Oxygen band system transition arrays

OD324633/89$3.00+ 0.00 MaxwellPergamon Macmillan plc

Planet. SpaceSci., Vol.37,No. 7,pp.881-887, 1989 Printed inGreatBritain.

OXYGEN BAND SYSTEM TRANSITION

ARRAYS

D. R. Bates Department of Applied Mathematics and Theoretical Physics, Queen's University, Belfast BT7 lNN, LJK

Abstract. Amended absolute transition probabilities are given for the bands of the Herzberg I, Chamberlain, Herzberg II and Herzberg III systems of molecular oxygen. 1.

Introduction

In a recent paper (Bates 1988) the results of the ab initio transition moment computations of Klotz and Peyerimhoff (1986) were applied to obtain absolute transition arrays for band systems of molecular oxygen that are of interest in the context of the nightglow. This entailed inter alia the calculation of a set of potentials by the RKR approximation discussed by Vanderslice et al (1959, 1961) and Gilmore (1965). Culpably the published formulae And unfortunately one of those used, Eq. 5 of were not rederived for checking purposes. Gilmore, has a transcription or more probably compositing error: the numerical factor (6/5)? appearing in the printed version should be replaced by 2(6)$/5. It has therefore been necessary to repeat the work. The opportunity is taken of adopting more accurate molecular constants where these are available. 2.

Calculations

and results

As before the recommendations of Krupenie (1972) and of Slanger (1978) were accepted for the X 3Z- and a lA states respectively. Changes were made for the other states. following arg the sour:es of the spectroscopic data used: c lc; , Ramsay (1986); The inner wall of the RKR Borrell et al (1986); A' 3Au, Coquart and Ramsay (1986). potential of the A 3C, state was extrapolated using the results of the ab initio computations of Guberman given by Cheung et al (1986). Following Yoshino et al (1988) an R-l2 variation is assumed for the other RKRxr walls requiring extrapolatic Tables 1, 2, 3 and 4 give the derived arrays of the spontaneous transition probabilities (A(v', v") for the Herzberg I, Chamberlain, Herzberg II and Herzberg III systems. The R substates of the upper level are assumed to be populated in accord with their weights. A sum is taken over all substates of the lower level. Table 1 agrees with a corresponding unpublished table calculated by Drs. R. P. Saxon and T. G. Slanger. A partial check on the other tables is that the A( 0, v") rows are in satisfactory agreement with results given by Klotz and Peyerimhoff (1986). Saxon and Slanger (1986) have used the transition moments of Klotz and Peyerimhoff to calculate the absorption cross section as a function of wavelength. The values they obtained are greater than those measured by Cheung et al (1986). They suggest that this is because the dipole moments are not accurate. They recommended that calculated transition probabilities should be multiplied by 0.6 (the correction factor inferred from the absorption cross sections). Since their work Yoshini et al (1988) have raised the measured cross sections by factors of up to 1.17 but at the longer wavelengths (the most relevant part of the continuum) the original correction factor would still seem appropriate. In the case of the Herzberg I system multiplication of the entries in Table 1 by 0.6 would bring them into quite good accord with the transition array of Degen (1977) except for the higher v" where the thus corrected values are greater than the Degen values. In a private communication Drs. D. E. Siskind and W. E. Sharp have pointed out that use of the present variation

4.3-3

1.4-2

3.3-2

6.8-2

1.2-l

1.8-1

2.4-l

2.9-l

2.7-l

9.5-2

2

3

4

5

6

7

8

9

10

11

Note:

9.5-4

1

0

1.1-4

v”

0

V’

5.5-l

1.8+0

2.3+0

2.6+0

2.5+0

2.3+0

1.7+0

1.2+0

6.5-l

2.8-l

8.4-2

1.3-2

2

2.9+0

2.9+0

2.4+0

1.7+0

9.0-l

3.3-l

6.1-2

3

1.9-1

7.4-l

1.3+0

1.9+0

2.5+0

1.1-4 = 1.1x10 -4

4.0-l

1.2+0

1.4+0

1.3+0

1.1+0

8.2-l

5.4-l

3.0-l

1.4-l

5.2-2

1.3-2

1.7-3

1

Table

1.2-2

7.0-3

1.6-2

2.0-l

6.8-l

1.5+0

2.3+0

2.8+0

2.6+0

1.8+0

8.6-l

2.0-l

4

2.2-l

6.1-1

6.1-l

3.9-l

8.9-2

2.8-2

5.0-l

1.5+0

2.4+0

2.5+0

1.6+0

4.9-l

5

1: Transition

1.1-l

4.6-l

7.9-l

1.1-i-O

l.,O+O

6.3-l

1.0-l

1.1-1

l.O+O

2.2+0

2.2+0

9.0-3

2.1-3

3.4-2

2.6-l

7.0-l

l.l+O

9.8-l

3.3-l

2.7-2

9.7-l

2.1+0

1.4+0

in s -1

A(v’,$‘) 9.5-l

7

6

array for Herzberg

1.3-1

3.8-l

3.5-l

1.5-1

3.5-5

2.5-l

8.3-l

1.0+0

3.6-l

7.3-2

1.4+0

1.8+0

8 9

A +X

4.7-2

2.3-l

4.5-l

6.1-1

4.9-l

1.2-1

5.4-2

6.3-l

9.2-l

1.7-1

4.5-l

1.8+0

I system,

10

2.0-2

1.9-2

6.1-3

1.6-1

4.8-l

6.1-1

2.5-l

2.1-2

6.3-l

6.8-l

1.4-2

1.5+0

.

8.5-2

2.6-l

2.5-l

9.2-2

6.8-3

2.8-l

5.7-l

2.4-l

6.9-2

7.4-l

1.3-l

1.1+0

11

1.1-2

8.5-2

2.4-l

3.6-l

2.5-l

1.0-2

1.9-1

5.1-1

9.0-2

3.3-l

4.5-l

6.4-l

12

2.7-2

4.0-2

1.9-4

8.1-2

3.0-l

3.0-l

1.6-2

2.3-l

3.8-l

2.1-2

6.0-l

3.2-l

13

4.6-2

1.6-1

1.7-l

6.1-2

1.3-2

2.4-l

2.6-l

1.1-4

3.5-l

6.1-2

5.2-l

1.3-1

14

2.5-3

1.0-2

2.8-2

5.7-2

9.9-2

1.4-1

1.8-1

2.2-l

2.3-l

2.2-l

1.9-1

2.0-5 = 2.0x10+

2.1-4

1.0-3

3.3-3

7.9-3

1.6-2

2.7-2

4.1-2

5.6-2

6.7-2

7.4-2

7.1-2

Note:

1

2

3

4

5

6

7

8

9

10

11 1.2-1

1.6-l

2.1-1

2.6-l

2.8-l

2.7-l

2.4-l

1.7-1

1.0-l

4.5-2

1.4-2

1.9-3

2.8-4

2.0-5

0

2

1

v”

0

V’

2.6-4

5.8-3

2.5-2

6.6-2

1.3-1

1.9-1

2.5-l

2.4-l

2.0-l

1.1-1

4.3-2

7.5-3

3

Table

5.8-2

5.6-2

4.0-2

1.4-2

2.6-5

1.9-2

8.1-2

1.6-1

2.1-1

1.8-l

9.3-2

2.1-2

4

3.7-2

6.0-2

8.5-2

9.4-2

7.8-2

3.5-2

1.5-3

2.1-2

1.0-l

1.6-1

1.4-1

3.3-3

2.9-5

5.1-3

2.8-2

6.5-2

8.8-2

7.0-2

1.7-2

6.2-3

7.8-2

1.4-1

7.2-2

6

3.6-2

4.0-2

3.2-2

1.2-2

4.0-6

1.9-2

6.1-2

6.9-2

2.0-2

7.8-3

8.8-2

9.2-2

in s-1

7

4.7-3

1.6-2

3.3-2

4.7-2

4.0-2

1.2-2

2.1-3

3.8-2

5.6-2

8.6-3

2.9-2

9.2-2

8

array for Chamberlain

A(v,v”) 4.5-2

5

2: Transition

1.3-2

6.9-3

4.6-4

5.4-3

2.6-2

4.1-2

2.2-2

1.1-4

3.2-2

3.7-2

7.3-4

7.4-2

9 10

A’+a

1.4-2

2.2-2

2.5-2

1.4-2

8.1-4

8.7-3

3.2-2

1.9-2

1.1-3

3.4-2

7.7-3

4.6-2

system,

7.4-4

4.1-4

6.9-3

2.0-2

2.2-2

5.8-3

3.3-3

2.4-2

9.5-3

9.6-3

2.2-2

2.3-2

11

.

1.1-2

1.1-2

4.9-3

1.9-5

8.3-3

1.9-2

6.5-3

3.5-3

1.9-2

7.1-5

2.3-2

8.1-3

12

1.2-3

5.6-3

1.2-2

1.1-2

1.9-3

3.4-3

1.5-2

2.8-3

8.8-3

6.5-3

1.4-2

2.3-3

13

4.3-3

1.6-3

1.6-4

5.7-3

1.1-2

2.9-3

3.0-3

1.0-2

1.3-4

1.0-2

5.7-3

4.5-4

14

1.1-3

4.6-3

1.3-2

2.7-2

1.7-l

1.9-1

2.0-l

4.3-4

1.4-3

3.4-3

7.1-3

1.3-2

2.2-2

3.1-2

4.3-2

5.5-2

6.5-2

2

3

4

5

6

7

8

9

10

11

2.0-l

1.8-1

1.6-1

1.5-1

8.1-2

7.8-2

8.0-2

13

14

15

16

7.8-2 1.2-1

1.1-1

1.2-2

4.3-2

7.8-2 7.6-3

3.1-3

1.1-1 5.6-2

1.6-3 2.1-4

1.4-1

1.2-2

3.3-2

2.0-l 1.7-1

1.1-1 6.8-2

2.2-l

1.5-1

1.8-1

1.9-1

1.6-1

1.1-1

5.9-2

5.3-4 2.0-2

6.3-2 2.1-2

1.8-2 4.2-3

5.3-2

6.2-2 8.9-3

3.1-2

5.6-2

5.8-2

4.8-2

4.2-2

6.2-2

7.5-2 6.6-2

2.1-2

7.1-2

4.5-3

5.0-2

1.3-2

1.1-3

5.8-2

1.2-1

1.1-1

1.5-l

1.5-1

2.3-2

1.1-2 4.9-2

2.1-2

6 7

1.9-2

1.6-2

1.1-2

4.9-3

3.8-4

1.9-3

1.4-2

3.6-2

5.9-2

6.7-2

4.8-2

1.5-2

6.1-4

3.2-2

8.3-2

8.9-2

3.8-2

1.7-2

2.2-2

2.9-2

3.4-2

3.5-2

2.8-2

1.4-2

2.0-3

2.6-3

2.2-2

4.7-2

5.1-2

2.3-2

1.5-5

2.7-2

7.2-2

4.9-2

A(v,v~) in s-1 3.8-3

5

4

3

2.2-l

2.1-1

1.8-l

1.4-1

9.1-2

5.0-2

2.2-2

6.4-3

9.2-4

2

Note: 9.9-6 = 9.9x10-6

2.1-1

7.5-2

8.0-2

12

1.4-1

1.1-l

7.9-2

5.0-2

1.4-4

9.9-6

9.3-5

1

0

1

v”

0

V’

1.7-3

3.2-4

3.5-4

3.8-3

1.2-2

2.3-2

3.4-2

3.4-2

2.0-2

3.2-3

3.2-3

2.6-2

4.0-2

1.9-2

4.7-4

3.6-2

5.2-2

8

5.6-6 1.2-2

1.5-2 4.1-5

1.6-2

8.4-4

2.6-3

6.7-3

1.5-2 1.6-2

1.2-2

1.2-2

1.7-2

1.2-2

1.7-3 5.9-3

2.9-3

1.2-2

1.8-2

6.6-4

2.5-2

6.7-4

1.1-2

2.6-2

2.1-2

1.4-2

1.1-2

1.9-2

2.9-2

8.1-7

3.1-2

10

8.1-3

8.5-3

4.4-2

9

Table 3: Transition array for Herzberg II system, c + X

11

6.9-3

5.2-3

2.8-3

5.0-4

3.9-4

4.5-3

1.2-2

1.5-2

9.5-3

7.9-4

3.8-3

1.5-2

9.2-3

2.7-4

1.4-2

3.8-3

1.8-2

.

8.1-3

5.3-5 3.0-4 1.2-3

5.9-3 3.9-3

1.4-3 8.3-3

9.4-3

4.5-3

7.8-3 7.7-3

7.4-3 3.3-3

2.8-3

5.7-5 4.9-5

2.8-3

9.8-3

4.8-3

2.2-3 1.0-2

1.7-3

2.6-3

7.5-3

2.5-5

9.2-3

3.8-3

13

1.9-3

1.1-2

3.4-3

4.3-3

8.5-3

9.2-3

12

3.8-3

4.3-3

4.0-3

2.6-3

6.1-4

1.8-4

2.9-3

6.0-3

4.2-3

1.3-4

2.9-3

5.6-3

2.1-4

4.6-3

1.6-3

6.1-3

1.4-3

14

1.3-4

1.2-3

8.5-6

9.4-5

4.7-4

1.6-3

4.1-3

8.6-3

1.5-2

2.3-2

3.3-2

4.1-2

4.6-2

4.5-2

0

1

2

3

4

5

6

7

8

9

10

11 1.5-1

2.0-l

2.4-l

2.6-l

2.6-l

2.3-l

1.8-1

1.2-1

6.6-2

2.7-2

7.4-3

9.2-4

2

Note: 8.5-6 = 8.5x10-6

1.5-l

1.7-1

1.7-1

1.6-1

1.3-1

9.3-2

6.2-2

3.4-2

1.6-2

5.3-3

1

0

t v”

V'

2.2-2

4.6-2

8.6-2

1.4-1

2.0-l

2.4-l

2.6-l

2.2-l

1.6-1

7.9-2

2.7-2

4.1-3

3

2.2-2

1.3-2

2.2-3

3.1-3

3.2-2

9.4-2

1.8-1

2.3-l

2.3-l

1.5-1

6.8-2

1.3-2

4

6.5-2

7.9-2

8.1-2

5.9-2

2.4-2

2.8-4

2.4-2

1.0-l

1.9-1

2.0-l

1.2-1

9.6-3

2.6-2

5.4-2

8.5-2

9.7-2

7.1-2

2.0-2

2.4-3

6.7-2

1.6-1

1.6-1

1.7-2

8.3-3

5.1-4

7.1-3

3.8-2

7.9-2

8.7-2

3.6-2

4.3-4

6.5-2

1.5-1

8.8-2

in s-1

A(v,vI) 5.9-2

7

6

3.1-2

5

3.3-2

4.4-2

4.4-2

2.6-2

3.6-3

7.4-3

5.1-2

7.6-2

3.1-2

4.2-3

9.3-2

1.1-1

8

8.0-4

7.7-3

2.4-2

4.4-2

4.5-2

1.8-2

4.1-4

3.5-2

6.3-2

1.2-2

3.1-2

1.1-1

9

1.6-2

1.1-2

1.9-3

3.0-3

2.4-2

4.3-2

2.4-2

1.1-4

3.8-2

4.4-2

1.3-3

9.4-2

10

1.3-2

2.2-2

2.6-2

1.6-2

8.6-4

1.0-2

3.6-2

2.1-2

2.2-3

4.3-2

6.9-3

6.5-2

11

Table 4: Transition array for Herzberg III system, A’+ X .

5.3-4

7.7-4

8.9-3

2.3-2

2.3-2

4.3-3

6.4-3

3.0-2

7.6-3

1.7-2

2.5-2

3.9-2

12

1.2-2

1.0-2

3.2-3

8.0-4

1.4-2

2.2-2

4.0-3

9.4-3

2.4-2

6.2-4

3.4-2

1.9-2

13

3.4-3

9.3-3

1.4-2

9.1-3

1.1-4

9.7-3

1.8-2

4.5-4

1.9-2

4.8-3

2.7-2

7.6-3

14

886

D. R. BATES

of A(v', v") along a v" row would reduce the anomalously high populations of the v' = 9 and 10 levels of A3Z,T that Stegman and Murtagh (1988) deduced from the intensities of the ultra violet (9,B) and (10,B) Herzberg I bands and the transition probabilities of Degen.

Table 5. Total System v'

transition

Herzberg

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

lo,5 10.7 10.8 11.3 11-3 11.2 11*1 10.4 9.5 8.2 6.2 2.0

I

probabilities

A(v',C)

Chamberlain

out of each v' level.

Herzberg A(v' ,C) in s-1

II

Herzberg

0.29 0.39

0,49

0.61 0,70 0.79 0.84 0.89 0.88 0.88 0.85 0,77 0.68 0.56

0.47 0.54 0.59 0.64 0.67 0.68 0.69 0069 0.67 0.65 0061 0.56 0.50 0.44 0.41

Table 5 gives for each of the four systems v' level

the total transition

III

0.64 0.75 0.81 0.91 0.92 0.96 0.94 0.91 0087 0.79 0069 0.56

probability

out of each

A(v',C)

: I:A(v', v") v" The values of A(O,Z) in Table 5 agree well with the values obtained from Tables 7 to 9 of The weighted mean transition probabilities for the nightKlotz and Peyerimhoff (1986). glow vibrational distributions of Slanger and Huestis (1981) may hence be derived. They are 11 s-1 for the Herzberg I system, 0.85 s-l for the Chamberlain system, 0.66 s-l for the Herzberg IL system and 0.90 s-1 for the Herzberg III system. Acknowledgements My thanks are due to Drs. R. P. Saxon, W. E. Sharp, D. E. Siskind and T. G. Slanger for jointly questioning the correctness of the earlier results and for helpful correspondence; and to the U.S. Air Force for to Mrs. Norah Scott for carrying out the computations; paying her salary under grant AFOSR-88-0190. References Bates, D, R. (1988) Transition probabilities of the bands of oxygen systems of the nightglow Planet. Space Sci, 5, 869. Borrell, P. M., Borrell, P, and Ramsay, D. A$ (1986) High resolution studies of the near ultraviolet bands of oxygen II the A 3~u - X 3~i system, Can. J, Phys. 2, 721. Cheung, A. S.-C., Yoshino, K., Parkinson, W. H., Guberman, S,L. and Freeman, D, E, (1986) Absorption cross section measurements of oxygen in the wave length region 195-241 nm of the Herzberg continuum, PlanetsSpace Sci., 36, 1007, Coquart, B. and Ramsay, D, A. (1986) High resolution studies of the near-ultraviolet bands of oxygen III the A' 3Au - X 3CS system, Can. J. Phys. 64, 726. Degen, V. (1977) Nightglow emission rates in the 0 Herzberg bands. J. Geophys. Res. 82, 2437, Gilmore, F. R. (1965) Potential energy curves for 4 2, O2 and corresponding ions. Jo Quant Spectrosc. Radiat. Transfer 5, 369. Klotz, R. and Peyerimhoff, S, Di p986)3Theoretical study of the spin or dipole forbidden transitions between the c Z , A' A , A 3C+ u and X 3C-g' a 1A g' b 'Z+g states of 0 2" g Molec. Phys. 57, 573. Krupenie, P. H. (1972) The spectrum of molecular oxygen. J, Phys,Chem.(Ref, Data) 1, 423,

Oxygen band system transition arrays

887

A. (1986) High resolution studies of the near-ultraviolet bands of oxygen I: the - X 3Ci system. Can. J. Phys. 64, 717. Saxon, R. P. and Slanger, T. G. (1986) Molecular oxygen absorption continua at 195-300 nm and 02 radiative lifetimes. J. Geophys. ys. 91,+9877. Slanger, T. G. (1978) Generation of 02 (c lx;, AU A-'Zg)from oxygen atom recombination. J. Chem. Phys. 2, 4779. Slanger, T. G. and Huestis, D. L. (1981) 0 (cl.Z + X 'xi) emission in the terrestrial nightglow. J. Geophys. Res. _, 86 3551. u Stegman, J. and Murtagh, D. P. (1988) High resolution spectroscopy of oxygen U.V. airglow. Planet. Space Sci. 2, 927. Vanderslice, 3. T., Mason, E. A., Maisch, W. G. and Lippintott, E. R. (1959) Ground state of hydrogen by the Rydberg-Klein-Rees method. J. molec. Spectrosc. 2, 17 Errata (1961) 5, 83. YoshiGo, K., Cheung, A.S.C., Esmond, J. R., Parkinson, W. H., Freeman, D. E., Guberman, S. L., Jenouvrier, A., Coquart, B. and Merienne, M. F. (1988) Improved absorption cross sections of oxygen in the wave length region 205-250 nm of the Herzberg continuum. Planet. Space Sci., 2, 1469. Ramsay,lDI

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