Systematic trends in atomic transition probabilities in neutral and singly-ionized zinc, cadmium and mercury

J. Quanf.

Sperrrosc.

Radior.

Transfer.

Vol.

13, pp. 369-376.

Pergamon

Press

1973. Printed

in Great

Britain

SYSTEMATIC TRENDS IN ATOMIC TRANSITION PROBABILITIES IN NEUTRAL AND SINGLY-IONIZED ZINC, CADMIUM AND MERCURY T. ANDERSEN and G. SORENSEN Institute of Physics, University of Aarhus, 8000 Aarhus C, Denmark (Received 29 August

1912)

Abstract-The beam-foil technique has been used to measure mean lives of excited levels in neutral and singly ionized zinc, cadmium, and mercury. In the neutral atoms, the lifetimes measured were in good agreement with those obtained by the Hanle-effect and phase-shift techniques, but discrepancies were found in some of the lifetimes measured by the delayed-coincidence method. For singly ionized zinc and cadmium, six mean lives have been measured, while seven were obtained in singly ionized mercury. For the ionized species, systematic trends show that some of the results recenily obtained by the phase-shift method may be in error. The mean lives reported were converted to f values for transitions for which reliable multiplet intensity ratios are available. The f value systematics show that for the same type of spectral transition, identical f values have been obtained within homologous atoms. 1. INTRODUCTION

THE BEAM-FOIL technique has proved to be a useful tool for systematic studies of atomic transition probabilities in a large variety of atoms and ions. Recently it has been shown that lifetimes consistent with those measured by other techniques may be obtained even for elements as heavy as thallium. (l) Foil-scattering processes and excessive energy loss in the foil are usually considered to be the major sources of systematic errors for heavy atoms. It has, however, been shown that the most serious errors in beam-foil lifetimes are caused by cascading from higher-lying levels and by difficulties with the proper performance of the energy-loss correction.“) Zinc, cadmium, and mercury are all elements with an appreciable vapour pressure at relatively low temperatures. Hence a large number of lifetimes of low-lying levels in the neutral atoms have been obtained with various techniques such as the phase-shift method, the Hanle-effect, and the delayed-coincidence techniques. Among the more recent lifetime experiments are the phase-shift measurements in Zn I, Zn II, and Cd I, Cd II by BAUMANN and SMITH,(~) and the delayed-coincidence measurements in zinc by OSHEROVICH et a1.,(4)and in mercury and cadmium by VEROLAINENand OSHEROVICH.(‘) The lifetimes of the 4p ‘P level in Zn I,‘6’ the 5p ‘P level in Cd I,“’ and the 6p ‘P level in Hg I (*) have been measured by applying the Hanle-effect method. Further, LANIEPCE”’ has measured the lifetimes of the 5d 3D levels in Cd I in a Hanle experiment. SCHAEFEX,(’ O) who used a modified Holzberlein invertron and delayed-coincidence technique, has reported 16 lifetimes in Cd I and 4 in Cd II. As to low-lying levels in Hg I, CAMHY-VAL(“) has used the delayed-coincidence technique to study the 7s 3Sl level. 369

370

T. ANDERSEN and G. SORENSEN

Beam-foil measurements have previously been performed to study the lowest-lying levels in Zn I, Cd I and Hg I in order to obtain information on the validity of lifetimes obtained by this technique. (I’) For the lowest-lying levels, where the contribution from cascading is appreciable, the accuracy of the beam-foil lifetimes is doubtlessly lower than obtained in, for example, a Hanle experiment. A comparative study of lifetimes obtained for selected levels in Cd I by the beam-foil technique and other methods has recently been published.‘i3’ The scope of the present investigation has been to measure atomic lifetimes in homologous atoms such as zinc, cadmium, and mercury in order to compare transition probabilities in atomic systems, which are much alike as far as the outer electrons are concerned. So far, identicalf values have been reported for homologous transitions in Al, Ga, In and Tl”’ and in ionized Ne, Ar, Kr and Xe.(‘) More experimental data are needed to investigate the f-value systematics present in homologous atoms. WIESE and WEIS have reported from theoretical calculations that for homologous atoms in the one-electron model, the line strength for the dominant transition array should be approximately the same for analogous spectral series as long as the coupling scheme does not change. 2. EXPERIMENTAL

TECHNIQUE

The 600-kV heavy-ion accelerator at the University of Aarhus was used in the present investigation. The beam-foil apparatus used has previously been described!i5’ For zinc and cadmium, the metals were directly evaporated into the ion-source volume from an electrically heated furnace immediately outside the ion source. To obtain a beam of mercury, the furnace was loaded with mercuric oxide which, in turn, was evaporated into the ionsource. Usually, ion currents of tenths of a microampere were passed through 5-pg/cm’, l-mm dia. carbon foils (Yissum Research Company, Israel). For zinc, the energy-loss in a 5-pg/cm2 carbon foil was estimated according to LINDHARD’S stopping theory.“@ However, the total energy loss for cadmium and mercury will be an overestimate using theoretical values, as already discussed by HVELPLUND. (l’) It has been observed experimentally that an appropriate value for the energy loss is measured in the forward direction of the scattering distribution, which exhibits a gaussian distribution.‘2’ The energy loss for a 300-keV mercury-ion beam in a 5-pg/cm2 carbon foil measured in the forward direction was 35 keV, whereas the theoretically estimated value was 82 keV. When evaluating the lifetimes, cascading components had to be subtracted. A variation of the initial ion energy facilitated this correction as discussed in detail in Ref. (2). 3. EXPERIMENTAL

RESULTS

(a) Zinc The measured lifetimes, belonging either to Zn I or Zn II, are listed in Table 1. The zinc resonance line at 2138 A (4s ‘S-Q ‘P) yielded a lifetime of 1.45 k 0.15 nsec, confirming LURIO’S level-crossing result@) (1.41 kO.04 ns) but slightly lower than the phase-shift result of BAUMANN and SMITH(~) (1.75 f0.2 nsec). As indicated in Table 1, the lifetime measurements were often based on more than a single transition. Within the experimental error, no difference in lifetime was observed for the three 4d 3D levels. The value reported in the present study is 25 percent lower than previously measured by OSHEROVICH et ~1.‘~’

Systematic trends in atomic transition probabilities

371

TABLE 1. ATOMICLIFETIMES OF ZINC

Spectrum

Level

ZnI

4p’P 5S3S 6s3S

Other lifetime measurements (10m9 set)

~(10~~ set)

1.45 7.6 13.0 6.7 11.2

+ + + + +

0.15 0.8 2.0 0.5 1.5

1.41 + 0.04’6’ 1.75 + 0.2”’ 11.8 ; 1.0’4’ 8.1:0.4*

5d3D

2138 4680,4722,48 11 3072 3345,3302,3280 2801

5s*s 4p2P 4dZD 6d*D 7d’D 4f’F

2501,2558 2063,2026 2103 3806,384O 3172, 3196 49 12,4924

2.0 3.0 2.3 9.1 12.0 6.6

+ * + f + +

0.2 0.3 0.2 0.8 1.5 0.6

3.85 f 0.7’3’ 3. t + 0.4’3’ 3’05 f 0.413’ 3.85 + 0.7@’

4d3D

Zn II

Transitions measured (A)

8.8 + 0.6’4’

For the 4p ‘P levels, the lifetimes obtained for the Zn II doublets are in excellent agreement with those of BAUMANN and SMITH.(3) For the 5s ‘S and 4d 2D levels, our values are significantly lower than those reported in Ref. (3). The transition at 2063 A used for the determination of the 4p 2P doublet was probably blended by a 2064-A transition from 4p ‘P-4d 2D, but nevertheless showed the same lifetime as the 2026-A line from the same doublet. (b) Cadmium The lifetimes measured for levels in Cd I and Cd II are listed in Table 2. For the sake of completeness, those reported previously’i3’ are included, where also a thorough discussion on the discrepancies between the beam-foil data on Cd I and the results obtained by SCHAEFER(“) is given. As shown in Table 2, the Hanle-effect measurements obtained by TABLE 2. ATOMIC LIFETIMESOF CADMIUM

Spectrum

Level

Transitions measured (A)

Cdl

5p’P 6s ‘S 7s ‘S 5d3D 6d “D 7d ‘D

2289 4800,5085 3133,308l 3612,3416,3404 2881 2764

Cd II

6s ‘S 5p 2P 5d ‘0 7d2D 8d2D 4f2F

2581.2748 2140.2263 2312 4084,4134 3418 5338.5380

~(10~~ set)

1.9 9.8 13.7 6.5 11.5 23

* + + + * +

0.15 0.8’r3’ 1.5”3’ 0.5”” 1.5”3’ 3

2.2 3.4 2.6 9.8 12.5 6.7

f 0.2 + 0.4 + 0.3 + 0.8 + 2.0 rf: 0.7

Other lifetime measurements (10e9 set) 2.1 + 0.3’3’ 1.66 + 0.05”’ 10.6 7 0.8t5’ 9.2 +-0.3@’ 18.5 + 2.0”” 14.6 + 1.2’5’ 6.8 + 0.3@’ 14.7 f 2.2”“’ 18.7 + 2.4”” 5.7 f 0.9”0’ 3.4 + - 0.7t3’4.8 + 1.ti3’ 11.7 * 0.5”0’

l Note added in proof: Recent Hanle-etTect result by G. CREMERand B. LNIEPCE, Compt. rend. 275, s&e B, 187 (1972).

T. ANDERSENand G. SORENSEN

312

LANIEPCE”) are in excellent agreement with the present study. Even though the difference is not significant, the lifetime of the 5d 3D3 level in the present study, as well as in Ref. (9), is slightly longer than the values obtained for the 5d 3D, and 5d 3D, levels. The lifetimes obtained in the present study are systematically shorter than those measured by the delayed-coincidence techniques reported in Refs. (5) and (10). For a number of levels in Cd II, SCHAEFER (lo) has attempted to measure the lifetimes, and it appears that the agreement with the present study for the 7d 2D level is within 20 percent, whereas the 6s 2S level disagrees by a factor of almost 3. Unfortunately, there is no overlap between the Cd II data reported in Refs. (3) and (lo), but it seems that the results obtained by the delayed-coincidence techniques depend too much on the experimental conditions.

(c) Mercury Mercury is one of the elements most frequently used in optical studies, and a number of Hg I lifetimes has appeared in the literature. Most of these are, however, too long for beam-foil studies. To give some indication as to the reliability of the published data, this study reports on a number of lifetimes ranging from 1.27 to 14 nsec, of which some have been measured previously by various techniques. The lifetimes measured by the beam-foil technique are shown in Table 3. For the 6p ‘P level in Hg I, the present value (1.27kO.10 nsec) is in excellent agreement with the Hanle-effect measurement of 1.31 f0.08 nsec by LURIO.@) As to the 7s 3S multiplet, MITCHELL and MARPHY(‘~) have reported a value of 8.0+ 1.0 nsec for the 4358-A and 4047-A transitions, whereas the 5460-A line yielded 6.0+ 1.0 nsec. The values of BRANNEN et al (lg) however, and those reported in Ref. (5), indicate a lifetime of the order of 10-l 1 nsec. In tte present study, where the measurements were based on the 4358-w, 4047-A, and 5461-A lines, a lifetime of 8.2kO.5 nsec was found in all three cases. This also confirms the value of 8.4kO.4 nsec recently obtained by CAMHY-VAL.(“) The 6d 3D3 level measured

TABLE 3. ATOMICLIFETIMES OF MERCURY

Spectrum

Level

Transitions measured

Other lifetime measurements (10m9 set)

~(10~~ set)

(A)

WitI

Hg II

6p ‘P IS 3s

1849 4358,4087,5461

8s ‘S 6d ‘D, 6d 3D, 6d 3D, Id ‘0

3341 3650 3125 2961 3021

IS 2s 9s *s 6p’P 6d ‘0 8d *D 9d ‘0 5fZF

2260,2847 4856 1649,1942 2225 3806 3608 5425,561l

1.27 f 0.10 8.2 f 0.5 14 + 1.5 1.4 f 0.5 6.2 & 0.6 14 * 3 1.9 f 10 f 1.9 f 2.2 + 8.5 f. 14.4 + 1.2 +

0.2 1.5 0.3 0.3 0.6 1.5 0.6

1.31 f 0.08”’ 8.0 + l.O”*’ 6.0 f 1.0”8’ 8.4 k 0.4’“’ 11.2 ;- 0.2’19’ 10.4 + 0.4’5’ 8

,0.6

(5)

Systematic trends in atomic transition probabilities

313

by VEROLAINEN and OSHEROVICH _ (5) (8+0.6 nsec) is in good agreement with our value of 7.4kO.5 nsec. For the 6d 3D levels, the present data indicate that the 6d 3D, level has a lifetime of 6.2 f0.6 nsec, whereas the 6d 3D, and 6d 3D3 yield 7.4 + 0.5 nsec. 4. EVALUATION OF TRANSITION PROBABILITIES The measurement of atomic lifetimes presents an accurate method for measuring atomic transition probabilities if intensity ratios within multiplets or branching ratios from the upper state are available from some other method. For the evaluation of systematic trends in homologous atoms, the atomic lifetimes must be converted intofvalues. This procedure can be rather uncertain due to lack of reliable data on the intensity ratios within multiplets and to branching from the upper state. In a recently published investigation on Ti II, thefvalues were found by a combination of lifetimes obtained by beam-foil spectroscopy and relative emission studies from a stabilized arc. (‘O)In the present study, no such detailed emission studies have been performed. For some of the spectral transitions used for lifetime measurements in the present study, an evaluation off values have been attempted. A number of investigations on intensity ratios of spectral lines in the second column of the periodic system have appeared in the literature. Thus, LES and NIEWODNICZA~~SKI”~) have performed measurements of intensity ratios for the sharp series of triplets in Zn I, Cd I and Hg I and summarized previous investigations. In a number of cases, discrepancies from the theoretically derived values based upon the sum rules were observed, and further, the intensity ratios were dependent on the excitation conditions in the light source. In the beam-foil light source, similar anomalies were found for intensity ratios of multiplets in Zn I, Cd I and Hg I. The multiplets showed a varying intensity ratio as a function of the ion energy.‘22’ For evaluation off values for the transitions np3P zlo-(n + 1)s 3S,, the branching ratios estimated theoretically from the sum rules were used because of lack of consistency between the experimental values. (21) For Zn I the theoretical and experimental intensity ratios were in agreement, but for Cd I and Hg I, larger discrepancies were found, particularly for Hg I due to the breaking down of the LS coupling. Thefvalues calculated from the present lifetimes are shown in Table 4. Concerning Hg I, thefvalues shown in brackets are based upon the theoretically estimated intensity ratio of 100: 143 :43 for the transitions 5461, 4358 and 4047 8. Intensity ratios based upon the L-S coupling are obviously not correct. To evaluate more appropriatefvalues it was assumed that the np 3P2-(n + 1)s 3S, transitions showed identicalfvalues for Zn I and Hg I. A similar feature had previously been observed for transitions in Ga I, In I, Tl I. (l) In Ref . (21) it was reported that the intensity ratio 435814047 in 6 independent measurements was 2.6kO.2, whereas the 546114358 ratio in the same measurements varied from 0.6 to 1.1. From these findings, thefvalues shown in Table IV were calculated. For the np3P-nd3D transitions in Zn I, Cd I and Hg I, three spectral lines were sufficiently intense for lifetime measurements. These were converted tofvalues for np 3P2nd 3D3,2,1, np 3P,-nd 3D2 1 and np 3Po-nd 3D,. For Zn I, the theoretical intensity ratio for the spectral lines 3345, 3303 and 3283 A on 100: 59 : 19 was utilized, in good agreement with the experimental results in Ref. (21). For the analogous transitions in Cd I, the intensity (5) of 119:71:24 was applied for the spectral lines ratio of VEROLAINEN and OSHEROVICH 36123416 and 3404 A.

374

T. ANDERSEN and

G. SRENSEN

For the doublets in Zn II and Cd II, the relative strengths of the doublet transitions calculated by BILAS-ZABAWA et ~1.‘~~’ were used. For the n 2P-(n+ 1) 2S, values of 1.89 for Zn II and 1.68 for Cd II were applied, whereas the LS value of 2 was used for the other doublets listed in Table 4, in good agreement with Ref. (23). Only f values for low-lying transitions, where no branching occurs from the upper-state, have been listed in Table 4.

TABLE

Spectrum

Spectral

4. f

VALUES

transition

EVALUATED

FROM LIFETIME

Wavelength

f value

MEASUREMENTS

Other

results

(A)

Znl

4p 3P,-5s

3s,

4810 4122 4680 5086 4358 4678

0.146 0.153 0.153 0.117 0.132 0.105

6p 3P,-7s ‘S,

5461

6p ‘PI-Is

3S,

4358

6p 3Po-ls 3S,

4047

(0.126) 0.146 (0.162) 0.138 (0.189) 0.137

Zn 1

4p ‘P,-4d ‘D,,, 4p 3P,-4d ‘D,, 4p 3PoAd 3D,

3345 3303 3282

0.42 0.39 0.42

Cd 1

5p 3P,-5d 5p3P,-5d 5p 3P,-5d

3612 3416 3404

0.51 0.46 0.45

Zn II

4P 2p3,,r5s 4P 2P,,,p5s

2558 2508

0.16 0.16

*S,,,

2749 2515

0.16 0.17

Zn II

4s 2S,,2-4P 2p3,2 4s %,,-4 zP,,*

2026 2062

0.41 0.21

Cd 11

5s 2S,,,p5P 2P3,2 5s 2S,,2p5P 2P,,,

2140 2263

0.39 0.23

4p 3P,-5s 3&s, Cd I

Hgl

Cd 11

4p 5p 5p 5p

3P,-5s 3.9, ‘i=-6s 3S, 3P,-6s3S, 3P,-6s 3S,

5~ 2P3,,-6s 5~ ‘P,,,-6s

3D,,3 ‘D,, 3D, 2s,,,

2S,,, ‘S,,,

0.12’26’ 0.121’25’ 0.125@’ 0.12’26’ 0.114’25’ 0.14’9’ 0.12’26’0.111’25)0.16(9’ 0.14’26’ 0.11’26’ 0. 10’26’

DISCUSSION

In the present study, systematic trends in atomic transition probabilities have been investigated. For the singlet transitions ns ‘S-np ‘P in Zn I, Cd I and Hg I, good agreement was found with the more accurate results previously published, as shown in Tables l-3. Thus the reported results for other transitions in these elements may be considered accurate with an uncertainty on the lifetimes of usually 10 percent. For transitions in Zn I, it appears that the delayed-coincidence techniques reported in Ref. (4) yield too long lifetimes. While the phase-shift value of Baumann and Smith (1.75kO.2 nsec)(3) is in agreement with the theoretically estimated value of 1.94 nsec by GARSTANG (24) the present value is more in agreement with the Hanle-effect value.@)

Systematic trends in atomic transition probabilities

315

For Cd I the agreement for the 5p ‘P and 6s 3S levels with previous measurements seems satisfactory (Table 2). ZILITIS (25) has used a semi-empirical calculation to obtain fvalues for Cd I and as shown in Table 4, a reasonable agreement is found with the present experimental results. Also GRUZDEV 06) has calculated f values for lines involving the transitions from the 3S 1 levels in Zn I, Cd I and Hg I, and the results are included in Table 4. Thefvalues reported by LANIEPCE (9) for transitions from the 5d 3D32, levels are in excellent agreement with the present results, whereas discrepancies are found for the transitions depopulating the 6s 3S, level presumably due to deviations in the applied intensity ratios. For the 6p ‘P in Hg I, the agreement with the value reported by LURIO@) is excellent. This certainly demonstrates that the foil-excitation technique may be used also for heavy elements. The present value for the 7s 3S level in Hg I supports both the old value of MITCHELL and MARPHY(‘~) and the recently published result of CAMHY-VAL.(“) When searching forf-value systematics for transitions in Zn I, Cd I and Hg I (Table 4), the present values for np 3P 21o-ns 3S, for Zn I and Hg I, and the values of LANIEPCE’~) for Cd I fit in with the systematics which yields identicalfvalues also found for Ga I, In I and Tl I.“’ For np 3P-nd 3D transitions, a small increase infvalues is observed from Zn I to Cd I. For a further study of this trend, more accurate intensity ratios are needed. For the doublet transitions in Zn II and Cd II listed in Table 4, it appears that within 5 percent, transitions in homologous atoms show identicalfvalues. This trend can certainly be used to evaluate f values in Hg II, for which intensity ratio within the doublets are unknown. From the present study, it appears that the main difficulty in obtaining very accurate fvalues is the lack of knowledge of intensity ratios. When applying systematics such as discussed above, rather precise values of intensity ratios independent of the excitation conditions in the light source may be evaluated in principle, and thus new information on the coupling schemes obtained. The present study has shown that a large number of atomic lifetimes in zinc, cadmium, and mercury may be measured by the beam-foil method. But in order to use these lifetimes for detailed studies of atomic transition probabilities, more accurate results are needed regarding the intensity ratios within multiplets and the branching ratios of spectral lines depopulating the same upper level.

REFERENCES

I. T. ANDERSENand G. SORENSEN,Phys. Rev. A 5,2447 (1972). 2. T. ANDERSEN.0. H. MADSENand G. SORENSEN,Physica Scripta, in press. 3. S. R. BAUMANNand W. H. SMITH,J. opt. Sot. Am. 60, 345 (1970). 4. A. L. OSHEROVICH, G. P. ANISIMOVA, M. L. BURSHTEIN,YA. F. VEROLAINEN, J. SZIGETIand E. A. LEDOVSKOYA, Opt. Spektrosk. 30,429 (1971). 5. YA. F. VEROLAINEN and A. L. OSHEROVICH, Opt. Spektrosk. 20, 517 (1966). 6. A. LURIO, Phys. Rev. 134, All98 (1964). 7. A. LURIOand R. NOVICK,Phys. Rev. 134, A608 (1964). 8. A. LURIO, Phys. Rev. 140, A1505 (1965). 9. B. LANIEPCE,J. Physique 31,439 (1970). 10. A. R. SCHAEFER,JQSRTll, 197 (1971). 11. C. CAMHY-VAL,Phys. Left. 32A, 233 (1970). 12. T. ANDERSEN,K. A. JIZ.SSEN and G. SBRENSEN,Nucl. Instr. Meth. 90, 35 (1971). 13. T. ANDERSEN,L. MQLHAVEand G. SBRENSEN,Astrophys. J. (in press).

376

T. ANDERSENand G. SQRENSEN

14. W. L. WISE and A. W. WEISS, Phys. Rev. 175,50 (1968). 15. T. ANDERSEN.K. A. JENSENand G. SORENSEN, J. out. Sot. Am. 59. 1197 (1969). 16. J. LINDHARD,M. SCHARFFand H. E. SCHI&, &I. Danske Videnskad. Sekkab, Mat.-Fys. Medd. 33, 14 (1963). 17. P. HVELPLUND,E. LAEGSGARD, J. 0. OLSENand E. H. PETERSEN,Nucl. Insir. Meth. 90, 315 (1970). 18. A. MITCHELand E. I. MARPHY, Phys. Rev. 46,53 (1934). 19. E. BRANNEN,F. R. HUNT, R. H. ALLINGTONand R. W. NICHOLLS,Nature 175,810 (1955). 20. T. ANDERSEN,J. R. ROBERTSand G. SBRENSEN,Astrophys. J. (in press). 21. Z. LES and H. NIEWODNICZA~~SKI, Acta Phys. Polon. 20, 701 (1961). 22. T. ANDERSEN.K. A. JENSEN and G. SBRENSEN.Nucl. Instr. Meth. 90.41 (1971). 23. A. BIALAS-ZABAWA, M. KUCHARSKI,E. SKULSKA,J. URBACZKAand Z. ‘WAL~CH,Acta Phys. Polon. 30, 897 (1966). 24. R. H. GARSTANG,J. opt. Sot. Am. 51,845 (1962). 25. V. A. ZILITIS,Opt. Spectrosc. 31,86 (1971). 26. P. F. GRUZDEV,Opt. Spectrosc. 22,89 (1967).