree–Fock ), RCG (energy matrix diagonalization), and RCE (least-squares parameter fitting) [12]. The Hartree–Fock code was run in a relativistic mode (HFR) with a correlation term in the potential. Breit energies were not included. For the initial calculations the HFR values were scaled by a factor of 0.85 for the direct electrostatic parameters Fk, the exchange electrostatic parameters Gk, and the configuration interaction (CI) parameters Rk'. The odd configurations 4s24p5, 4s24p45p, 4s24p44f, and 4s4p54d were treated as a single group.

The Hartree–Fock and LSF parameters for the odd configurations are given in table 4. For these calculations, the 4p45p exchange electrostatic parameters, G0(4p5p) and G2(4p5p), were linked at their HFR ratio. The LSF/HFR ratio of 0.856 is satisfactory. The CI parameters for the 4s24p5–4s24p45p interaction were held fixed at their scaled HFR values. All other CI parameters and parameters for 4s24p44f and 4s4p54d were fixed at their scaled HFR values. The value of the effective interaction parameter α(4p4p) for the 4p45p configuration was fixed at the value observed for the 4p4 core of Zr VII [15]. In table 4 only values for the observed configurations 4s24p5 and 4s24p45p are given.

Table 4.  Hartree–Fock and least-squares fitted parameters (cm−1) for the odd configurations of Zr VI. Mean error of fit 229 cm−1.

Configuration Parameter HFR LSF Unc. LSF/HFR
4s24p5 Eav(4s24p5) 9676 9927 172  
  ζ4p 9986 10481 217 1.049
4s24p45p Eav(4s24p45p) 448691 443928 52 0.989
  F2(4p4p) 84030 69669 504 0.829
  α(4p4p)   −59a    
  ζ4p 10556 10858 133 1.031
  ζ5p 2371 2725 108 1.148
  F2(4p5p) 26016 24044 484 0.924
  G0(4p5p) 5518 4725 62b 0.856
  G2(4p5p) 7441 6372 84b 0.856
Config. interaction          
4s24p5–4s24p45p R0(4p4p, 4p5p) 2417 2054c   0.850
  R2(4p4p, 4p5p) 11574 9837c   0.850

aFixed at value from 4p4 of Zr VII [15]. bLinked in LSF fit. cFixed at scaled HFR value.

The calculated level values and eigenvector compositions for the odd configurations are given in table 5. This table gives the percentage compositions for the three leading eigenvector states in LS-coupling and the percentage for the leading eigenvector state in jl-coupling. As can be seen there is not much mixing between the 4s24p5 and the 4s24p45p configurations. Their mutual repulsion is only about 320 cm−1.

Table 5.  Calculated energy levels (cm−1) and percentage compositions for the odd levels of Zr VI.

J Observed Calculated O−C % jl Percentage composition (LS-coupling)
3/2 0 0 0   99% 4s24p5(1S)2P        
1/2 15 603 15 603 0   99% 4s24p5(1S)2P 1% 4s4p54d(1P)2P    
3/2 421 258 421 351 −93 40%(3P2)[1] 63% 4p45p(3P)4P 9% 4p45p(3P)4S 9% 4p45p(1D)2P
5/2 421 991 421 956 36 79%(3P2)[2] 68% 4p45p(3P)4P 24% 4p45p(3P)4D 4% 4p45p(1D)2D
1/2 425 678 426 061 −383 54%(3P2)[1] 44% 4p45p(3P)4P 24% 4p45p(3P)2P 20% 4p45p(1D)2P
5/2 427 119 427 158 −40 73%(3P2)[3] 60% 4p45p(3P)2D 15% 4p45p(3P)4P 13% 4p45p(3P)4D
7/2 427 649 427 446 203 90%(3P2)[3] 90% 4p45p(3P)4D 10% 4p45p(1D)2F    
1/2 434 798 434 708 89 55%(3P1)[0] 38% 4p45p(3P)4P 27% 4p45p(3P)4D 17% 4p45p(3P)2P
3/2 435 428 435 079 348 35%(3P2)[2] 33% 4p45p(3P)4D 23% 4p45p(3P)2D 18% 4p45p(3P)2P
1/2 436 859 436 807 52 57%(3P0)[1] 56% 4p45p(3P)4D 16% 4p45p(3P)4P 15% 4p45p(3P)2S
3/2 437 477 437 528 −51 35%(3P1)[2] 49% 4p45p(3P)4D 32% 4p45p(3P)2P 10% 4p45p(1D)2P
5/2 440 555 440408 147 96%(3P1)[2] 60% 4p45p(3P)4D 25% 4p45p(3P)2D 14% 4p45p(3P)4P
3/2 442 454 442 494 −40 67%(3P0)[1] 25% 4p45p(3P)2D 25% 4p45p(3P)4S 17% 4p45p(3P)4P
3/2 444 879 444 863 17 64%(3P1)[1] 44% 4p45p(3P)2D 43% 4p45p(3P)4S 5% 4p45p(3P)4P
1/2 444 340 444 928 −587 63%(3P1)[1] 68% 4p45p(3P)2S 13% 4p45p(3P)2P 10% 4p45p(3P)4D
5/2 449 731 449 565 166 84%(1D2)[3] 84% 4p45p(1D)2F 9% 4p45p(3P)2D 4% 4p45p(1D)2D
7/2 453 000 452 862 138 89%(1D2)[3] 89% 4p45p(1D)2F 10% 4p45p(3P)4D    
3/2 455 878 455 924 −46 58%(1D2)[1] 58% 4p45p(1D)2P 20% 4p45p(1D)2D 10% 4p45p(3P)2P
3/2 459 078 458 938 139 71%(1D2)[2] 71% 4p45p(1D)2D 20% 4p45p(3P)2P 8% 4p45p(1D)2P
5/2 459 581 459 514 67 90%(1D2)[2] 90% 4p45p(1D)2D 4% 4p45p(1D)2F 3% 4p45p(3P)4P
1/2 464 724 464 776 −52 62%(1D2)[1] 62% 4p45p(1D)2P 34% 4p45p(3P)2P 2% 4p45p(1S)2P
1/2 482 699 482 755 −56 79%(1S0)[1] 79% 4p45p(1S)2P 9% 4p45P(3P)2P 6% 4p45p(3P)4D
3/2 484 897 484 952 −55 81%(1S0)[1] 81% 4p45p(1S)2P 4% 4p45p(3P)2D 4% 4p45p(3P)4D

4.2. Even parity configurations

The parameters for the even configurations are given in table 6. Here, the 4s4p6, 4p44d, 5s, 5d, 6s, 6d, and 7s configurations were treated as single group. For the initial calculations the HFR values were scaled by a factor of 0.85 for the direct electrostatic parameters Fk, the exchange electrostatic parameters Gk, and the CI parameters Rk. All the parameters that were allowed to vary were well defined in the fit and have reasonable ratios to the HFR values. The exchange parameters G1(4p5d) and G3(4p5d) were linked at their HFR ratio. The CI parameters for the 4s4p6–4s24p44d and 4s4p6–4s24p45d interactions were also linked at their HFR ratio. The fitted values are reasonable. The other CI parameters and those for 4p46d and 4p47s were held fixed at their scaled HFR values. As described in [4] the interaction of 4s4p6 2S1/2 with the 4s24p4(1D)4d 2S level is great, with a mutual repulsion of ∼33 000 cm−1. On the other hand, interaction between 4s4p6 and 4s24p45d is negligible. The value of the effective interaction parameter α(4p4p) for the 4p44d, 5s, 5d, and 6s configurations was again fixed at the value observed for the 4p4 core of Zr VII [15]. The calculated level values and eigenvector compositions for the even levels are given in table 7. This table gives the percentage compositions for the three leading eigenvector states in LS-coupling and the percentage for the leading eigenvector state in jl-coupling, where appropriate. As can be seen, the purity of the states of the 4p44d configuration in LS-coupling is low, leading to low leading percentages for many of the levels. In order to avoid duplicate names, we have used the second component for the level observed at 279 457 cm−1 to designate the level. Even though the 4p45d and 4p46s configurations are practically coincident, there is not much mixing of states. The percentage compositions for the 4s4p6, 4s24p44d, and 4s24p45s configurations are close to those given in [4].

Table 6.  Hartree–Fock and least-squares fitted parameters (cm−1) for the even configurations of Zr VI. Mean error of fit 303 cm−1.

Configuration Parameter HF LSF Unc. LSF/HFR
4s4p6 Eav(4s4p6) 238 204 225 794 545 0.945
4s24p44d Eav(4s24p44d) 291 306 286 394 61 0.982
  F2(4p4p) 82 691 68 538 720 0.829
  α(4p4p)   −59a    
  ζ4p 10 169 10 463 168 1.029
  ζ4d 719 853 81 1.186
  F2(4p4d) 69 587 60 676 549 0.872
  G1(4p4d) 86 663 69 960 180 0.807
  G3(4p4d) 53 745 45 371 1036 0.844
4s24p45s Eav(4s24p45s) 388 500 383 302 110 0.986
  F2(4p4p) 83 691 69 792 1010 0.834
  α(4p4p)   −59a    
  ζ4p 10 481 10 832 274 1.033
  G1(4p5s) 8701 7486 414 0.860
4s24p45d Eav(4s24p45d) 538 379 533 803 70 0.991
  F2(4p4p) 84 085 70 231 594 0.835
  α(4p4p)   −59a    
  ζ4p 10 550 10 927 141 1.036
  ζ5d 217 274 76 1.265
  F2(4p5d) 19 526 16 999 721 0.871
  G1(4p5d) 10 862 7658b 275 0.705
  G3(4p5d) 8028 5660b 203 0.705
4s24p46s Eav(4s24p46s) 566 615 562 487 112 0.992
  F2(4p4p) 84 157 69 956 914 0.831
  α(4p4p)   −59a    
  ζ4p 10 581 11 023 237 1.042
  G1(4p6s) 2783 2415 380 0.868
Config. interaction          
4s4p6–4s24p44d R1(4p4p, 4s4d) 95 949 74 285c 461 0.774
4s4p6–4s24p45d R1(4p4p, 4s5d) 32 261 24 977c 155 0.774
4s4p6–4s24p45s R1(4p4p, 4s5s) 3749 3186d   0.850
4s4p6–4s24p46s R1(4p4p, 4s6s) 875 744d   0.850
4s24p44d–4s24p45s R2(4p4d, 4p5s) −8467 −7197d   0.850
  R1(4p4d, 5s4p) −1073 −912d   0.850
4s24p44d–4s24p46s R2(4p4d, 4p6s) −5150 −4378d   0.850

aFixed at value from 4p4 of Zr VII [15]. b, cLinked in groups in LSF fit. dFixed at scaled HFR value.

Table 7.  Calculated energy levels (cm−1) and percentage compositions for the even levels of Zr VI. Observed levels with asterisk were not included in the least-squares fits.

J Observed   Calculated O−C % jl Percentage composition (LS-coupling)
1/2 191 571   191 569 2   77% 4s4p6(2S)2S 23% 4p44d(1D)2S    
5/2 248 940   248 803 137   88% 4p44d(3P)4D 3% 4p44d(3P)4F 3% 4p44d(3P)4P
7/2 249 323   249 305 18   91% 4p44d(3P)4D 6% 4p44d(3P)4F 2% 4p44d(1D)2F
3/2 250 018   249 861 157   86% 4p44d(3P)4D 4% 4p44d(3P)4P 3% 4p44d(1D)2D
1/2 251 819   251 854 −35   85% 4p44d(3P)4D 7% 4p44d(1D)2P 5% 4p44d(3P)2P
9/2 26 1643   261 550 93   90% 4p44d(3P)4F 10% 4p44d(1D)2G    
7/2 266 145   265 981 164   66% 4p44d(3P)4F 17% 4p44d(3P)2F 13% 4p44d(1D)2G
1/2 266 279   267 364 −1085   44% 4p44d(1D)2P 37% 4p44d(3P)2P 14% 4p44d(3P)4D
3/2 271 296   271 001 295   47% 4p44d(3P)4F 16% 4p44d(3P)4P 13% 4p44d(1S)2D
5/2 271 374   271 025 349   93% 4p44d(3P)4F 3% 4p44d(3P)4D 2% 4p44d(1S)2D
1/2 272 091   272 034 57   91% 4p44d(3P)4P 5% 4p44d(3P)2P 3% 4p44d(1D)2P
3/2 272 834   272 884 −50   38% 4p44d(3P)4P 30% 4p44d(3P)4F 18% 4p44d(1D)2P
3/2 274 666   274 573 93   36% 4p44d(1D)2D 21% 4p44d(3P)2D 15% 4p44d(3P)4F
7/2 276 491   276 813 −322   42% 4p44d(3P)2F 25% 4p44d(3P)4F 20% 4p44d(1D)2G
5/2 278 742   278 634 108   74% 4p44d(3P)4P 9% 4p44d(1S)2D 7% 4p44d(3P)2D
3/2 279 457   279 886 −429   40% 4p44d(3P)4P 24% 4p44d(1D)2P 22% 4p44d(3P)2P
5/2 283 112   282 808 304   41% 4p44d(1D)2D 21% 4p44d(3P)2D 18% 4p44d(3P)4P
7/2 285 967   285 629 338   65% 4p44d(1D)2G 24% 4p44d(3P)2F 10% 4p44d(1D)2F
9/2 286 412   285 935 477   90% 4p44d(1D)2G 10% 4p44d(3P)4F    
5/2 287 142   287 795 −653   65% 4p44d(3P)2F 21% 4p44d(1D)2F 9% 4p44d(1D)2D
5/2 299 609   299 713 −104   76% 4p44d(1D)2F 13% 4p44d(3P)2F 9% 4p44d(1D)2D
7/2 303 517   303 641 −124   80% 4p44d(1D)2F 17% 4p44d(3P)2F 2% 4p44d(1D)2G
3/2 319 336   319 335 1   63% 4p44d(1S)2D 25% 4p44d(1D)2D 5% 4p44d(1D)2P
5/2 325 577   325 582 −5   73% 4p44d(1S)2D 14% 4p44d(1D)2D 5% 4p44d(3P)2F
1/2 334 695   334 774 −79   69% 4p44d(1D)2S 20% 4s4p6(2S)2S 5% 4p44d(1D)2P
3/2 339 683   339 272 411   50% 4p44d(3P)2P 36% 4p44d(1D)2P 7% 4p44d(1D)2D
5/2 343 710   344 309 −599   64% 4p44d(3P)2D 21% 4p44d(1D)2D 11% 4p44d(1S)2D
1/2 346 346   345 581 764   48% 4p44d(3P)2P 41% 4p44d(1D)2P 7% 4p44d(1D)2S
3/2 358 168   358 453 −285   57% 4p44d(3P)2D 19% 4p44d(1S)2D 14% 4p44d(1D)2D
5/2 364 827   364 804 23 92%(3P2)[2] 92% 4p45s(3P)4P 8% 4p45s(1D)2D    
3/2 369 712   369 708 4 82%(3P2)[2] 51% 4p45s(3P)2P 38% 4p45s(3P)4P 10% 4p45s(1D)2D
1/2 377 452   377 471 −19 63%(3P0)[0] 90% 4p45s(3P)4P 9% 4p45s(1S)2S    
3/2 379 777   379 741 36 92%(3P1)[1] 61% 4p45s(3P)4P 37% 4p45s(3P)2P 2% 4p45s(1D)2D
1/2 384 781   384 780 1 72%(3P1)[1] 94% 4p45s(3P)2P 5% 4p45s(1S)2S 1% 4p45s(3P)4P
5/2 393 555   393 590 −35 92%(1D2)[2] 92% 4p45s(1D)2D 8% 4p45s(3P)4P    
3/2 394 196   394 238 −42 87%(1D2)[2] 87% 4p45s(1D)2D 12% 4p45s(3P)2P 1% 4p45s(3P)4P
1/2 423 224   423 190 34 85%(1S0)[0] 85% 4p45s(1S)2S 8% 4p45s(3P)4P 6% 4p45s(3P)2P
5/2 514 465   514 521 −56 55%(3P2)[2] 70% 4p45d(3P)4D 10% 4p45d(3P)4F 10% 4p45d(3P)4P
7/2 514 487   514 569 −82 91%(3P2)[3] 73% 4p45d(3P)4D 19% 4p45d(3P)4F 6% 4p45d(1D)2F
3/2 515 171   515 206 −35 61%(3P2)[2] 59% 4p45d(3P)4D 20% 4p45d(3P)4P 6% 4p45d(1D)2D
1/2 516 444   516 516 −72 77%(3P2)[1] 43% 4p45d(3P)4D 27% 4p45d(3P)4P 17% 4p45d(3P)2P
9/2 517 360 * 517 149 211 90%(3P2)[4] 90% 4p45d(3P)4F 10% 4p45d(1D)2G    
7/2 518 062   517 900 162 87%(3P2)[4] 65% 4p45d(3P)2F 22% 4p45d(3P)4F 11% 4p45d(1D)2G
1/2 520 378 * 520 366 12 82%(3P2)[0] 53% 4p45d(3P)4P 29% 4p45d(3P)2P 11% 4p45d(1D)2S
3/2 521 740   521 749 −9 65%(3P2)[1] 37% 4p45d(3P)4P 34% 4p45d(3P)2D 13% 4p45d(3P)2P
5/2 522 036   521 991 45 54%(3P2)[3] 40% 4p45d(3P)2D 24% 4p45d(3P)2F 15% 4p45d(3P)4P
1/2 528 358   528 514 −156 88%(3P1)[1] 53% 4p45d(3P)4D 30% 4p45d(3P)2P 9% 4p45d(3P)4P
3/2 528 976   528 938 38 68%(3P0)[2] 69% 4p45d(3P)4F 12% 4p45d(3P)4D 11% 4p45d(1S)2D
5/2 529 352   529 301 51 52%(3P0)[2] 59% 4p45d(3P)4F 14% 4p45d(3P)4D 13% 4p45d(3P)4P
7/2 529 945   529 891 54 97%(3P1)[3] 54% 4p45d(3P)4F 23% 4p45d(3P)2F 22% 4p45d(3P)4D
3/2 530 539   530 479 60 59%(3P1)[1] 28% 4p45d(3P)4P 26% 4p45d(3P)4D 19% 4p45d(3P)2D
5/2 532 403   532 272 131 97%(3P1)[2] 52% 4p45d(3P)4P 27% 4p45d(3P)2F 11% 4p45d(3P)4F
5/2 533 737   533 656 81 59%(3P1)[3] 43% 4p45d(3P)2D 42% 4p45d(3P)2F 4% 4p45d(1S)2D
3/2 534 553   534 777 −224 46%(3P1)[2] 64% 4p45d(3P)2P 17% 4p45d(3P)2D 7% 4p45d(1D)2P
7/2 542 227 * 542 081 146 88%(1D2)[4] 88% 4p45d(1D)2G 8% 4p45d(3P)2F 3% 4p45d(3P)4F
9/2 542 643 * 542 576 67 90%(1D2)[4] 90% 4p45d(1D)2G 10% 4p45d(3P)4F    
1/2 543 296   543 203 93 79%(1D2)[0] 79% 4p45d(1D)2S 10% 4p45d(3P)4P 9% 4p45d(1D)2P
3/2 544 423   544 296 127 76%(1D2)[1] 76% 4p45d(1D)2P 7% 4p45d(3P)4P 6% 4p46s(3P)2P
5/2 545 413   545 437 −23 91%(3P2)[2] 91% 4p46s(3P)4P 9% 4p46s(1D)2D    
5/2 545 666   545 709 −43 76%(1D2)[2] 76% 4p45d(1D)2D 17% 4p45d(1D)2F 2% 4p45d(3P)4D
5/2 547 214   547 087 127 73%(1D2)[3] 73% 4p45d(1D)2F 15% 4p45d(1D)2D 7% 4p45d(3P)2D
3/2 547 472   547 461 11 82%(3P2)[2] 63% 4p46s(3P)2P 20% 4p46s(3P)4P 9% 4p46s(1D)2D
7/2 547 178 * 547 229 −51 92%(1D2)[3] 92% 4p45d(1D)2F 3% 4p45d(3P)4D 2% 4p45d(3P)2F
1/2 547 791   547 844 −53 67%(1D2)[1] 67% 4p45d(1D)2P 23% 4p45d(3P)2P 8% 4p45d(1D)2S
3/2 548 806   549 016 −210 78%(1D2)[2] 78% 4p45d(1D)2D 18% 4p45d(3P)2D 1% 4p45d(1D)2P
1/2 558 209   558 212 −3 70%(3P0)[0] 86% 4p46s(3P)4P 12% 4p46s(1S)2S 2% 4p46s(3P)2P
3/2 559 357   559 340 17 99%(3P1)[1] 78% 4p46s(3P)4P 22% 4p46s(3P)2P    
1/2 561 050   561 077 −27 81%(3P1)[1] 92% 4p46s(3P)2P 4% 4p46s(3P)4P 3% 4p46s(1S)2S
5/2 573 102   573 108 −6 91%(1D2)[2] 91% 4p46s(1D)2D 9% 4p46s(3P)4P    
3/2 573 301   573 265 36 88%(1D2)[2] 88% 4p46s(1D)2D 9% 4p46s(3P)2P 2% 4p45d(1S)2D
5/2 574 495   574483 12 85%(1S0)[2] 85% 4p45d(1S)2D 4% 4p45d(3P)2F 3% 4p45d(3P)4P
3/2 574 889   574 920 −31 81%(1S0)[2] 81% 4p45d(1S)2D 6% 4p45d(3P)4F 4% 4p45d(3P)2D
1/2 602 660   602 671 −11 85%(1S0)[0] 85% 4p46s(1S)2S 9% 4p46s(3P)4P 5% 4p46s(3P)2P

5. 4s4p6–4s24p45p transitions

Transitions between the 4s4p6 and 4s24p45p configurations are normally forbidden as two electron jumps. However, because of CI between 4s4p6 and 4s24p44d, they can in fact take place. We observe six of them in Zr VI. In lower members of the isoelectronic sequence, these transitions occur at wavelengths that are long relative to the resonance lines and serve to improve the accuracy of the excited levels. However, as the separation of configurations with different principal quantum number increases with increasing ionization stage, these transitions move to lower wavelength, and their inclusion does not improve the accuracy of the excited levels. For Zr VI, these transitions fall in the same wavelength region as the 4s24p5–4s24p44d resonance transitions, so they have practically no effect on the Ritz values for the resonance lines.

6. Ritz wavelengths

We determined Ritz wavelengths for a number of the lines by differencing the energy level values in tables 2 and 3. The uncertainties of the calculated wavelengths were taken to correspond to the square root of the sum of the squares of the uncertainties of the combining levels. In table 1 we show the Ritz wavelengths and uncertainties for lines likely to be suitable as wavelength standards, that is where the uncertainty of the Ritz wavelength is ±0.0020 Å or less. (This table contains all observed lines together with those with Ritz values.) The Ritz values have uncertainties that vary from ±0.0003 Å to ±0.0020 Å.

7. Oscillator strengths

Table 1 lists the transition probabilities gUA and log gLf for each observed line as calculated with wavefunctions obtained from the fitted energy parameters. Here, f is the oscillator strength, gU is the statistical weight of the upper level 2JU + 1 and gL is the statistical weight of the lower level 2JL + 1. The A-values are compared with recently published ab initio values in section 9 below.

Since there are no experimental values for the transition probabilities of Zr VI, it is difficult to estimate the uncertainty of the calculated values. One guide is the cancellation factor. This is the ratio of the calculated transition probability to a value calculated with all parts of the wave function taken as positive [12]. Low cancellation factors generally indicate a larger uncertainty in the calculated values. Indeed, many of the values in table 1 have low cancellation factors. To try to obtain a more quantitative estimate of the uncertainties, we attempted to judge the sensitivity of the values to the parameter values used for the calculation. For this, an alternate calculation was performed with parameters that varied by small amounts from those used for the main calculation. The differences in the results were then used to put the uncertainties on a semi-quantitative basis with code letters, as are often used for this purpose. The letter codes define categories of uncertainties in A-values: C (≤25%), D + (≤40%), D (≥50%), E (>50%).

8. Ionization energy

In [4] an estimated value of n*(4p45s) of 3.12 ± 0.02 was used to determine an ionization energy of 773 000 ± 5000 cm−1. In [6] this was revised upward to 776 500 ± 500 cm−1 on the basis of a Ritz diagram for the 4p45s, 6s, and 7s configurations. (No details of the determination were given.) Since four of the eight levels of 4p46s in [6] have now been found to be spurious, this value must be re-determined.

For our new determination we use the centers-of-gravity of the 4p45s and 4p46s configurations together with an estimated value for the change in effective quantum number Δn*(4p46s–4p45s) = n*(4p46s)–n*(4p45s). This allows us to find the limit of the 4p4ns series, which is the center-of-gravity of the 4p4 configuration of Zr VII.

From the observed levels in table 3, we find the centers-of-gravity of the 4p45s and 4p46s configurations as 383 198.13 and 562 514.9 cm−1, respectively. Our value for Δn*(4p46s–4p45s) is taken from Δn*(4p66s–4p65s) for the one-electron atom Mo VI [16], 1.0338. We use Cowan's Hartree–Fock code to estimate the change in going from Mo VI to Zr VI. For Mo we calculate Δn*(4p66s–4p65s) as 1.0367 and for Zr VI we calculate Δn*(4p46s–4p45s) as 1.0341, a difference of 0.0026. We thus estimate Δn*(4p46s–4p45s) for Zr VI as 1.0338 − 0.0026 = 1.0312, with an estimated uncertainty of ±0.0015. This produces a limit of 793 780 ± 300 cm−1. The effective quantum numbers for Zr VI are n*(5s) = 3.102(1) and n*(6s) = 4.133(3). Correcting for the energy of the center-of-gravity of 4p4 in Zr VII, 16 402 cm−1 [15], we obtain for the ionization energy of Zr VI the value 777 380 ± 300 cm−1 (96.38 ± 0.04 eV) [17].

9. Comparison with ab initio calculations

Recently, two sets of ab initio calculations for the levels and oscillator strengths of Zr VI have appeared. Singh et al [18] used a multiconfiguration Dirac–Fock approach to make calculations for transitions within the n = 4 complex; 4s24p5, 4s4p6, 4s24p44d. Aggarwal and Keenan [19] used the general-purpose relativistic atomic structure package GRASP for calculations within the same complex of n = 4 configurations. Both calculations are based on new versions of the Grant atomic structure code, as described in their papers [18, 19]. Froese Fischer [20] has recently discussed the accuracy that might be expected from calculations for complex atoms with GRASP, in particular as applied to the Br-like ion W39+. Aggarwal and Keenan also used the flexible atomic code [21].

A comparison of the results of the ab initio calculations [18, 19] for the wavelengths and transition probabilities with our present values is given in table 8. The wavelengths for Aggarwal and Keenan [19] in this table are differences of the GRASP3 energies in their table 4. Overall, the wavelengths obtained by Singh et al [18] are in better agreement with our present observed wavelengths than those of Aggarwal et al [19]. A notable disagreement for the transition probabilities is for the 4s24p5 2P3/2–4s24p44d (3P)4F3/2 transition (indices 1–12), observed at 368.600 Å. (The indices are sequential numbers used in [18] and [19] in their enumeration of the energy levels.) Both Singh et al [18] and Aggarwal and Keenan [19] find an extremely low transition probability. However, we obtain a fairly high A-value, and it is indeed observed as a fairly strong line. This transition is nominally forbidden as an inter-combination line in LS-coupling because of the change of spin. However, although the 4p44d level (271 296 cm−1 observed value) has a leading percentage composition in LS coupling of 47% 4p44d (3P)4F3/2, the full percentage compositions show that it actually has a total doublet character of about 36%. This accounts for our calculated transition probability and observed line strength. Singh et al [18] report a composition of 74% 4p44d (3P)4F3/2 for this level, with no secondary percentage mentioned. Percentage compositions were not reported by Aggarwal and Keenan [19].

Table 8.  Comparison of wavelengths λ(Å) and transition probabilities A(s−1) for Zr VI calculated with the MCDF2 method of Singh et al [18] and the GRASP3 method of Aggarwal and Keenan [19] with present values. Numerals following level names are index numbers used in [18] and [19]. Blank spaces indicate that line was not observed. Acc. is the accuracy estimate.

Lower level   Upper level   λ[18] λ[19] λ(pres.) A[18] A[19] A(pres.) |CF| Acc. Int.(obs)
4s24p5 2P3/2 1 4s4p62S1/2 3 528 494.113 522.000 5.30E + 08 1.0518E + 09 1.31E + 09 0.04 D+ 2000
    4s24p44d (3P)4D5/2 4 410 392.117 401.701 1.17E + 07 2.0308E + 07 9.49E + 06 0.00 E 80
    (3P)4D3/2 6 408 390.213 399.967 7.76E + 06 1.1017E + 07 1.22E + 07 0.00 E 80
    (3P)4D1/2 7 405 387.245 397.112 4.75E + 06 5.6982E + 06 1.40E + 07 0.01 E 30
    (1D)2P1/2 10 376 359.833 375.546 1.28E + 07 2.1200E + 08 1.49E + 07 0.00 E 30
    (3P)4F3/2 12 372 359.150 368.600 3.35E + 05 5.1086E + 05 2.13E + 08 0.01 D+ 250
    (3P)4F5/2 11 374 360.799 368.494 1.41E + 08 1.0789E + 07 2.14E + 08 0.61 D+ 300
    (3P)4P1/2 13 368 353.993 367.523 4.67E + 08 5.9759E + 08 8.61E + 08 0.15 D+ 300
    (3P)4P3/2 14 368 353.991 366.522 5.50E + 08 7.0038E + 08 5.27E + 08 0.02 D+ 200
    (1D)2D3/2 15 365 351.232 364.080 3.37E + 08 2.5390E + 08 3.80E + 08 0.01 D+ 300
    (3P)4P5/2 17 360 346.875 358.755 1.60E + 08 1.5603E + 08 2.85E + 08 0.02 D+ 300
    (1D)2P3/2 18 358 344.980 357.837 6.97E + 07 1.7608E + 07 5.52E + 07 0.00 D+ 30
    (1D)2D5/2 19 354 340.992 353.221 3.82E + 08 2.6359E + 08 4.00E + 08 0.01 D+ 250
    (3P)2F5/2 22 348 335.698 348.262 1.96E + 08 3.0306E + 08 1.56E + 08 0.01 D+ 200p
    (1D)2F5/2 23 330 318.897 333.768 3.24E + 08 3.9608E + 08 4.95E + 08 0.10 D+ 400
    (1S)2D3/2 25 306 304.453 313.150 1.68E + 09 4.0018E + 09 3.18E + 09 0.11 D+ 300
    (1S)2D5/2 26 301 300.149 307.148 3.16E + 02 2.1104E + 09 5.26E + 05 0.00 E 30
    (1D)2S1/2 28 279 280.532 298.779 1.63E + 11 9.7116E + 10 1.41E + 11 0.71 C 300
    (3P)2P3/2 27 281 283.619 294.395 1.56E + 11 1.2527E + 11 1.46E + 11 0.90 C 500
    (3P)2D5/2 30 274 277.998 290.949 1.29E + 10 1.6154E + 11 1.75E + 11 0.85 C 500
    (3P)2P1/2 29 275 273.019 288.730 1.91E + 11 6.3978E + 10 1.38E + 10 0.11 D+ 200
    (3P)2D3/2 31 265 268.277 279.198 7.17E + 09 7.1045E + 09 4.46E + 09 0.05 D+ 90p
4s24p5 2P1/2 2 4s4p62S1/2 3 574 534.239 568.284 2.40E + 08 4.7253E + 08 5.97E + 08 0.05 D+ 2000
    4s24p44d (3P)4D3/2 6 435 414.818   3.21E + 05 1.2890E + 00 2.31E + 06 0.00 E  
    (3P)4D1/2 7 431 411.465 423.344 4.55E + 06 4.8266E + 06 9.63E + 06 0.00 E 5
    (1D)2P1/2 10 398 380.653 398.919 6.32E + 07 6.0598E + 07 7.66E + 07 0.00 E 80
    (3P)4F3/2 12 395 379.890 391.094 3.56E + 07 5.1666E + 07 9.18E + 06 0.00 E 100p
    (3P)4P1/2 13 390 374.124 389.881 2.37E + 07 2.6970E + 07 7.14E + 07 −0.01 E 100p
    (3P)4P3/2 14 390 374.122 388.754 1.58E + 07 3.2332E + 06 8.46E + 06 0.00 E 20
    (1D)2D3/2 15 386 371.042 386.007 3.78E + 08 4.0027E + 08 3.88E + 08 −0.01 D+ 250
    (1D)2P3/2 18 379 364.072 378.992 2.06E + 07 1.1180E + 07 1.51E + 07 0.00 E 80
    (1S)2D3/2 25 321 319.226 329.242 2.20E + 09 6.9689E + 08 3.28E + 09 -0.06 D+ 300
    (1D)2S1/2 28 291 293.028 313.389 8.16E + 09 3.9101E + 10 1.27E + 10 −0.11 C 300
    (3P)2P3/2 27 294 296.397 308.569 3.20E + 09 2.5940E + 09 1.16E + 09 0.02 D+ 100
    (3P)2P1/2 29 286 284.840 302.351 1.52E + 11 9.6829E + 10 1.28E + 11 −0.87 C 300
    (3P)2D3/2 31 276 279.682 291.920 1.80E + 11 1.5364E + 11 1.65E + 11 0.85 C 500p

A number of other striking differences can be seen in table 8. The values found by all three calculations for the 4s24p5 2P3/2–4s24p44d(1S)4D5/2 transition (indices 1–26) are extremely discrepant. The present value is about in the middle of the two found with GRASP. The values for the 4s24p5 2P1/2–4s24p44d(3P)4D3/2 transition (indices 2–6) also disagree by a large amount. Still, they all predict that this will be a very weak line, and in fact it has not been observed.

Both Singh et al [18] and Aggarwal and Keenan [19] compare their calculated level values with the observed values given in the NIST Atomic Spectra Database [22]. Since we have made a number of revisions to the 4p44d levels, a new comparison is called for. This is given in table 9.

Table 9.  Comparison of level energies E(cm−1) for Zr VI calculated with the MCDF2 method of Singh et al [18] and the GRASP3 method of Aggarwal and Keenan [19] with present experimental energies. Index numbers are those used in [18] and [19].

Configuration Term J Index E[18] E[19] E(present)
4s24p5 2P 3/2 1 0 0.00 0.00
  2P 1/2 2 15 132.68 15 200.72 15 602.78
4s4p6 2S 1/2 3 189 416.50 202 382.92 191 570.67
4s24p44d (3P)4D 5/2 4 243 856.87 255 025.79 248 940.11
  (3P)4D 7/2 5 243 977.58 255 226.61 249 322.89a
  (3P)4D 3/2 6 245 129.81 256 270.21 250 017.63
  (3P)4D 1/2 7 247 050.21 258 234.49 251 818.7a
  (3P)4F 9/2 8 257 617.85 268 478.41 261 642.9a
  (3P)4F 7/2 9 262 852.29 273 655.78 266 145.41
  (1D)2P 1/2 10 266 287.05 277 906.98 266 278.49
  (3P)4F 3/2 12 267 351.49 278 434.81 271 296.05
  (3P)4F 5/2 11 268 547.62 277 162.97 271 374.36
  (3P)4P 1/2 13 271 422.72 282 491.78 272 091.26
  (3P)4P 3/2 14 271 795.83 282 492.88 272 834.44
  (1D)2D 3/2 15 274 341.72 284 711.75 274 665.60
  (3P)2F 7/2 16 275 087.93 285 754.25 276 491.34a
  (3P)4P 5/2 17 278 072.77 288 288.07 278 742.23
  (1D)2P 3/2 18 279 170.13 289 871.57 279 457.21
  (1D)2D 5/2 19 282 736.58 293 262.43 283 112.00
  (1D)2G 7/2 20 285 041.05 295 528.49 285 967.09a
  (1D)2G 9/2 21 285 304.42 295 244.28 286 411.5
  (3P)2F 5/2 22 287 334.54 297 886.73 287 142.42
  (1D)2F 5/2 23 303 235.39 313 598.83 299 608.66
  (1D)2F 7/2 24 306 845.73 317 300.25 303 517.22
  (1S)2D 3/2 25 327 037.28 328 458.27 319 336.18
  (1S)2D 5/2 26 332 337.56 333 168.17 325 576.82a
  (1D)2S 1/2 28 358 608.52 356 465.26 334 694.92
  (3P)2P 3/2 27 355 733.42 352 586.07 339 682.78
  (3P)2D 5/2 30 364 819.62 359 714.56 343 709.55
  (3P)2P 1/2 29 363 414.99 366 274.62 346 345.56
  (3P)2D 3/2 31 377 428.37 372 749.08 358 168.09

aLevel energy revised in present work.

The percentage compositions for the states of the 4s4p6 and 4s24p44d configurations obtained in the present work are compared with those obtained in the MCDF calculations of Singh et al [18] in table 10. The general agreement is qualitatively reasonable. However, there are some striking differences. For example, as a result of the large 4s4p6 2S1/2–4s24p44d (1D)2S1/2 interaction mentioned above, we find that the level designated as 4s4p6 2S1/2 (index 3) has an admixture of 23% 4p44d (1D)2S1/2. Singh et al [18] find a similar admixture for this level. Correspondingly, we find the level designated as 4p44d(1D)2S1/2 (index 28) to have an admixture of 20% 4s4p6 2S1/2, as would be generally expected. No such admixture is given by Singh et al [18]. Presumably, their 4s4p6 2S1/2 percentage calculated for this state is below about 16%, the lowest percentage present in their table 3. Other striking differences can be seen for the levels at 271 296 (index 12), 272 834 (index 14), 279 457 (index 18), and 346 346 (index 29) cm−1. Of course, the calculated oscillator strengths depend largely on the admixtures represented by the percentages.

Table 10.  Comparison of present percentages (in bold type) for the 4s4p6 and 4s24p44d configurations with the percentage compositions of Singh et al [18] (in parentheses). Level values are in cm−1. Index numbers are those used in [18] and [19]. Where there are no values in parentheses, no percentage was given by Singh et al [18].

Index Singh label J E(obs)a Percentage composition
3 4s 2S 1/2 191571 77(72)% 4s 2S 23(27)% (1D)2S        
4 (3P)4D 5/2 248940 88(90)% (3P)4D 3% (3P)4F 3% (3P)4P    
5 (3P)4D 7/2 249323 91(93)% (3P)4D 6% (3P)4F 2% (1D)2F    
6 (3P)4D 3/2 250018 86(88)% (3P)4D 4% (3P)4P 3% (1D)2D    
7 (3P)4D 1/2 251819 85(89)% (3P)4D 7% (1D)2P 5% (3P)2P    
8 (3P)4F 9/2 261643 90(92)% (3P)4F 10% (1D)2G        
9 (3P)4F 7/2 266145 66(75)% (3P)4F 17% (3P)2F 13% (1D)2G    
10 (1D)2P 1/2 266279 44(44)% (1D)2P 37(39)% (3P)2P 14% (3P)4D    
12 (3P)4F 3/2 271296 48(74)% (3P)4F 16% (3P)4P 13% (1S)2D    
11 (3P)4F 5/2 271374 93(94)% (3P)4F 3% (3P)4D 2% (1S)2D    
13 (3P)4P 1/2 272091 91(91)% (3P)4P 5% (3P)2P 3% (1D)2P    
14 (3P)4P 3/2 272834 38(50)% (3P)4P 30% (3P)4F 18(20)% (1D)2P    
15 (1D)2D 3/2 274666 36(40)% (1D)2D 21(24)% (3P)2D 15% (3P)4F    
16 (3P)2F 7/2 276491 42(50)% (3P)2F 25(17)% (3P)4F 20(20)% (1D)2G    
17 (3P)4P 5/2 278742 74(84)% (3P)4P 9% (1S)2D 7% (3P)2D    
18 (3P)4P 3/2 279457b 40(24)% (3P)4P 24(36)% (1D)2P 22(22)% (3P)2P    
19 (1D)2D 5/2 283112 40(43)% (1D)2D 21(23)% (3P)2D 18% (3P)4P    
20 (1D)2G 7/2 285967 65(69)% (1D)2G 24(21)% (3P)2F 10% (1D)2F    
21 (1D)2G 9/2 286412 90(92)% (1D)2G 10% (3P)4F        
22 (3P)2F 5/2 287142 65(64)% (3P)2F 21(19)% (1D)2F 9% (1D)2D    
23 (1D)2F 5/2 299609 77(79)% (1D)2F 12% (3P)2F 9% (1D)2D    
24 (1D)2F 7/2 303517 80(81)% (1D)2F 16(16)% (3P)2F 2% (1D)2G    
25 (1S)2D 3/2 319336 63(66)% (1S)2D 25(25)% (1D)2D 5% (1D)2P    
26 (1S)2D 5/2 325577 73(74)% (1S)2D 14% (1D)2D 5% (3P)2F    
28 (1D)2S 1/2 334695 69(42)% (1D)2S 20% 4s 2S 5(21)% (1D)2P 4(20)% (3P)2P
27 (3P)2P 3/2 339683 50(52)% (3P)2P 36(40)% (1D)2P 7% (1D)2D    
30 (3P)2D 5/2 343710 64(66)% (3P)2D 21(22)% (1D)2D 11% (1S)2D    
29 (3P)2P 1/2 346346 48(32)% (3P)2P 41(27)% (1D)2P 7(30)% (1D)2S    
31 (3P)2D 3/2 358168 57(60)% (3P)2D 19(17)% (1S)2D 14(17)% (1D)2D    

aPresent value from table 3. bLabel for this level in present work is 4p44d(1D)2P3/2.

Acknowledgments

The code letters to represent the uncertainties of the transition probabilities were obtained in calculations by Alexander Kramida. We gratefully acknowledge this contribution as well as other helpful discussions. We thank Gillian Nave and Csilla Szabo for their assistance with the image plate measurements.

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10.1088/0031-8949/91/2/025401