Optics and Spectroscopy, Vol. 88, No. 1, 2000, pp. 11–16. Translated from Optika i Spektroskopiya, Vol. 88, No. 1, 2000, pp. 16–21. Original Russian Text Copyright © 2000 by Azarov, Churilov.

ATOMIC SPECTROSCOPY

Assignment of the 5d6s–5d6p Transitions in the PtIX Ion: Comparison of Two Calculations of the 5d2, 5d6s, and 5d6p Configurations in the Ion V. I. Azarov and S. S. Churilov Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, 142092 Russia Received March 12, 1999

Abstract—The spectrum of platinum is studied in the region from 250 to 1250 Å. The twenty-two 5d6s–5d6p spectral lines of the PtIX are assigned. All levels of the 5d6s configuration are found. The assignment of the previously known 5d6p levels is confirmed and their positions are refined. The 5d2, 5d6s, and 5d6p configurations are theoretically described by the method of orthogonal operators. These calculations are compared with the data obtained by a conventional method using the Cowan program. © 2000 MAIK “Nauka/Interperiodica”.

INTRODUCTION This paper is a part of our systematic study of ions of the platinum group, which are of great astrophysical interest. Within the framework of this program, we assigned the 5d2–5d6p resonance transitions in the PtIX ion [1]. The 5d6s–5d6p transitions were not studied because of the absence of the intense hot spectra at λ > 350 Å. EXPERIMENTAL The spectrum of platinum was detected in the 250– 1250-Å region with high-resolution VUV spectrographs. In the 350–1250-Å region, a 6.65-m normal incidence spectrograph with a 1200 l/mm diffraction grating and a reciprocal linear dispersion about of 1.25 Å/mm was used. In the 250–350 Å region, spectra were detected with a 3-m grazing incidence spectrograph with a 3600 l/mm holographic grating. The angle of incidence of radiation on a grating was 85° and a reciprocal linear dispersion was 0.40–0.45 Å/mm in the 250–350 Å region. The spectra were excited in a plasma by a threeelectrode low-inductance vacuum spark, the operating discharge voltage being 4.0–4.5 kV. The spark was fed from a low-inductance 10-µF capacitor, the discharge peak current was varied from 30 to 10 kA by introducing an additional 0.1–1.5-µH inductance to the discharge circuit. The anode of a source was an aluminum rod 4 mm in diameter with a 3-mm chemically pure (0.9999) platinum wire pressed into it. A flat graphite washer was used as a cathode. To select spectral lines in accordance with their ionization multiplicity, we also detected “cooler” spectra (the electric potential difference 1 kV) of the slipping spark with the peak discharge current varying from 1 to 3 kA.

The spectra were photographed on an Ilford Q2 plate. To obtain normal darkening in spectral lines, the exposure by 500 pulses of the vacuum spark was required. The actual resolution of the spectrograms mainly determined by the Doppler broadening of the lines in a plasma discharge was 0.015–0.050 Å in the 250–1250 Å region. The spectrograms were scanned with an automated ISAN microdensitometer [2] with a step of 1 µm and were processed by means of an automated system for spectrogram processing [3]. The procedure included: (i) The transformation of the darkening density to the incident-radiation intensity, taking into account the characteristic curve of the photographic emulsion; (ii) the estimate of the background by a spline; (iii) the automated search for spectral lines, including the correction, determination of their coordinates and profile parameters; and (iv) the calculation of the wavelengths of the detected lines by the inter- and extrapolation of the wavelengths of the known lines observed in the spectrum (wavelength references). As the latter, the lines of impurity oxygen ions were used, as well as the lines of the additionally photographed spectra of copper ions (in the 350–600 Å region) and titanium (in the 250–350 Å region) [4]. The accuracy of the wavelength measurements was 0.003 Å below 350 Å and 0.005 Å above 350 Å. The preliminary analysis of the spectra showed that the 5d2–5d6p lines of PtIX assigned earlier [1] are the most intense for the discharge current of the vacuum spark in the range from 20 to 30 kA; they substantially decrease at 10 kA and completely disappear in the spectra of the slipping spark. The lines exhibiting a similar behavior could be assigned to the unstudied part of the spectrum of the PtIX ion. The calculations were performed using both the Cowan program [5] and the program based on the method of orthogonal operators, which allows one to introduce and vary the parameters describing many-

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Table 1. The (5d2 + 5d6s)–5d6p spectral lines of the PtIX ion assigned in the paper gA × 107, s–1 237 297 28 33 295 723 1493 1957 1932 515 1093 3975 5528 1571 2227 1159 1682 196 199 234 986 872 549 554 605 563 329 Note:

a

λ, Å

ν, cm–1

25 144 30 65 197 275 588 794 700 192 456 1313

327.777 351.503 359.123 412.833 655.592 705.129 718.828 719.101 729.051 731.438 732.464 736.320

305085.6 284492.7 278456.0 242228.8 152533.9 141818.0 139115.3 139062.5 137164.6 136717.0 136525.5 135810.5

637 606 552 536 125 134 244 485 243 231 242 221 324 774

751.022 761.261 764.800 764.969 834.731 848.569 971.945 981.958 994.309 995.136 1018.405 1041.273 1043.913 1055.171

133151.9 131361.0 130753.2 130724.2 119799.1 117845.4 102886.5 101837.3 100572.3 100488.7 98192.8 96036.3 95793.4 94771.4

I

∆, cm–1 Even level 5d6p level Eeven , cm–1 E(5d6p), cm–1 N1 –1.7 –1.7 –1.8 0.0 0.6 0.0 –0.3 –4.2 1.3 –0.4 –0.1 1.1 –0.4 0.2 –1.1 –0.3 –0.2 –2.6 0.3 –0.2 –0.1 0.1 0.3 0.9 0.0 –0.2 0.3

5d23P2 5d21D2 5d21S0 5d21S0 5d6s 3D2 5d6s 3D1 5d6s 3D1 5d6s 1D2 5d6s 3D3 5d6s 3D2 5d6s 3D3 5d6s 3D2 5d6s 3D3 5d6s 3D1 5d6s 1D2 5d6s 3D2 5d6s 1D2 5d6s 3D3 5d6s 3D2 5d6s 3D1 5d6s 3D3 5d6s 3D3 5d6s 3D2 5d6s 3D1 5d6s 1D2 5d6s 3D2 5d6s 1D2

3D 3 3F 2 3P 1 3D 1 3P 2 3P 0 3P 1 1P 1 1F 3 3P 1 3P 2 3D 3 3F 4 1D 2 1F 3 1D 2 3P 2 3D 3 3F 3 3D 1 3F 3 3D 2 3D 1 3F 2 3F 3 3F 2 3D 2

44997 25575 72535 72535 214275 211877 211877 236084 230283 214275 230283 214275 230283 211877 236084 214275 236084 230283 214275 211877 230283 230283 214275 211877 236084 214275 236084

350085 310069 350993 314764 366809 353695 350993 375151 367446 350993 366809 350085 366094 345029 367446 345029 366809 350085 332120 314764 332120 330855 314764 310069 332120 310069 330855

5 8 3 3 7 5 5 5 6 7 6 7 6 5 5 7 5 6 7 5 6 6 7 5 5 7 5

N2 8 4 7 5 7 2 7 6 7 7 7 8 4 6 7 6 7 8 8 5 8 6 5 4 8 4 6

Commentsa

B1

B1

M

(B1) blended line; (M) masked line.

particle electrostatic and magnetic effects. This method has a better fitting stability than the Cowan program and permits the study of fine effects comparable with the accuracy of measurements of level positions (<1 cm−1). It was theoretically substantiated and developed in papers [6–14], where the physical meaning of the introduced parameters and the related effects are explained. This method was used, for example, in [10, 12] for parametric fitting of the 3dn and 3dn4s configurations of ions of the iron group (the III–VI ions), where it was shown, in particular, that the introduction of two-particle magnetic operators substantially improves the results. The many-particle electrostatic and magnetic effects should be even greater manifested in the 4d and 5d ions, which was already confirmed in a number of papers [14–17]. The preliminary calculation of positions of the energy levels in PtIX was based on the measurement of parameters of the 5d6s configu-

ration for known ions of the YbI sequence. The classification of the lines, the search and optimization of the configuration levels were performed by means of the IDEN program for identification of complex spectra [18, 19]. RESULTS AND DISCUSSION Table 1 lists twenty-two 5d6s–5d6p spectral lines and four new lines corresponding to transitions to the ground state. The number of the transitions between the first two excited configurations in PtIX agrees with that observed in ions of the isoelectronic sequence: in ReVI [20], OsVII, and IrVIII [21], 24, 23, and 20 spectral lines were observed, respectively. Table 1 presents the calculated transition probability gA, the spectral line intensity I, the wavelength λ, the wave number ν and its deviation ∆ from the calculated value, the level parity, OPTICS AND SPECTROSCOPY

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Table 2. Energy levels of the 5d2, 5d6s, and 6s2 configurations of the PtIX ion Eexp , cm–1 J=0 – 72535 18617 J=1 211877b 28517 J=2 236084b 214275b 44997 25575 0 J=3 230283b 15253 J=4 41618 25362

Etheor , cm–1

∆c, cm–1

∆cc, cm–1

N

437244.3 72531.6 18642.9

– 3.4 –25.9

– –8.7 64.4

– 3 3

100% 6s21S 88% 5d21S + 12% 5d23P 88% 5d23P + 12% 5d21S

211877.0 28491.0

0.0 26.0

67.5 –62.4

5 5

100% 5d6s 3D 100% 5d23P

236084.0 214275.0 44994.5 25586.3 –27.1

0.0 0.0 2.5 –11.3 27.1

20.4 –70.9 23.5 –12.5 –33.8

5 7 5 8 8

77% 5d6s 1D + 23% 5d6s 3D 77% 5d6s 3D + 23% 5d6s 1D 53% 5d23P + 43% 5d2 1D + 3% 5d23F 43% 5d21D + 45% 5d23P + 12% 5d23F 85% 5d23F + 14% 5d21D + 1% 5d23P

230283.0 15272.5

0.0 –19.5

–17.1 2.0

6 7

100% 5d6s 3D 100% 5d2 3F

41616.7 25365.5

1.3 –3.5

–14.8 42.2

4 4

73% 5d2 1G + 27% 5d23F 73% 5d23F + 27% 5d21G

Composition of the wave functionsa

Note: a the level title corresponds to the first component; b new levels; c ∆ = Eexp – Etheor : calculations with orthogonal parameters, ∆c = Eexp – Etheor/Cowan : calculations by the Cowan program.

Table 3. Energy levels of the 5d6p configuration of the PtIX ion Eexp , cm–1 J=0 353695 J=1 375151 350993 314764 J=2 366809 345029 330855 310069 J=3 367446 350085 332120 J=4 366094

Etheor, cm–1

∆b, cm–1

∆cb, cm–1

353661.1

33.9

21.1

2

100% 3P

375144.8 351040.9 314757.4

6.2 –47.9 6.6

–47.3 –69.4 372.2

6 7 5

66% 1P + 28% 3P + 6% 3D 61% 3P + 28% 3D + 12% 1P 66% 3D + 22% 1P + 12% 3P

366822.5 345005.5 330856.2 310078.4

–13.5 23.5 –1.2 –9.4

26.9 41.9 –141.8 –355.3

7 6 6 4

60% 3P + 30% 1D + 8% 3D 28% 1D + 41% 3D + 25% 3F 48% 3D + 33% 3P + 17% 1D 70% 3F + 25% 1D + 4% 3D

367443.8 350091.7 332114.6

2.2 –6.7 5.4

–189.4 –0.7 137.0

7 8 8

51% 1F + 49% 3D + 1% 3F 25% 3D + 43% 3F + 31% 1F 56% 3F + 26% 3D + 18% 1F

366093.2

0.8

204.8

4

100% 3F

N

Composition of the wave functionsa

Note: a the level title corresponds to the first component; b ∆ = Eexp – Etheor : calculations with orthogonal parameters, ∆c = Eexp – Etheor/Cowan : calculations by the Cowan program. OPTICS AND SPECTROSCOPY

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Table 4. Parameters of the theoretical description of the 5d2, 5d6s, and 6s2 configurations of the PtIX ion. Calculations by means of the Cowan program Parameter

Semiempirical (se) valuea, cm–1

Hartree-Fock (HF), cm–1

se/HF

29133.4 84008.5 57155.3

0.9465 0.855 0.861

Table 5. Parameters of the theoretical description of the 5d2, 5d6s, and 6s2 configurations of the PtIX ion. Calculations by means of the orthogonal operators Parameter

5d2 Eav F2(dd) F4(dd) α β ζd 5d6s Eav ζd G2(ds) 6s2 Eav R2(dd, ds) R2(dd, ss) Sigma

27574.6(28) 71825.0(326) 49201.8(455) 29.1(8) –550.2(158) 7151.5(22) 224905.1(38) 7396.2(34) 20012.7(324) 437000.0 –22658.7 21262.6 75

7254.2 230892.1 7487.3 23869.3 451654.7 –27299.6 25617.6

0.9858

HartreeSemiempirical (se) Fock (HF), a, cm–1 value cm–1

5d2 Eav

27575.2(11.3)

29133.4

0.9465

O2

8090.5(20.1)

9468.7

0.8545

O '2

5237.8(13.3)

6309.1

0.8302

Eα

102.3(15.9)

Eβ

123.5(18.2) 7254.2

0.9891

0.9781b

ζd

0.9878 0.838

Ac

29.0

A3

5.4

A4

8.3

A5

8.3

A6

11.6

A1

–3.1

A2

3.4

0.969b 0.83 0.83

Note: a Errors of the varied fitting parameters are presented in parentheses; b the ratio [Eav , se – Eav, se(5d2)]/[Eav, HF – Eav, HF(5d2)] is presented.

the level energy, and the numbers N1 and N2 of transitions from which the even and odd levels were determined and averaged. Note a good agreement between the calculated transition probabilities and the observed spectral line intensities. It is interesting that the wave numbers of the two most intense 5d6s 3D2–5d6p 3D3 and 5d6s 3D3–5d6p 3F4 transitions are so close that the corresponding spectral lines are unresolved. The following proves that this is not due to the incorrect assignment. First, there is no a second intense PtIX line in the vicinity. Although, this line can be masked by a strong line of another platinum ion. Second, the calculated wave numbers of the two transitions are specified by four levels determined from several transitions (see the corresponding numbers N1 and N2); i.e., they are quite reliable. Third, the distances between the corresponding spectral lines for ions from ReVI to PtIX yield a monotonic sequence 210.7, 118.7, 50.3, 0.0 cm–1, which confirms the identification. The assignment and averaging of the known levels over the wave numbers of the observed transitions gave the energies of all four levels of the 5d6s configuration. We confirmed the assignment of the levels of the 5d2 and 5d6p configurations and refined their energies. Tables 2 and 3 present the experimental and calculated energy levels of the 5d2, 5d6s, and 5d6p configurations (columns 1 and 2), as well as deviations of the experimental values from those calculated with the orthogo-

se/HF

7175.0(8.7)

5d6s 0.9780b

Eav

224896.6(15.4)

230892.1

Cds

3422.5(25.6)

4134.3

0.8278

ζd

7417.4(14.8)

7487.3

0.9907

Amso

55.0(16.0)

6s2 Eav

437000.0

451654.7

0.969b

R2(dd, ds)

–22658.7

–27299.6

0.83

R2(dd, ss)

21262.6

25617.6

0.83

Sigma

30

a Errors of the varied fitting parameters are presented in parentheses. b The ratio [E 2 2 av, se – Eav, se(5d )]/[Eav, HF – Eav, HF(5d )] is presented.

nal parameters, taking into account the magnetic interaction (∆), and with parameters used in the Cowan program (∆c). In addition, the number N of transitions specifying the level and the composition of the wave functions are given. The new levels in the first column are denoted by the superscript b, their titles correspond to the first component of the wave-function composition. One can see from tables that calculations with the orthogonal operators and the introduction of new parameters significantly improves fitting. For the 5d2 configuration, the rms deviation of the experimental level energies from the calculated ones decreases from 37 to 17 cm–1; for the 5d6s configuration, it decreases from 51 cm–1 to zero; and for the 5d6p configuration, it decreases from 181 to 19 cm–1, i.e., almost ten times. A OPTICS AND SPECTROSCOPY

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Table 6. Parameters of the theoretical description of the 5d6p configuration of the PtIX ion. Calculations by means of the Cowan program Parameter

Semiempirical (se) valuea, cm–1

Hartree-Fock (HF), cm–1

se/HF 0.9893b

348041.9(79)

353077.3

ζd

7480.0(64)

7539.7

0.992

ζp

Eav

23683.9(120)

22121.6

1.071

2(dp)

33769.4(940)

41971.6

0.805

G1(dp)

10960.4(433)

14392.1

0.762

3(dp)

8137.6(931)

13728.6

0.593

F

G

Sigma

255

Note: a Errors of the varied fitting parameters are presented in parentheses; b the ratio [Eav, se – Eav, se(5d2)]/[Eav, HF – Eav, HF(5d2)] is presented.

similar improvement in calculations is observed for other ions of the isoelectronic sequence of YbI. At present, this sequence has been systematically studied up to HgXI. The results of this study will be published in the near future. Consider in more detail the parametric description of the configurations under study. One can see from Table 4 that the 5d2 configuration is calculated by varying six parameters, Eav, F2(dd), F4(dd), α, β, and ζd, in the Cowan program. It was shown in [7–9] that such a set of parameters is not complete for the d2 configuration. The calculations show that the deviation of the calculated 5d2 levels from the experimental ones continuously changes along the isoelectronic sequence, suggesting the presence of the neglected effect. To describe the two-particle magnetic interaction in a system with two and more d electrons (holes) (the dd effect), the parameters Ac and A0–A6 are introduced [7]. It is clear that in this case we cannot vary the additional eight parameters because of a small number of the d2 levels (only nine). However, we can estimate these parameters using the data for neighboring, more complex ions, which we are now studying or already have studied. These estimates are presented in Table 5. By using the program with the orthogonal operators, we varied six parameters, Eav, O2, O '2 , Eα, Eβ, and ζd, which represent an orthogonal analog of the six generally accepted parameters presented above (see the relationships in [15]), the magnetic parameters Ac and A0–A6 being fixed. This resulted in the above-mentioned fitting improvement. We hope that the refinement of these parameters further decreases the deviation of the calculated levels from the experimental ones. The ds configuration containing four levels is usually described by three parameters, Eav, G2(ds), and ζd (Table 4). This set is also incomplete, which is demonstrated by a great regular deviation of the calculated 5d6s levels from the experimental ones along the isoelectronic sequence (up OPTICS AND SPECTROSCOPY

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to 71 cm–1 in PtIX). It is obvious that some effect was not taken into account. The two-particle magnetic interaction in the dns system was described by introducing the parameter Amso [11], which eliminates the discrepancy for the 5d6s levels. The study of the isoelectronic sequence showed a very regular behavior of the parameter Amso. Note that in the cases of both orthogonal and Table 7. Parameters of the theoretical description of the 5d6p configuration of the PtIX ion. Calculations by means of the orthogonal operators Parameter Eav C1(dp) C2(dp) C3(dp) S1(dp) S2(dp) ζd ζp Sd. Lp Sp. Ld Zp2pp' Zp2dd' Zp1pp' Zp1dd' Zp3pp' Zp3dd' Sigma

Semiempirical (se) Hartree-Fock valuea, cm–1 (HF), cm–1 348044.9(10.4) 4126.4(22.6) 2685.2(23.0) 1541.3(16.2) 2.4(16.4) –48.3(29.9) 7509.3(8.6) 23647.3(17.6) –130 –30 –60 60 160 0 70 0 33

se/HF

353077.3 4853.9 3696.6 1758.7

0.9893b 0.8501 0.7264 0.8763

7539.7 22121.6

0.9960 1.0690

Note: a Errors of the varied fitting parameters are presented in parentheses; b the ratio [Eav, se – Eav, se(5d2)]/[Eav, HF – Eav, HF(5d2)] is presented.

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AZAROV, CHURILOV

nonorthogonal parameters, the calculations were preformed taking explicitly the interaction of three configurations, 5d2, 5d6s, and 6s2. The average energy of the 6s2 configuration and the interaction parameters were fixed during fitting and equal to the corresponding values estimated for the neighboring ions. An analogous procedure was applied to the 5d6p configuration. The generally accepted six parameters Eav, ζd, ζp, F2(dp), G1(dp), and G2(dp) were replaced by the orthogonal set Eav, ζd, ζp, C1(dp), C2(dp), and C3(dp), and two variable parameters S1(dp) and S2(dp) and eight parameters Sd.Lp, Sp.Ld (spin–other orbit), Zp2pp', …, Zp3dd' (spin-orbit interaction of the dp pair) were introduced, which were estimated for the neighboring ions and were fixed during the fitting (Tables 6 and 7). One can see from Table 3 that the fitting was drastically improved. We performed the oneconfiguration calculations, because in this case the level calculations in the isoelectronic sequence based on the Cowan program gave rather large but regular deviations from the experiment (up to 580 cm–1 in OsVII and IrVIII). On the other hand, the use of other excited configurations in the calculations resulted only in a slight improvement of the fitting. This suggests that the main reason for the deviation of the calculated levels from the experimental ones is the neglect of the effects inside the configuration, similarly to the situation for even configurations. Note also that the calculation with the orthogonal set of parameters results in substantially lower errors (the values in parentheses in Tables 4–7), which shows that in this case the fitting procedure is more stable, ACKNOWLEDGMENTS The authors thank P. H. M. Uylings for placing at our disposal his programs for calculations. This work was partially supported by the Russian Foundation for Basic Research. REFERENCES 1. R. R. Kildiyarova, Y. N. Joshi, S. S. Churilov, et al., Phys. Scr. 55, 438 (1997).

2. V. I. Azarov, Preprint, ISAN (Institute of Spectroscopy, Russian Academy of Sciences, Troitsk) (1987). 3. V. I. Azarov, Preprint, ISAN (Institute of Spectroscopy, Russian Academy of Sciences, Troitsk) (1991). 4. R. L. Kelly, J. Phys. Chem. Ref. Data 16, Suppl. No. 1, 1 (1987). 5. R. D. Cowan, The Theory of Atomic Structure and Spectra (Univ. of California Press, Berkely, 1981). 6. B. R. Judd, J. E. Hansen, and A. J. J. Raassen, J. Phys. B: At., Mol. Opt. Phys. 15, 1457 (1982). 7. J. E. Hansen and B. R. Judd, J. Phys. B: At., Mol. Opt. Phys. 18, 2327 (1985). 8. B. R. Judd and R. C. Leavitt, J. Phys. B: At., Mol. Opt. Phys. 19, 485 (1986). 9. J. E. Hansen, P. H. M. Uylings, and A. J. J. Raassen, Phys. Scr. 37, 664 (1988). 10. J. E. Hansen, A. J. J. Raassen, P. H. M. Uylings, et al., Nucl. Instrum. Methods Phys. Res., Sect. B 31, 134 (1988). 11. P. H. M. Uylings, G. J. van het Hof, and A. J. J. Raassen, J. Phys. B: At., Mol. Opt. Phys. 22, L1 (1989). 12. G. J. van het Hof, A. J. J. Raassen, and P. H. M. Uylings, Phys. Scr. 44, 343 (1991). 13. P. H. M. Uylings, A. J. J. Raassen, and J.-F. Wyart, J. Phys. B: At., Mol. Opt. Phys. 26, 4683 (1993). 14. J.-F. Wyart, A. J. J. Raassen, P. H. M. Uylings, et al., Phys. Scr. 47, 59 (1993). 15. A. J. J. Raassen, V. I. Azarov, P. H. M. Uylings, et al., Phys. Scr. 54, 56 (1996). 16. V. I. Azarov, A. J. J. Raassen, Y. N. Joshi, et al., Phys. Scr. 56, 325 (1997). 17. A. N. Ryabtsev, A. J. J. Raassen, L. Tchang-Brillet, et al., Phys. Scr. 57, 82 (1998). 18. V. I. Azarov, Phys. Scr. 44, 528 (1991). 19. V. I. Azarov, Phys. Scr. 48, 656 (1993). 20. J. Sugar, J.-F. Wyart, G. J. van het Hof, et al., J. Opt. Soc. Am. B: Opt. Phys. 11, 2327 (1994). 21. G. J. van het Hof, Y. N. Joshi, J.-F. Wyart, et al., J. Res. Natl. Inst. Std. Technol. 100, 687 (1995).

Translated by M. Sapozhnikov

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