Transition probabilities for triplet levels of Sr(I)

J. Quanr. Spectrosc. Radiaf. Transfer Vol. 39, No. 6, pp. 471-403,1988 Printed in Great Britain. All rights reserved

TRANSITION

0022-4073/88 53.00+ 0.00 Copyright0 1988Pergamon Press plc

PROBABILITIES FOR LEVELS OF Sr(1)

GUSTAVO

GARCIA

and Josh

TRIPLET

CAMPOS

Laboratorio de Fisica At6mica y Lkeres C.I.E.M.A.T., CBtedra de Fisica Atbmica Experimental, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid Ciudad Universitaria, 28040-Madrid, Spain (Received 10 August

1987)

Abstract-Relative transition probabilities for 64 lines arising from excited triplet levels of Sr(1) have been determined from emission line-intensities in a hollow-cathode discharge. These values were put on an absolute scale by using, where possible, the experimental lifetimes published by other authors. In addition, absolute transition probabilities were obtained by using line-strength sum rules and the results were found to be in agreement with data derived from lifetime measurements. Comparison have also been made with previously published experimental and theoretical studies. 1. INTRODUCTION

Absolute transition probabilities of alkaline earth elements have been the subject of a large number of experimental and theoretical studies. Important results concerning Be, Mg and Ca have been published by Wiese et al.’ Similarly, results for Ba have been summarized by Miles and Wiese.’ There are fewer data for Sr and, especially, for transitions between triplet states. Experimental studies of these levels were carried out by Eberhagen3 in 1955 by means of emission measurements and, more recently, by Penkin and Shabanova4 using the hook method. Calculations in the Coulomb approximation were performed by Gruzdev.’ The discrepancies between the results of these authors and the lack of experimental data for configurations of interest have prompted the present work. In this study, we present transition probabilities for 64 lines arising from the triplet levels of Sr(1). Relative values have been obtained from measurements of emission line intensities in a hollowcathode discharge. We have used two different methods in order to place the data on an absolute scale. First, where possible, experimentally determined lifetimes published by other authorsc9 have been used. Secondly, we report the results obtained from line-strength sum rules” for all of our measurements. The present results have been employed to obtain the population distributions of the emitting triplet levels as a function of their energies for our experimental conditions. 2. EXPERIMENTAL

SET-UP

AND

PROCEDURE

We have measured emission intensities of lines with a common upper level by means of single-photon counting. The light source was a hollow-cathode lamp or Sr operating at a current of 10 mA. The cathode was cylindrical, had a length of 14 mm and an internal bore of 5 mm. The gas used to fill the tube was Ar at a pressure of about 6 torr. The transition wavelengths range from 4300 to 7600 A and were isolated by using a 1.2 m monochromator with 0.3 ,& resolution in the first order. Photons were detected with an EM1 9558 QB photomultiplier cooled with dry ice. Calibrated tungsten-strip and deuterium lamps were used to determine the spectral response. We recorded emission spectra in order to obtain the relative transition probabilities with statistical uncertainties of less than 5%. These relative values were put on an absolute scale by using the experimentally determined lifetimes for the upper levels given by other authors.“’ The data employed are listed in Table 1. For the 5d ‘D,, 5d ‘D,, 5d ‘D, and 5p* ‘P, levels, we used the accurate lifetimes published by Andr% et a1,6 which were obtained by laser excitation of a fast beam of neutralized ions. For the 5p* 3P, level, which is not included in the aforementioned work, we have Q.SR.T 39,b~'

477

478

GUSTAVOGARCIAand Josh CAMPOS Table 1. Lifetimes of the triplet levels of S(I) used to determine the absolute transition probabilities.

Level

Lifetime (ns)

5d

3,3

16.2g_+o.24

5d

3D2

16.3420.14

5d

3Dl

16.4g_+o.lo

5P2

3P2

7.89_fo.o5

5P2 3P1

6.glto.20

6s

3S1

12.9 Lo.7

7s

3s1

34.8 il.3

Experimental Method

Author

Andra et al6

Laserexcitation of atomicbeam

Kelly and Mathur7

Havey

et al

8

Zero-field level-crossing

Two-step laser excitation

Gornik '

taken the result of Kelly and Mathur,’ which were performed by employing the zero-field-levelcrossing technique. For the 6s 3S, and 7s 3S, levels, we used the latest measurements carried out with two-step laser excitation by Havey et al8 and by Gornik,’ respectively. Absolute transition probabilities have also been obtained by combining our experimentally measured branching ratios with line-strength sum rules,‘O viz., c SJr = [(2J + 1)/(21 + l)] x I,,,,, x I R,,(r) x r x IL(r) /

s

x dr I*,

where SJY is the line strength for 1nl,J > +ln’Z’,J’> transitions and l&(r) x r x R,,(r) x dr is the single-electron radial integral. This sum rule has been applied while assuming that configuration mixing is not important for the triplet states of alkaline earth atoms.” The radial wavefunctions [R,,(r)] were obtained by numerical integration of the Schrodinger equation and using a semiempirical potential that takes into account core and external electron shielding. This potential has been adjusted in order to obtain agreement between calculated and experimental values for ionization potentials of SrII and Sri and for the appropriate energies of the external configurations. The energy eigenvalues calculated for the 5s, 5p, 6p, 4d, 5d, and 4forbitals are in agreement, within 5%, with experimental values given by Moore.”

3.

RESULTS

AND

DISCUSSION

The absolute transition probabilities obtained from lifetime and branching-ratio measurements are shown in the first column of Table 2. The quoted experimental errors are the result of statistical uncertainties (5%), spectral response determination (5%) and errors in the lifetime measurements. The second column shows values obtained from the combination of branching-ratio measurements and line-strength sum-rules. In these results, only statistical and spectral calibration errors have been included. The agreement is generally within 10% between the results obtained by us for the two methods, except for lines arising from the 6s 3S, and 7s ‘S, levels. For these levels, larger discrepancies (about 20%) have been found between calculated and experimentally-measured energy eigenvalues. We consider the results derived from lifetime measurements to be more reliable. Data given by other authors have been included in Table 2 for comparison. The values of Eberhagen3 for lines arising from the 5d ‘D, 4f 3Fo, 5p 2 3P and 5p’ 3Fo levels differ by less than 40% from those obtained in the present studies. The remaining values show discrepancies between 40 and 78%. Blended lines among the results of Eberhagen3 are not included in Table 2. The results of Penkin and Shabanova4 are in agreement, within estimated limits of experimental error, with the present data.

S(I) transition probabilities

479

Table 2. Absolute transition Ix0 babilities of lines arising from triplet levels of S(I). ABSOLUTE TRANSITION PROBABILITIES (x

TRANSITION

Experlme Levels Jpper

Lower

Line

This

Work

ii

t

$

61.

U-+o.g

3D3

5p 3P;

4962.2

jd 3D*

5P 3P;

4967.9

12.Go.9

co.01

id

heory

tef.3

58.5

66

63.4

12.8-+0.9

25

16.1

48.223

60

51.8

4872.5

48.423

5P 1';

7503.5


5P 3P;

4971.7

1.320.1

1.320.1

5P 3P"1

4876.1

26.321.8

27.121.9

29

5p 3P;

4832.0

33.122

34.122

47

5P lPO 1

7512.0

co.01

co.01

4f 3F4"

4d 3D3

4892.0

4f 3F;

4d 3D3

4892.6

4d 3D2

4868.7

34.222

46 1D2

5374.1

to.01

4d 3D3

4893.1

4.920.3

4d 3D2

4869.2

7.5zo.5

4d 3D1

4856.2

26.351.8

4d lD2

5374.6

to.01

5P 3P;

4811.9

go.o-+6

5P 3P;

4722.3

35.9-+3

39.923

5p 1P;

7153.1

co.1


5p 3P;

Sd 3D1

4f 3F2"

5p2 3P2

Lef.4

1.8

37.9

4.320.3

10027

25

69

go.0

38

35.6

ief.5

480

GIJSTAVO GARCIA

and Josh CAMPOS

Table 2-continued 5P2 3P 1

5P 3P;

4876.3

76.126

72.025

65

5P 3P4

4784.3

30.2-+2

28.6?2

50

40.5

5P 'P8

4741.9

38.623

36.5?3

57

46.1

5P IPi

7296.4



5~' 3F$

4d 3D3

6408.5

5~' 3";

4d 3D3

6546.8

4d 3D2

6504.0

47.323

4d 1D2

7438.4

0.5o:o.o

4d 3D3

6688.2

0.10~0.0

lid3D2

6643.5

9.310.6

5P' 3F2"

4d 3D1

5~' 3D;

5~’

3D;

5~' 3D;

6617.3

58.5

7.8i0.5

31.6-f2

41

11 40

46

4d lD2

7621.5

4d 3D3

5480.9

79.025

aa

4d 3D2

5450.8

14.721

24

4d lD2

6092.2

10.01

4d 3D3

5534.8

22.7i1.6

4d 3D2

5504.2

54.l-f4

4d 3Dl

5486.1

15.3+1

4d ID2

6158.9

<0.04

4d 3D2

5540.0

28.421.9

4d 3Dl

5521.8

62.9-f4

4d lD2

6203.9


7.8iO.5

Q(I) transition probabilities

Table 2-continued. 5P' 3PS

4d 3D3

5256.9

81.326

4d 3D2

5229.3

22.751.6

4d 3Dl

5213.0

l.$O.l

4d ID2

5816.8

0.30-+0.02

4d 3D2

5238.5

73.025

4d 3Dl

5222.2

34.322

4d 1D2

5828.3

0.2l-fO.02

5p' 3D;

4d 3D1

5225.1

6s 3S1

5P 3p;

7070.1

5P 3q

6878.3

5p 3P;

6791.0

4d 3D2

6388.2

4.620.3

4d 3D1

6363.9

1.o-fo.l

4d 1D2

7287.2

0.80-f0.06

6p 3P" 0

4d 3Dl

6369.9

6.820.5

6~ 3P;

4d 3D3

6386.5

3.120.2

4d 3D2

6345.7

0.60+0.04

4d 3Dl

6321.7

0.025~0.001

4d lDl

7232.1

2.120.1

55

5p 3P;

4438.0

15.521.2

9.1-+0.6

5P 3q

4361.7

9.720.8

5p 3Pi

4326.4

3.120.2

5p lp;

6357.0

5P' 3P;

6~ 3Pi

7s 3s1

122 32 235

44

108-+8

150

41.5-f4

30.4-+2

56

37.5

30.9

27.122

19.821.4

33

23.8

19.6

6.520.4

16

8.6

6.7

12

16.2

9.0

5.7io.4

7

8.7

5.6

1.8-+0.1

2.6

4.0

1.9

8.9-fo.8

0.4l-fO.03 0.24-+0.02

I' Valuesobtained from lifetime measurements. * Valuesobtained from line strength sum rules.

18

8

GUSTAVOGA&A

482

and

Josh CAMPOS

\ I

II

1

1 30 Energy

1

1

1

1

of emitting

1

35

1

levels

1

1

1

1

40

1

I

(x lo3 cm-‘)

Fig. 1. Semilogarithmic plot of the triplet level population divided by its statistical weight vs the level energy; O-values obtained from lifetime measurements; e-values determined from line-strength sum rules.

Employing our estimated transition probabilities, the quantity ln[ZU/(gix A,)] - ln(Ni/gi) has been plotted vs the energy of the emitting level. Here, 4 is the line-emission intensity, A, the corresponding transition probability, Ni the population of the upper level, and gi its statistical weight. For levels differing only in the quantum number J, an average was used for the N,/g, values. As may be seen from Fig. 1, the experimental points obtained in this manner lie on a straight line. Therefore, for our experimental conditions and for the levels studies by us, statistical distributions of populations may be inferred. This result agrees with the population distribution found by other authors’3*14for hollow-cathode discharges. Acknowledgement-This

work was performed with partial financial support

of the SpanishDGICYT (project PB86/0543).

REFERENCES 1. W. L. Wiese, M. W. Smith, and B. M. Miles, “Atomic Transition Probabilities,” NSRDS-NBS 4, Vol. I, p. 22, Washington, DC, 20402(1966); NSRDS-NBS 22, Vol. II, pp. 25, 245, Washington DC, 204020( 1969). 2. B. M. Miles and W. L. Wiese, Atom. Data 1, 1 (1969). 3. A. Eberhagen, Z. Phys. 143, 392 (1955). 4. N. P. Penkin and L. N. Shabanova, Opt. Spektrosk. 12, 3 (1962); Opt. Spectrosc. 12, 1 (1962). 5. P. F. Gruzdev, Opt. Spektrosk. 22, 169; 22, 89 (1967). 6. H. J. Andrg, H. J. Pliihn, W. Withmann, A. Gaupp, J. 0. Stoner, Jr., and M. Gaillard, JOSA 65, 1410 (1975). 7. F. M. Kelly and M. S. Mathur, Can. J. Phys. 54, 800 (1976). 8. M. D. Havey, L. C. Balling, and J. J. Wright, JOSA 67, 488 (1977). 9. W. Gornik, Z. Phys. A 283, 231 (1977).

Sr(1) transition probabilities

483

10. R. D. Cowan, The Theory of Atomic Structure and Spectra, p. 422, University of California Press, Berkeley and Los Angeles, CA (1981). 11. H. Friedrich and E. Trefftz, JQSRT 9, 333 (1969). 12. C. E. Moore, “Atomic Energy Levels,” NBS 467, Vol. II, p. 189, Washington 25, DC (1949). 13. M. R. Teixeira and F. C. Rodrigues, J. Phys. D 12, 2173 (1979). 14. R. A. Keller, B. E. Warner, E. F. Zalewski, P. Dyer, R. Engleman, Jr., and B. A. Palmer, J. Phys. 44, Suppl. No. 11, C7-23 (1983).