1074 J. Opt. Soc. Am./Vol. 73, No. 8/August 1983 JOSA Letters

Intensity ratios of multipole lines of Bi II

Jerry Kwela and Stanislaw Zachara*

Institute of Physics, University of Gdansk, 80-952 Gdansk, Poland

Malcom Hults

Department of Physics and Astronomy, Ball State University, Muncie, Indiana 47306

Received May 20, 1982; revised manuscript received April 11, 1983 The intensity ratios of the multipole lines corresponding to transitions between levels of the 6s26p2 ground elec­tronic configuration of Bi II have been measured. Two ratios were found to be I 368.3/I 324.1 = 0.17 ± 0.03 and I 591.3/ I 485.0

= 0.65 ± 0.13. These values are compared with the theoretical predictions and other experimental results. The ratios found are used to calculate the value of the radial integral s2 = e ∫ ∞

0 Pnl(r)r2Pn'i'(r)dr, which is found to be 8.5 ± 0.8[ea0

2].

1. INTRODUCTION Multipole transitions, permitted for second-order radiation, occur between levels of the same parity. These transitions can be magnetic-dipole (Ml), electric-quadrupole (E2), or of mixed type, i.e., permitted for both M l and E2 types of ra­diation. It is not difficult to calculate the transition proba­bilities of the Ml-type lines. The difficulties appear when the E2 transition probabilities are calculated because of the estimation of the value of the radial integral s2 = e∫∞

0 ∫∞

0 -Pn l(r)r2Pn ' l '(r)dr. Since the radial parts of the wave functions of heavy elements are not well known, it is difficult to calculate the s2 value theoretically. Therefore there have been several experimental methods developed1 by which the s2 value can be obtained. The simplest one is based on the relative intensity measurements of multipole lines originating from a common upper level.

The semiempirical value of the square of the radial integral s22(nl, n'l') for mixed multipole lines λγJ,γ'j' and λγJ,γ″J″ from the common upper level γJ is expressed by the for­mula

where AM1 is a theoretically calculated value for the sponta­neous transition probability of the magnetic-dipole fraction and C E 2 is a numerical coefficient that, multiplied by the s2

value, gives the A E 2 transition probability for the electric-quadrupole fraction; the γ's denote the sets of the quantum numbers nLS. In order to obtain the S2

2 value, we must first experimentally determine the intensity ratio IγJ,γ″J″/IγJ,γ′J′ for the lines under consideration. In the case when the rela­tive intensities of the pure magnetic-dipole and electric-quadrupole lines are determined, the formula simplifies to

0030-3941/83/081074-03$01.00 © 1983 Optical Society of America

Since, in general, the intensity of multipole lines increases and the difference between the intensities of the magnetic-dipole and electric-quadrupole lines decreases with increasing atomic number Z, such a semiempirical value of s2 is obtained more accurately for heavy elements than for the light ones. A fa­vorable case for determination of the s2 value from such a ratio of intensities is the 6s26p2 ground configuration of ionized bismuth, Bi II. In this case, two mixed multipole lines, i.e., 591.3 and 485.0 nm, originating from the common upper level 1D2, and also two lines starting from the common 1S0 level, which are of pure M l and E2 character, i.e., 324.1 and 368.3 nm, are observed. These multipole lines were first obtained by Cole and Mrozowski and investigated in detail by Cole.2

The intensity ratio of the pure magnetic-dipole line to the pure electric-quadrupole line, I 324.1/I 368.3, was determined some­time later by Kolyniak et al.3 using a photoelectric detection technique.

In this work we have measured, using a photographic technique, the intensity ratio of the mixed multipole lines 591.3 and 485.0 nm as well as the ratio of the pure magnetic-dipole and electric-quadrupole lines 324.1 and 368.3 nm, re­spectively.

2. EXPERIMENT

The apparatus used for the excitation of the forbidden lines of Bi II was essentially similar to that used by Hults and Mrozowski.4 A quartz tube with outside electrodes was connected to the pumping system and to a bulb reservoir containing a piece of metal. The metal was distilled several times under high vacuum before the final distillation into the bulb reservoir. This reservoir was connected at the side to the main discharge tube, the tube and the reservoir being surrounded by separate furnaces. The temperature of the discharge tube was held at 600°C, which was 50°C above that

JOSA Letters Vol. 73, No. 8/August 1983/J. Opt. Soc. Am. 1075

of the bulb reservoir to prevent condensation of the metal anywhere in the discharge tube. A U trap between the dis­charge tube and the diffusion pump was kept immersed in liquid nitrogen in order to prevent the vacuum grease and oil vapors from entering the discharge tube. The optimum conditions for excitation of the forbidden lines of Bi II were the same as those described by Cole.2 The discharge was excited by a 100-MHz rf oscillator. The light was observed along the main axis of the tube. The pressure of the helium buffer gas was about 15 Torr. The spectra were taken with a PGS-2 grating spectrograph on Kodak 103-F plates. The exposure time was 2 h. The experimental data were obtained from several microdensitometer scannings of each line from five different plates.

3. RESULTS A N D DISCUSSION

In order to compare experimentally obtained s2 values with theoretical ones, it is necessary to know the intermediate coupling wave functions. The procedure for developing in­termediate coupling wave functions for the ground configu­rations of Bi II is as follows:

Figure 1 shows the level scheme of the ground configuration of Bi II with the transitions of interest. It is possible to fit the observed energies by eigenvalues of the fine structure Ham-iltonian. The matrix elements of this Hamiltonian can be expressed as a linear combination of five parameters: F 0 , F2 , ξp, α, and Q(2). Parameters F0 and F 2 are the Slater integrals, and ξp is the spin-orbit interaction constant. Parameter α is connected with the two-electron effective electrostatic in­teractions between np2 and distant configurations. Param­eter Q(2) is responsible for the electrostatically correlated spin-orbit interactions. The two last parameters α and Q(2)

come out if the second-order perturbation theory is used for description of the np2 configuration.

Fig. 1. Energy levels of the 6p2 ground configuration of Bi II. Wavelengths of the corresponding transitions are given in nanome­ters.

Table 1. Coefficients in Intermediate Coupling Wave Functions for 6p2 Electron Configuration of Bi II

All the five fine-structure parameters for the ground con­figuration of Bi II were calculated by Arcimowicz and Dembczynski,5 and values of these parameters in inverse centimeters are as follows: F0 = 25 568, F2 = 1139, ξP = 12 001, α = -215 , and Q(2) = 1371. The energy levels ob­tained by using these values agree exactly with the experi­mental data given in Ref. 3. This is a consequence of the fact that the number of energy levels is equal to the number of free parameters.

In terms of LS-coupled states, the eigenvectors of the fine structure Hamiltonian of the np2 configuration are given by

Values of the expansion coefficients a,b,c, and d obtained by us are given in Table 1. In Table 1, Garstang's6 data are given for comparison. Garstang's calculations were based on experimental values of the energy levels taken from Moore's National Bureau of Standards tables.7 Our values were ob­tained by using the data for the energy levels given in Ref. 3. Differences between these two sets of the expansion coeffi­cients are significant. This is a consequence of the fact that our calculations are based on the five fine-structure parame­ters, whereas Garstang's calculations considered only the first-order perturbation theory parameters, F 0 F 2 , and ξp .

The a and b values were also determined by Arcimowicz and Dembczynski.5 Their values differ from ours. In our opinion the differences are due to their mistake in sign of the nondi-agonal matrix element +3P2|1D2, of the fine-structure Hamiltonian (Table 1 in Ref. 5). Data collected in our Table 1 suggest that the coupling of the angular momentum of the electrons in the 6s26p2 configuration of Bi II is close to the pure jj case.

The intensity ratios of the multipole lines of Bi II found by us are I591.3/I 485.0 = 0.65 ± 0.13 and I 368.3/I 324.1 = 0.17 ± 0.03. The transition probabilities of the multipole lines in question were calculated by Garstang.6 From his data, the calculated intensity ratios of the lines are 0.72 and 0.15, respectively. As was mentioned previously, Garstang's calculations are based on intermediate-coupling wave functions neglecting the effect of second-order perturbation theory. For the radial integral s2 of the 6s26p2 configuration, Garstang adopted the s2 value obtained by extrapolation of the theoretical results for the configurations 2p2 ,3p2 , and 4p2 assuming a linear dependence of the s2 parameter on the atomic number Z.

1076 J. Opt. Soc. Am./Vol. 73, No. 8/August 1983 JOSA Letters

Table 2. Theoretical and Semiempirical Values of the One-Particle Radial Integral s2 = e ∫∞

0 Pnlr2

× Pn'l' (r)dr for Neutral and Ionized Atoms of Bismuth

By taking Garstang's value of s2 and by using the interme­diate-coupling wave functions determined by us, we obtain the following ratios: I 591.3/I 485.0 = 0.69 and I 368.3/I 324.1 = 0.18. By comparing the two sets of intensity ratios with our exper­imental values, we can see that better agreement is obtained for our wave functions.

Using formulas (1) and (2) and the intensity ratios found experimentally by us, we have calculated a semiempirical value of the radial integral s2. Since it follows from the theory that, when the electric-quadrupole admixtures in mixed lines are small, the intensity ratios of mixed lines depend weakly on changes in the s2 values. This leads to some inaccuracy in estimations of the value of the radial integral determined from these ratios. For this reason the s2 value for the ground configuration of Bi II, as determined from the intensity ratio I 368.3/I 324.1, is considered more reliable. In this case the s2

value is given with an error of about 10% and is equal to 8.5 ± 0.8[ea0

2]. As was mentioned earlier, the latter intensity ratio was also

determined by Kolyniak et al.3 Their result was I 368.3/I 324.1

= 0.14 ± 0.6, which is slightly smaller than ours. By using the expansion coefficients for wave functions determined by us for the intermediate coupling and their value for the intensity ratio, one obtains the following value of the radial integral: s2

= 7.7 ± 0.3[ea02].

The values of s2 for the ground configurations of Bi I, Bi II, and Bi III as calculated directly from definition by using var­ious approximations and determined by different experi­mental methods are given in Table 2. All the semiempirical values for Bi I are obtained by using expansion coefficients for intermediate-coupling wave functions given in Ref. 8.

It would be interesting to find the experimental value of the s2 in the case of 6s26p configuration of Bi III to complete Table 2. This would give us better information about the depen­dence of the s2 value on the atomic number Z.

ACKNOWLEDGMENTS

The authors wish to express their appreciation to J. Heldt for his interest and advice during the investigation. This research was supported by the research project MR.I.5.1.05 and the Polish-U.S. exchange program under the Maria Sklodow-ska-Curie Fund (grant no. J-F7F012-P).

* Present address, Laboratory of Acoustics and Spectros­copy, University of Gdansk, 80-952 Gdansk, Poland.

REFERENCES

1. M. Hults, "Interference effect between magnetic-dipole and electric-quadrupole radiation in the atomic spectra of lead," J. Opt. Soc. Am. 56, 1298-1304 (1966).

2. C. D. Cole, "Multipole lines in the spectra of Bi II and Pb II," J. Opt. Soc. Am. 54, 859-863 (1964).

3. W. Kolyniak, T. Kornalewski, and K. Roszkowska, "Multiple lines in spectrum of Bi II," Acta Phys. Pol. A 49, 679-682 (1976).

4. M. Hults and S. Mrozowski, "Multipole lines in spectra of ele­ments from the fifth group," J. Opt. Soc. Am. 54, 855-858 (1964).

5. B. Arcimowicz and J. Dembczynski, "Relativistic effects in the hyperfme structure of the second spectrum of the Bi II ion," Acta Phys. Pol. A 56, 661-671 (1979).

6. R. H. Garstang, "Transition probabilities of forbidden lines," J. Res. Nat. Bur. Stand. Sect. A. 68, 61-73 (1964).

7. C. Moore, "Atomic energy levels," Nat. Bur. Stand. Circ. 3 (1958).

8. D. A. Landman and A. Lurio, "Hyperfine structure of the 6p3

configuration of Bi209," Phys. Rev. A 1, 1330-1338 (1970). 9. V. N. Novikov, O. P. Sushkov, and I. B. Kriplovich, "Faraday

effect and parity violation in Ml transitions in bismuth," Opt. Spektrosk. 43, 621-626 (1977).

10. C. E. Loving, D. Phil. Thesis (Oxford University, Oxford, 1978).

11. S. T. Dembinski, J. Heldt, and L. Wolniewicz, "Zeeman effect in the multipole line 4615 Å of Bi I," J. Opt. Soc. Am. 62, 555-561 (1972).

12. L. Augustyniak, J. Heldt, and J. Bronowski, "Zeeman effect of the 6476 Å mixed multipole line of bismuth," Phys. Scr. 12, 157-163 (1975).

13. G. J. Roberts, R. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, and D. N. Stacey, "The Faraday effect and magnetic circular dichroism in atomic bismuth," J. Phys. B 13, 1389-1402 (1980).

14. J. Kwela, A. Kowalski, and J. Heldt, "Determination of the value of the radial integral for electric-quadrupole transitions by measurement of the relative intensity of mixed multipole lines of Bi I," J. Opt. Soc. Am. 72, 1550-1552 (1982).