Absorption by vibrationally excited molecular oxygen in the Schumann-Runge continuum

Planet. Space Sci. 1971, Vol. 19, pp. 1463 to 1473. Pergamon Press. Printed in Northern Ireland

ABSORPTION BY VIBRATIONALLY EXCITED MOLECULAR OXYGEN IN THE S C H U M A N N - R U N G E C O N T I N U U M A. C. ALLISON, A. DALGARNO and N. W. PASACHOFF* Harvard College Observatory and Smithsonian Astrophysical Observatory, Cambridge, Massachusetts, U.S.A.

(Received 22 June 1971) A theoretical model is constructed of the initial and final state interaction potentials and of the transition dipole moment that reproduces the measured discrete and continuum absorption cross sections and the measured relative band emission intensities of the SchumannRunge system of molecular oxygen. The model is used to calculate continuous absorption cross sections from the excited v" = 1 and 2 vibrational levels of the ground electronic state. The cross sections are calculated at various gas temperatures and the values are in harmony with measurements. Tables are given of absolute band oscillator strengths and transition probabilities. 1. INTRODUCTION The absorption of ultraviolet radiation in the Schumann-Runge continuum of molecular oxygen plays a critical role in the photochemistry of the atmosphere. Calculations o f the absorption in the atmosphere have assumed, in effect, that all the oxygen molecules are in the ground vibrational state v" = 0 so that the continuum dissociation threshold occurs at 57127 cm -1 or 1750.5 A (cf. Hunt, 1966; Shimazaki, 1967, 1968; Leovy, 1969; Bowman, Thomas and Geisler, 1970; Shimazaki and Laird, 1970). Some small fraction of the oxygen molecules are in vibrationally excited states and the importance in the interpretation of laboratory measurements of discrete and continuum absorption by molecules in the v" = 1 state has been demonstrated by Hudson, Carter and Stein (1966), Hudson and Carter (1968), and Hasson and Nicholls (1971). Recently the significance of discrete absorption by v" = 1 molecules to atmospheric transmission of ultraviolet radiation has been stressed by Ackerman, Biaum6 and Kockarts (1970). The v" = 1 state has a threshold for continuous dissociation of 55571 cm -1 or 1799-5 tit and the v" = 2 state a threshold of 54038 cm - t or 1850.5 A. Dissociation can also occur at these wavelengths by line absorption in the bands of the discrete Schumann-Runge system followed by predissociation but only the continuum absorption process contributes to the production of metastable oxygen atoms in the mesosphere and stratosphere. A detailed study is prevented by the lack of cross section data and in this paper we construct a theoretical model that reproduces the measured discrete and continuum absorption cross sections and the measured relative band emission intensities and use it to predict cross sections for continuum absorption by molecular oxygen in the v" ----0, 1 and 2 vibrational states. We obtain incidentally band oscillator strengths and transition probabilities that should be more reliable than those now available in the literature. Abstract

2. THEORY The extension of the theoretical formulation to continuum absorption is given by Jarmain and Nicholls (1964). I f ~ , ( r ) is the initial discrete vibrational wave function and the final state is either a discrete wave function ~ , ( r ) or a continuum wave function normalised as

[2# <-" I , g

1 k1/, • r(2tzE,~,,2 r ] s'n L ! +7,

• Now at Courant Institute of Mathematical Sciences, New York University, New York. 1463

(1)

1464

A . C . ALLISON, A. DALGARNO and N. W. PASACHOFF

where # is the reduced mass of the oxygen atoms and r/is a scattering phase shift, and if Dr (is) the transition dipole moment in atomic units, the band oscillator strength of a discrete transition is

_ 101.3 i f f

re'v" -- 2v,,~,"

%,,(r)O(r)~p¢(r) dr

z,

(2)

where 2~,~, A is the transition wavelength. The spontaneous transition probability is A.,.,, =

6"670 ×

10 -15

f¢,~, sec-l.

(3)

Franck-Condon factors are defined by

q¢,,, = fo ~ %,(r)D(r)v2¢(r ) dr 2

(4)

and r-centroids by

fo

°~Ov,,(r)r~o~,(r) dr

re,v, =

~

(5)

fo %,,(r)~pv,(r) dr The band cross section ~r~ for continuum absorption in the X3Zg - -- BaZu- SchumannRunge system of oxygen at a frequency v cm -1 is given by ~rv = 4"083 × lO-~4vSv~,, cm 2,

(6)

Svv,, -= Ifo ~ y~¢,(r)D(r)~oz,(r ) dr 2,

(7)

where S,~, is the band strength

measured in atomic units. The energy E' is related to the frequency v by the conservation of energy. The continuum oscillator strength is given by

dL - -

1"130 ×

dv

1012o'vcm.

(8)

Continuum Franck-Condon densities are defined by (Jarmain and Nicholls, 1964)

q¢'E" =

Ijo %,,(r)~o~,(r) dr

(9)

and the continuum r-centroids by

f o°~o¢,(r)r~oE,(r) dr (10)

re, E, = f~°%,,(r)~vE,(r ) dr do The Franck-Condon factors and densities satisfy the sum rule

~. qv"¢ + V'

f/ qv"E' dE' =

1.

(11)

ABSORPTION BY VIBRATIONALLY EXCITED OXYGEN

1465

3. P O T E N T I A L E N E R G Y C U R V E S

For the interaction potential V"(r) of the ground state, X3Zg-, we adopted a RydbergKlein-Rees curve, provided by Albritton (1970), that matches energy levels up to v" = 21, and extends out to r = 3.5 a 0. For larger r, Albritton (1970) uses a Hulbert-Hirschfelder fit, which gives rise to a potential maximum of 300 cm-1 at 5 ao. We have chosen a different extrapolation of the form v"(r) = ar -b which avoids the insertion of a potential maximum. Different forms of V"(r) appear in a paper by Vanderslice, Mason and Maisch (1960), in the York Atlas (H6bert, Innanen and Nicholls, 1967) and in unpublished material of Jarmain (1970). For the interaction potential V'(r) of the excited state, B3Z,,-, we adopted a KleinRydberg-Rees curve, provided by Albritton (1970), that reproduces the observed vibrational levels up to v' = 14. We supplemented these values by the energy levels and outer turning points for v' = 15 to 20 quoted by Ginter and Battino (1965). For our preliminary calculations we retained the values of Albritton (1970) for the short range repulsive portion of v'(r), but we later modified them to conform to the continuum absorption data (cf. Section 5) Other forms of V'(r) appear in papers by Vanderslice, Mason, Maisch and Lippincott (1960), Singh and Jain (1962), Richards and Barrow (1964) and Ginter and Battino (1965), in the York Atlas (H~bert, Innanen and Nicholls 1967) and in unpublished material of Jarmain (1970). We shall discuss later the form adopted by Bixon, Raz and Jortner (1969). 4. FRANCK-CONDON FACTORS AND DENSITIES We computed the vibrational wave functions %,, ~%. and ~o~,, for the potentials V"(r) and V'(r) by numerical integration using the procedures described by Allison (1969). The Franck-Condon factors q~,~, agree to within 5 per cent with the values calculated by Harris, Blackledge and Generosa (1969). Values have also been given previously by Nicholls (1960), by Jarmain (1963), by Ory and Gittleman (1964), by Halmann and Laulicht (1966, 1967) and by Albritton (1970) that for small v" and v' are not significantly different. Discrepancies occur at larger values because of the different assumptions about the potential energy curves. The Franck-Condon densities for v" = 0 are shown in Fig. 1 as a function of frequency 24

I --

I

7_.z~ 6

F~r~ 12

8 8 4

0

60000

70000

80000

FREQUENCY ~ (cm -I)

FIG. 1.

VARIATION

OF FRANCK-CONDON

DENSITIES

WITH

FREQUENCY.

1466

A.C. ALLISON, A. DALGARNO and N. W. PASACHOFF

v. The integrated density is 0.997. Values have also been given for v" ---- 0 by Jarmain and Nicholls (1964), by Bixon, Raz and Jortner (1969) and by Jarmain (1970). Considerable discrepancies occur between all the sets of values which can be attributed to different choices of the short range portions of the final state interaction potential, V'(r). The decrease that occurs in our values around 73000 cm -1 appears to be necessary if we are to reproduce the observed absorption cross sections. In addition, Bixon et al. predict structure in the form of two shoulders on either side of the peak which they attribute to resonances induced by scattering in the attractive potential V'(r). Structure due to shape resonances often occurs close to the dissociation threshold of molecular absorption continua but the origin of the structure computed by Bixon et al. is obscure. Despite a careful numerical search we found no evidence of shoulders with our adopted form of V'(r). It may be noted that the representation of the attractive part of V'(r), taken by Bixon et al. from Singh and Jain (1962), has been severely criticised by Ginter and Battino (1965). 5. T R A N S I T I O N D I P O L E M O M E N T

The band strength S~,~, or S~, may be written in the form

S1/2 ~'~" = [q,,Y'l 1/2 I/3~,~,,l or

S1/2 ,,,,, =

Iqv,,,,[ 1/~

[bv~,,[, say.

(12)

The mean value of the magnitude of the dipole moment [13[ can be regarded as a function of the transition frequency Figure 2 illustrates the behaviour of I/3o( )1 derived from discrete (Bethke, 1959; Hudson and Carter, 1968; Hasson, Hrbert and Nicholls, 1970) and continuum absorption measurements (Goldstein and Mastrup, 1966; Blake, Carver and Haddad, 1966; Bixon, Raz and Jortner, 1969). Similar analyses have been carried out by Marr (1964) and by Jarmain and Nicholls (1964). Figure 2 demonstrates that 1/30(,)I is a slowly varying function of v that, as expected theoretically, is continuous through the dissociation edge. .

.

.

.

.

.

I

-

i

I

I

J

1.5

o

I0

! I

20000

40000 FREQUENCY v

60000

2___

80000

(crn"1)

FIG. 2. THE MEAN VALUE OF THE TRANSITION MOMENT /~(v) AS A FUNCTION OF FREQUENCY.

ABSORPTION

BY

VIBRATIONALLY

EXCITED

OXYGEN

1467

The continuity at the dissociation edge can be presented more directly in terms of oscillator strengths. Jarmain and Nicholls (1964) compare f0~, and dfo,/dv but it is more instructive to comparef0~,(dv'/dr) and df0/dv (Allison and Dalgarno, 1971), as we do in Fig. 3. The continuity of the oscillator strengths is apparent. - - .....

"

•

F-

:--

,

9

V-

i +L _

81

~0C00

+

1

[

+

55000

EGOC'O

65000

70000

75000

80000

85000

V {cm -i) FIG. 3. D E M O N S T R A T I O N

OF THE CONTINUITY OF THE OSCILLATOR THE D,SSOCIA~ON THRESHOLD.

STREI'~G'I~S T H R O U G H

Figure 2 also contains values of IDv,v. [ for non-zero values of v", obtained from absorption studies (Treanor and Wurster, 1960; Hasson, H6bert and Nicholls, 1970) and from emission intensity measurements (H6bert and Nicholls, 1961). To within the experimental error, Dv.v. depends upon v' and v" only through the frequency of the transition: [D,,,.] ----

ID(")I.

Of greater theoretical interest is tbe dependence of D on nuclear separation. If D(r) is a slowly varying function of r, then to a close approximation (Fraser, 1954), b~,o. = D(,o,~.), (23) r~.v, being the r-centroid defined in (5). The r-centroids r~.~, can be regarded as a function r~"(v) of the corresponding transition frequency v that may be used to transform D(r) into a function D(r). Figure 4 is the corresponding transform of Fig. 2. The derived dipole moment is sensitive to the adopted potential energy V'(r). We have used a trial and error procedure to find a plasusible combination of V'(r) and D(r) that reproduces the measured absorption and emission data. The rapid decrease in absorption toward shorter wavelengths places severe restrictions upon the possible selections. The cross section for photoabsorption of molecular oxygen at Lyman-0~, 1215 A, generally accepted to be less than 10-2° cm2 (Ackerman and Biaum6, 1970) is grossly overestimated by previous studies of Franck-Condon densities and dipole moment functions. We suggest that the slope of V'(r) is less steep than that adopted previously and that D(r) falls off rapidly with decreasing r from a maximum at 2.4 a o. The form of D(r), shown in Fig. 4, is consistent with the suggestion by Jarmain and Nicholls (1964) of a maximum in the dipole moment function and the steep decrease is in accord with the

1468

A . C . ALLISON, A. DALGARNO and N. W. PASACHOFF

I I

15

I

o

05 22

..I 2.4

I 26

I 28

" / ~ 30

"~

32

R (%1

D(r) AS A FUNCTION OF INTERNUCLEAR T H E SOLID LINE IS THE FUNCTION USED I N THIS W O R K .

FIG. 4. T H E MEAN VALUE OF DIPILE MOMENT SEPARATION.

arbitrary correction factor introduced by Evans and Schexnayder (1961). In Fig. 5 our predicted values are compared with the experimental results of Goldstein and Mastrup (1966) and of Bixon, Raz and Jortner (1969). The secondary peak in the theoretical curve at 1240/~ occurs because the transition matrix element passes from positive to negative values at 1280 A; our Franck-Condon densities behave similarly. The structure in the measurements that does not appear in the theoretical curve can be attributed to absorption in other band systems (Tanaka, 1952). r e . i _ _

I

i

I

II 11.5II"1>i +."++÷++ "I-I I ;7 + +++ +\i.i

10-17

?

"I

~ +xb

l

+

S" IO.~8 b

I°-19

io-2o ii//~ 1200

1300

1

I l I f

I

I

1400

I

1500

xc~,)

I

1600

f

1700

I

I

1800

F I G . 5. T H E S C H U M A N N - R U N G E PHOTODISSOCIATION C O N T I N U U M OF MOLECULAR OXYGEN FOR t ,a = 0 " I G O L D S T E I N A N D M A S T R U P (1966); + B l X O N , R A Z AND JORTNER ( 1 9 6 9 ) ; / T H I S W O R K .

ABSORPTION BY VIBRATIONALLY EXCITED OXYGEN

1469

There is the possibility t h a t the c o n t i n u o u s a b s o r p t i o n at s h o r t e r wavelengths is affected by interference with a n o t h e r a b s o r p t i o n c o n t i n u u m . I f so, o u r semi-empirical analysis is p r o b a b l y still valid in p r o v i d i n g a q u a n t i t a t i v e p r e s c r i p t i o n for c o m p u t i n g c o n t i n u o u s a b s o r p t i o n f r o m v i b r a t i o n a l l y excited levels b u t o u r derived d i p o l e m o m e n t w o u l d n o t refer to the direct X~Y~g- -- B3Zu - transition. 6. DISCRETE OSCILLATOR STRENGTHS AND TRANSITION PROBABILITIES The p o t e n t i a l energy curves V"(r) a n d V'(r) a n d the d i p o l e m o m e n t function D(r) have been used to calculate the a b s o r p t i o n b a n d oscillator strengths a n d the s p o n t a n e o u s b a n d emission transition p r o b a b i l i t i e s for the discrete transitions XaY~g-(v ") -B3Z~-(v'). T h e a b s o r p t i o n oscillator strengths f r o m v" = 0, 1 a n d 2 to all the discrete levels v' : 0(1)21 are given in T a b l e 1 a n d the s p o n t a n e o u s t r a n s i t i o n p r o b a b i l i t i e s A~,v- for v', v" = 0(1) 21 are given in T a b l e 2. ABSORPTION OSCILLATOR STRENGTHS, fo.~,, FOR THE SCHUMANN--RUNGE BANDS OF MOLECULAR OXYGEN

TABLE 1.

v"

foo,

Ao,

A~,

0

0-277--9 3.308--9 2'030--8 8"622--8 2'862--7 7-874--7 1'846--6 3"749--6 6"706--6 1"077--5 1"580--5 2-137--5 2"668--5 3-070--5 3"254--5 3-178--5 2"932--5 2"562--5 2-090--5 1"595--5 1"061 - - 5 6"739--6

7"573 - - 9 8.203 - - 8 4"576--7 1"769--6 5.352--6 1"345--5 2.888--5 5"386--5 8.874--5 1-318--4 1"796--4 2"268--4 2-661 - - 4 2"898--4 2"929--4 2"751 - - 4 2-458--4 2'094--4 1-675--4 1"260--4 8-295 - - 5 5'236--5

9"869--8 9-615--7 4"825--6 1-679--5 4"574--5 1"037--4 2-011 - - 4 3"395--4 5"078--4 6'868--4 8-559--4 9"937--4 1-079--3 1'097--3 1'044--3 9"322--4 7"994--4 6'586--4 5"134--4 3"788--4 2"462--4 1'541 - - 4

1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7. CONTINUOUS ABSORPTION The c o m p u t e d photodissociation cross sections for the v" = 1 and 2 vibrational levels o f the XaY, g- state are shown in Figs. 6 a n d 7. A p a r t f r o m the zero at 1280 A the v a r i a t i o n o f cross section with wavelength tends to follow the shape o f the initial v i b r a t i o n a l wave function. T h e e x p e r i m e n t a l a b s o r p t i o n cross section d e p e n d s u p o n the gas t e m p e r a t u r e T a c c o r d ing to a,/,(2) exp (--G~,,,hc k T )

,r(T, ~.) = ~"

exp (--G,/,hc/k T) 'o"

(14)

/3,'

.,

SUM

9 I0 11 12 13 14 15 16 17 18 19 20 21

8

5 6 7

4

2 3

0 1

/),','

2.

6.153 + 5

5"422+6

3

1"977+7

3.824+7

1'409+2 1"092+3 1.414+3 9.749+3 7'300+3 4.474+4 2'609+4 1.420+ 5 7.292+4 3.523 + 5 1'693+5 7.257+5 3.359+ 5 1'277+6 5.791+4 1-955+6 8.833+5 2'649+6 1.217+6 3.247+6 1'541+6 3'670+6 1.816+6 3"875+6 1.999+6 3"845+6 2.055+6 3.596+6 1.975+6 3'176+6 1-777+6 2"658+6 1'533 + 6 2.159+6 1.270+6 1'701+6 9'936+5 1.281+6 7.351+5 9"204÷5 4.786+5 5.872+ 5 3.000+ 5 3.635+ 5

2

4"289+7

6'024+3 4.721+4 1'896+ 5 5"248+5 1.132+6 2'019+6 3.069+6 4"039+6 4.687+6 4.898+6 4.705+6 4.216+6 3'554+6 2.836+6 2'156+6 1'574+6 1'135+6 8"067+ 5 5.585+ 5 3.757+5 2.288+ 5 1"375+ 5

4

3.269+7

2.519+4 1.704+ 5 5-867+ 5 1'383+6 2"516+6 3-750+6 4'700+6 5"022+6 4.635+6 3.749+6 2.692+6 1.721+6 9.730+5 4.788+ 5 1.992+5 6.621+4 1.541 + 4 1'209+3 3.779+2 2'266+3 3.026+3 2'647+ 3

5

2-699+7

8-293+4 4.738+ 5 1.363+6 2.642+6 3"876+6 4.533+6 4-287+6 3'252+6 1-920+6 8.099+5 1-780+ 5 1'369+1 1.062+5 3'094+5 4.776+5 5"541 ÷ 5 5"532+5 5.001+ 5 4'125÷5 3.152+5 2'091÷5 1-324+ 5

6

2"635+7

2'204+5 1-035+6 2'397+6 3.627+6 3'964+6 3'191+6 1'781+6 5'405+5 1.233+4 1'876+5 7.034+5 1'190+6 1.447+6 1"450+6 1.274+6 1.019+6 7.785+5 5'742+5 4.065+5 2.772+ 5 1.701 ÷ 5 1.027+ 5

7

2-055+7

4.807+5 1'791 + 6 3'162+6 3.414+6 2'338+6 8.488+5 3.475+4 2'511 + 5 1.018+6 1"644+6 1"791+6 1.522+6 1.069+6 6'368+5 3.260+5 1-440+5 5"548+4 1-760+4 4.115+3 4.909+2 2.592--3 7.160+ 1

8

TRANSITION PROBABILITIES FOR THE S C H U M A N N - R U N G E SYSTEM OF MOLECULAR OXYGEN

1.154+ 1 1'286+ 2 7.375+2 1.517 + 2 2 . 9 2 6 + 3 5"156 + 2 9 ' 0 7 4 + 3 1"451 + 3 2 . 3 3 5 + 4 3'476 + 3 5 . 1 2 3 q - 4 7.200 + 3 9 . 7 5 1 + 4 1"312 + 4 1-638+ 5 2.144 + 4 2 " 4 7 6 + 5 3.195 + 4 3 . 4 2 8 + 5 4"381 + 4 4 . 3 9 2 + 5 5.537 ÷ 4 5 . 2 1 9 + 5 6.442 + 4 5 . 7 4 8 + 5 6.889 + 4 5 . 8 6 5 + 5 6.778 + 4 5 . 5 4 9 + 5 6.291 + 4 4 . 9 8 9 + 5 5.523 + 4 4 " 2 7 0 + 5 4.521 + 4 3 " 4 2 8 + 5 3.460 + 4 2 - 5 8 5 + 5 2"306 + 4 1"706+ 5 1"466 + 4 1 . 0 7 8 + 5

4.507 + 1 5"526 + 0 3.482 + 1

1

TABLE

1'640 + 7

8-708 + 5 2.448 + 6 3.015 + 6 1'917 + 6 4-461 + 5 2.490 + 4 7.222 + 5 1.562 + 6 1"752 + 6 1.269 + 6 6.130 + 5 1.580 + 5 2'283 + 3 4.978 + 4 1"613 ÷ 5 2.450 + 5 2'781 + 5 2.694 + 5 2.309 + 5 1.803 + 5 1.211 + 5 7.715 + 4

1'497 + 7

1"321 + 6 2"600 + 6 1"883 + 6 3.711 + 5 8"449 + 4 9.507 + 5 1"567 + 6 1'240 + 6 4"804 + 5 3'026 + 4 8"716 + 4 4'019 + 5 6'763 + 5 7'746 + 5 7"140 + 5 5"731 + 5 4"287 + 5 3'060 + 5 2"092 + 5 1'380 + 5 8"248 + 4 4"890 + 4

10

m o ,.I1

Z

e~

0

> t-'

.>

©

>

.>

v'

9"189+6

1"116+7

SUM

7.806+6

1.686+6 3.167+5 2-842+ 5 9.728+ 5 4-082+ 5 7.954+3 4-812+5 7.987+ 5 4"831+5 7.772+4 2-394+4 2.283+5 4.209+ 5 4'698+5 4"003+5 2"882+ 5 1.902+ 5 1.189+ 5 7"133 + 3 4"181 + 4 2"271+4 1'261+4

13

5"631 + 6

1'326+6 3.558+3 6.793+5 4.936+ 5 1.077+3 4-473+ 5 6.465+ 5 2.217+ 5 2"732+ 3 2'397+5 4.979+ 5 4.944+5 3.106+ 5 1.264+ 5 2"669+4 2"279+2 6.807+3 1"924+4 2"615+4 2.624+4 2.031+4 1-399+4

14

4.843+6

8"887+5 1"191+5 6.247+5 3"242+4 3.057+5 5.331+ 5 1.172+5 5.267+4 3.827 + 5 4"697+5 2.456+5 3.800+4 8.344+4 8.748+4 1.636+5 1-892+ 5 1-763+3 1.453+ 5 1.093+ 5 7.696+4 4.797+4 2.916+4

15

3.678+6

5.057+5 3'480+ 5 2'638+ 5 9.271+4 4-501 + 5 1.069+ 5 7.199 + 4 3-813 + 5 3.107+ 5 5-096q-4 2.296+4 1'758+5 2.816+ 5 2.639+ 5 1"801 + 5 9.830+4 4-598+4 1.854+4 6-403 + 3 1"851 -t- 3 4'237+2 9.041 + 1

16

2-756+6

2.436+ 5 4'431+ 5 1'954+4 3"037+ 5 1"670+5 3'800+4 3-191 + 5 1.983 + 5 1'155+ 3 1'236+5 2.801+ 5 2'419+ 5 1"061+ 5 1.633+4 1'462+ 3 2"185+4 4.242+4 5.166+4 4"945 + 4 4.087 + 4 2"823+4 1.824+4

17

The signed integer indicates the power of ten by which the previous number should be multiplied.

1-829+6 1'124-t-6 2.022+3 6"880+5 1"141 + 6 4.725+5 7.890+1 3"634+5 8.515+5 8-409+5 4.643+5 1.213+5 6-307+2 5.095+4 1"476+5 2.106+5 2"269+ 5 2.099+5 1'731 + 5 1"311 + 5 8"606+4 5"407+4

12

1'689+6 2'067+6 5"642+ 5 5'266+4 9"176+ 5 1'344+6 7'385+5 7"659+4 1'049+5 5"715+5 9'107+5 8"957+5 6"445+ 5 3'582+5 1-541+5 4'833+4 8"821 + 3 8.173+ 1 1"700+3 4"307+3 4'771+3 3"882+3

I1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

v" + + + + + + + + + + + + + + + + + + + + + +

4 5 4 5 1 5 5 3 5 5 4 3 4 5 5 5 4 4 4 4 4 3 2"316 -1- 6

9.931 3-695 3.623 2'639 4"268 2"303 1"576 1"780 1"695 2"383 9"772 1.731 3'688 1'084 1.387 1"242 9.333 6.330 4.005 2"430 1-350 7.594

18 + 4 -t- 5 + 5 + 4 + 5 + 5 + 2 + 5 + 5 + 4 + 4 -t- 5 + 5 + 5 + 4 + 4 + 2 + 3 + 3 + 3 + 3 + 3 1-601 + 6

3'429 2"274 1"511 7"774 1 '040 1"641 2'196 1"535 1'669 2"047 2"856 1"311 1'596 1'073 4-494 1'035 3"647 1"226 4"105 5'600 4"988 3"679

19 + + + + + + + + + + + + + + + + + + + + + +

3 5 5 1 5 4 5 5 3 4 5 4 4 3 4 4 4 4 4 4 4 4 1'320 + 6

9"998 1"093 1'935 6"286 1-643 1"019 1'035 1-261 2"843 6"818 1"449 9"116 1'600 2"137 2"713 4"915 5'526 4"987 3"916 2'812 1'765 1 "075

20 + + + + + + + + + + + + + + + + + + + + + +

3 4 5 4 4 4 5 3 4 5 4 3 4 4 4 4 4 3 3 2 2 1 9-740 + 5

2.457 4.212 1.488 4.918 7.547 3.503 1.127 2.478 7.214 1.111 2.812 3.928 5.201 8.377 7.311 4.523 2.254 9-347 3.236 9.156 1-984 3.804

21

>

X

0 :Z

0 X

X ,-]

t,<

X >

> ,..]

,< <

Z

,.q

©

O']

1472

A.C.

ALLISON, A. D A L G A R N O and N. W. PASACHOFF

10-t7

i0-~8 tM

b i0-,9I~ >

162011 I 1200

1300

t400

! 1600

1500

I

1700

1800

1900

FIG. 6. THE SCHUMANN-I{UNGE PHOTODISSOCIATION CONTINUUM FOR v" = I .

,62°11 1200

Ill 1300

p H 1400

I I 1600

I 1500

~I 1700

I 1800

1900

x(~,) FIG. 7. THE SCHUMANN-RUNGE PHOTODISSOCIATION CONTINUUM FOR V" = 2. TABLE

3. THE ABSORPTION CROSS SECTIONS OF THE SCHUMANN-RUNGE CONTINUUM IN UNITS OF 10 -is AT 3 0 0 , 600 AND 9 0 0 K

).(A) 1600 1650 1700 1750 1780 1820

300 K This work 4.1 2.0 0-75 0"22 0-002

Exp. 4-5 2.1 0.80 0'24 0.004

600 K This work 4.1 2.1 0.89 0.32 0-064 0"004

Exp. 4.1 2.2 0.90 0.34 0'084 0-017

Experimental results are those of Hudson, Carter and Stein (1966).

900 K This work Exp. 4-3 2.4 1-2 0"54 0-24 0.04

0.62 0'30 0"094

cm 2

ABSORPTION BY VIBRATIONALLY EXCITED OXYGEN

1473

where G~" is the c o n v e n t i o n a l spectroscopic c o n s t a n t (cf. Herzberg, 1950). It has been measured by H u d s o n , Carter a n d Stein (1966) at T = 3 0 0 , 6 0 0 a n d 900 K a n d a c o m p a r i s o n o f their data with the theoretical results is presented in Table 3. The agreement is very close a n d appears to confirm the accuracy of the a b s o r p t i o n cross sections predicted for the i n d i v i d u a l v i b r a t i o n a l levels.

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