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Laser spectroscopy and microwave-optical double resonance of a supersonicexpansion ICl A 3п (1) υ = 19S.G. Hansen a , J.D. Thompson a , C.M. Western a & B.J. Howard aa Physical Chemistry Laboratory , South Parks Road, Oxford, OX1 3QZ,EnglandPublished online: 23 Aug 2006.

To cite this article: S.G. Hansen , J.D. Thompson , C.M. Western & B.J. Howard (1983) Laser spectroscopyand microwave-optical double resonance of a supersonic expansion ICl A 3п (1) υ = 19, Molecular Physics:An International Journal at the Interface Between Chemistry and Physics, 49:5, 1217-1229

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MOLECULAR PHYSICS, 1983, VOL. 49, NO. 5, 1217-1229

Laser spectroscopy and microwave-optical double resonance of a supersonic expansion

ICI A 3II(1) ~) ---- 19

by S. G. HANSEN]' , J. D. T H O M P S O N , C. M. W E S T E R N and B. J. H O W A R D

Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, England

(Received 9 November 1982 ; accepted 20 April 1983)

The 19-0 band of the IasC1A alI(1)-X iN+ system is examined at sub- Doppler resolution using a single mode dye laser and a supersonic jet. Complex hyperfine structure is resolved and assigned with the aid of micro- wave-optical double resonance spectroscopy. Twenty-two microwave transitions were observed within the excited vibronic state and the subse- quent analysis results in values for the rotational constant, t~-doubling constant, two electric quadrupole constants and a magnetic hyperfine con- stant.

1. INTRODUCTION

The diatomic halogens and interhalogens possess two accessible low-lying excited electronic states and have rich visible spectra. These two states are of aI](1) and aII(0+) symmetry and, within a simple MO framework, have identical orbital occupation. The fact, that the transitions from the 1~+ ground state to these triplets are observed and are rather strong, is attributable to the tendency of the heavier halogens towards case (c) coupling (for a review of diatomic halogen spectroscopy see [1]).

In 12 and Br 2 it is the B aF[(0u+)~-X ty.g+ absorption bands which dominate the visible spectrum while in IC1 it is the A aII(1)<--X lY~ +. The main reasons for this difference are the favourable A<--X Franck-Condon factors and the fragmentary nature of the B all(0+) state of IC1, even though transitions to the B aFI(0 +) states have higher oscillator strengths than those of the A aII(1) states [2].

Recently, Coxon and co-workers [3] combined new spectroscopic data with previous work, primarily the absorption spectra of Hulthdn et al. [4], to obtain very accurate molecular constants for IC1 A aI](1). Although this work was quite complete, it relied entirely on a large data set of low resolution spectra to achieve its precision. There has, as yet, been no high resolution experiment performed to study the hyperfine structure in this state directly.

The hyperfine level patterns of the X ly,+ and B a[I(0+) states of the halogens have received considerable attention in recent years. The ground states of the

t NATO postdoctoral fellow.

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1218 S . G . Hansen et al.

interhalogens have been extensively studied by conventional microwave spectro- scopy [5] and knowledge of the X and B states of 12 [6, 7] and Br 2 [8, 9] has been obtained using the high resolution techniques of molecular beam laser spectroscopy [6, 8] and saturated absorption spectroscopy [7, 9]. The v = 2 level of IC1 B ~1-I(0 +) was studied by Kn6ckel and Tiemann [10] using micro- wave optical double resonance (MODR) and very recently we examined the elusive v = 0 level of this state by combining M O D R with a seeded supersonic expansion [11]. There has however been no similar high resolution study of an A 3H(1) state for any of the halogens or interhalogens. In the present work the IC1 (A-X) system is examined at high resolution by performing laser induced fluorescence on a supersonic beam and the hyperfine structure in the A state is directly probed via MODR.

2. EXPERIMENTAL

The basic molecular beam-laser fluorescence setup is described elsewhere [12] and will be discussed only briefly here. The additions required to perform microwave spectroscopy are described in greater detail.

Figure 1 schematically shows the experimental arrangement used to obtain M O D R spectra from a molecular beam. Light from a single mocJe, frequency stabilized (linewidth _~2 MHz), continuous wave, tunable dye laser (Coherent CR-599-21) is focused into a vacuum chamber. Brewster angle entrance and exit windows are located at the ends of 75 cm long sidearms and the sidearms contain optical baffles to limit the amount of scattered laser light seen by the photomultiplier tube (PMT).

The laser beam crosses an uncollimated supersonic molecular beam at right angles. The uncollimated, unskimmed beam, more properly called a free jet, is formed by passing argon at 200-300 Torr over solid IC1 and expanding the mixture into the vacuum chamber through a glass nozzle. In the present study an orifice diameter of 135/x was used ; since the vapour pressure of IC1 at 25°C is 30 Torr, the free jet contained ~ 10 per cent IC1. In this expansion IC1 is cooled to a rotational temperature of 3 K and a vibrational temperature of 230 K [12].

Total fluorescence resulting from the absorption of laser radiation by the molecules is collected and focused onto the photocathode of an EMI 9558A photomultiplier tube. A wedge-shaped adjustable spatial filter (not shown in figure 1) is located between the first two lenses in the optical detection train and can be used to limit the fraction of the free jet seen by the photomultiplier tube. The wedge effectively decreases the angular divergence of the beam, thus reducing the Doppler width in the fluorescence spectrum. The angular divergence as seen by the photomultiplier tube is also reduced by increasing the distance between nozzle and laser interaction zone; in the present work this value was 2-4 cm and sub-Doppler resolution was easily obtained.

Microwave power is produced by either a solid state sweep oscillator (Hewlett Packard 8620C) or a klystron. The solid state source operates at frequencies below 18 GHz and because of its low output power (< 50 mW), a travelling wave tube (TWT) (Hughes Aircraft Co.) is used to amplify the microwaves. Output powers of > 1 W are readily attainable. An electronic frequency counter (Hewlett Packard 5345A) continuously displays microwave the frequency.

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Laser spectroscopy and MODR of ICl 1219

LENS ~q....~ / ,~.

~PUMP F~gurc 1. The experimental arrangement.

Several klystrons are available for frequencies above 1g GHz and because of their higher output powers (100-400 mW) further amplification is not used. Because of difficulties in scanning the klystrons linearly and accurately measuring frequencies above 18 GHz, the solid state oscillator was generally preferred. The microwaves are directed into the vacuum system using a short section of rectangular wave guide, which is located at 180 ° with respect to the nozzle, and terminates in the vacuum system approximately 2 cm away from the laser interaction zone.

MODR spectra are obtained by tuning the laser to the desired fluorescence feature and electronically sweeping the microwave frequency. Because of the relatively high laser power density used, we operate in the strong-pumping limit [13] which implies that a microwave transition involving either the ground or electronically excited levels pumped by the laser causes an increase in total fluorescence. The change in total fluorescence may be small but by using phase sensitive detection large signal to noise ratios can be realized. This is done by square-wave modulating the microwave frequency with an amplitude of 5-10 MHz at a frequency of 1 kHz and monitoring the photomultiplier output with a lock-in amplifier. Both the integral and differential fluorescence signals are sent to a chart recorder ; microwave frequency calibration is obtained simultaneously by visually monitoring the frequency counter'and using an event marker.

Rhodamin 6G dye, which gave 100-150 mW single mode power when pumped with 4 W (several lines) from a Kr + laser, was used in this study. Typical microwave powers were 50-500 mW which resulted in the saturation of most rotational transitions. Microwave power was held constant throughout a scan by actively feeding a fraction of the amplified power level back into the solid state oscillator.

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1220 S . G . Hansen et al.

3. RESULTS

The level v= 19 of I3aC1 A aII(l) was chosen for study primarily because the A3H(1)-X1Z + v ' = 1 9 - v " = O has a favourable Franck-Condon factor (1.84 x 10 .2 [14]) and its origin is near the peak of the Rhodamin 6G power curve. Figure 2 (a) shows a simple high resolution excitation spectrum taken in the vicinity of the 19-0 bandhead. Considering that only six rotational transitions are present in this 0-55 cm -1 scan, the spectrum appears quite complex. The extra structure is attributable to the difference in hyperfine interactions in the A and X states. The expected locations of the R(0) to R(3) and Q(1) to Q(2) lines which can be calculated using tabulated constants [3] are also indicated in figure 2 (a).

13SC[ A-X 1 9 - 0

I 0 2 3

t

i 1665293 cm -I

I 1 6 6 5 2 . 3 8 c m - I

I,l 5

l,i ,'o ,'~ 2'o

ii,II I I

255055 40

Lll

Figure 2. (a) High resolution fluorescence scan of the Ia~C1A-X19-0 bandheado (b) Theoretical hyperfine pattern of fluorescence spectrum. It results from the analysis of the present MODR spectra. The assignment for the individual hyper- fine components is given in table 1.

The open hyperfine structure in figure 2 (a) is particularly noteworthy in comparison to the appearance of individual rotational lines in the B 3II(0+)- X 12+ system of IC1. At similar resolution to the present study, only a hint of hyperfine structure was resolved [11]. For the only non-overlapped line in figure 2 (a), Q(2), eight peaks are clearly visible and they span a frequency range of over 2.2 GHz. The width (full width at half maximum) of the in- dividual hyperfine lines in figure 2 (a) is 150 MHz ; resolution is limited by the angular divergence of the fraction of the beam seen by the optical detection system.

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Laser spectroscopy and M O D R o[ ICI 1221

Table 1. Assignments for the hyperfine components shown in figure 2 (b).

Line F'-F" Line F'-F" Line F'-F"

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(lO)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

R(1) e-~7 ~ (19) R(2) ~-~s 3 (36) 0 (1 ) 5 3

R(1) ~-~5 5 (20) R(21 ~-~ 3 (37) R(3) ~__a2 2 R(1) 9 7 (21) R(2) ~-~a 1 (38) R(3) 3 3 ~--~ ~--~

R(1) 27 7 (22) R(2) * * (39) 0 ( 1 ) 3 a 2 ~--~

R(0) 7 5 (23) Q(1) ~-~' s (40) R(3) 3 1 ~--~ ~--~

R(1) 3 ~ (24) Q( I ) ~-~-' 7 (41) 0 (2) 9 7

R(1) ~-,~5 7 (25) R(3) /-I-~ -~-° (42) Q(2) ~-~ R(1) 5 3 (26) R(3) ~-~-9 9 (43) 0 (2) 7 7 ~--~ ~-~-

R(0) 5 ~-~ (27) R(3) 9 7 ~-~ (44/ 0 (2) 7 s

R(1) ~ ~ (28) R(3) ~-~7 7 (45/ 0 ( 2 / s 7

R(1) * ~ (29) Q(1) ~-~ ~ (46) 0 (2 ) 7 9

R(2) ~-~9, (30) R(3) ½*-g~- (47) Q(2) ~--~

R(2) 7 7 (31) R(3) ½-~ -½-* (48) Q(21 a

R(0) a ~ (32) R(3) 7 s (49) 0 (2) 5 3 ~--~ ~--~g ~--~

R(21 7_~ (33) 0(1) ~-~ (50) Q(2) 1 3

R(2) ~-~9 9 (34) R(3) ~-~-~ ~ (51) Q(2) a ,

R(2) ,_~ 9 (.35) Q(1) ~-~ 7 (52) Q(2) ~ 1

R(2) ~ ~

13sCl XIZ + v=O J=?-I =2_Z

• J - , I

1375 13"70 GHz

Figure 3. A typical M O D R line, Experimental conditions : 60 m W microwave power ; 100 m W laser power ; modulate 6 M H z at 1 kHz ; 1 s t ime constant ; scan rate 0.5 M H z s -1.

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1222 S . G . Hansen et al.

A rough picture of the A state hyperfine level structure could be obtained if a complete assignment for the spectrum in figure 2 (a) could be made. Un- fortunately this is not easily done because, unlike the B a[I(0 *) and X ' E k~ states of the halogens and interhalogens, a simple first order nuclear electric quadrupole interaction model [15] is not sufficient for describing the A state. The a l l ( l ) state will exhibit both a magnetic interaction and an additional electric quadrupole effect due to interactions between the (nominally) degenerate A = + 1 and - 1 electronic states. As an added complication both the e and f levels resulting from the (.,~ (or A)-doubling are observed [16]. In the B all(0'-) states, only the e levels are generally seen.

The assignment for the spectrum in figure 2 (a) (shown in figure 2 (b) and table 1, and discussed later) was accomplished by performing M O D R on many of the fluorescence lines. Figure 3 shows a typical M O D R signal. It was obtained by tuning the laser to the top of the tall peak located second from the left in figure 2 (a), and scanning the microwave frequency. Using the known values [17] for the rotational constant (B") and electric quadrupole coupling constant of the I atom (eQq"i) in the ground vibronic state of IaaC1, the micro- wave transition is readily assigned as the F = ~2-~7 component of J = 2-1 in v = 0 of the A" 1E" state. While monitoring the same fluorescence line, transitions were also observed near 13 160 and 13 320 MHz. These are easily assigned as the F = ? ~ and 5 7 ~-~ ~-oc components respectively of the same rotational transition. This observation proves that this fluorescence line connects the F " = ~,7 j , ,= 1 level of the ground state with the A a|l(1) state. From intensity considerations [15] and the fact that this line is very near the expected position of the R(1) line, one might speculate that the A state level involved is F' 9 j , = = ~, 2. Fur- thermore it would be an e component ; the parity selection rule g+-+u restricts the P and R lines to e levels, and Q lines to f levels. The subsequent analysis proves this assignment to be correct.

RI RO R2 QI R3 Q2 R4 P2 Q3

Figure 4. The lower trace records the fluorescence spectrum while the upper trace moni- tors modulated fluorescence caused by the J" = 2-1 F" = ~- - ~ microwave transition.

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By examining various fluorescence lines we observed all nine allowed ( A F = 0 , + l ) transitions between the J " = l, F " = ~,7 ~,5 ~a a n d J " = 2 , F " - 9 7 5 ~, ½ levels as well as many of the hyperfine components of the J" = 3-2 transition in the 19.9-20.7 G H z range. In order to obtain efficiently an assignment for the ground state levels associated with the various fluorescence lines, the micro- wave f requency was held constant and the laser f requency was scanned. The results of such a run are shown in figure 4. Here, the microwave frequency has been set at that of the positive wing (see figure 3) of the F"-9_7 j , - ~ ~, = 2 - 1

transition. As the laser is scanned the total fluorescence spectrum and the modulated signal are displayed simultaneously. If the laser excitation involved either the F " = ~ , J " = 2 or F " - v j,,= - 2 , 1 levels of the ground electronic state, the upper pen deflects. In this manner it was possible to obtain quickly infor- mation pert inent to assigning the ground state component associated with the various lines. No J"=2-1 or J"=3-2 transitions were observed for the lines located third and sixth from the left in figure 2 (a) which is highly suggestive that they correspond to two of the three R(0) hyperfine components.

From the known rotational constant for I aaC1 A a l l ( l ) v = 1 9 [3] one can predict that hyperfine components of the J ' = 4 - 3 transition in this vibronic level will occur near 15 GHz. Figure 5 shows the results of a rapid scan of microwave frequency through this region with the laser tuned to the tallest component of the Q(3) line. Both the integral and differential fluorescence signals are shown and five lines are clearly seen. The fact that more than three lines appear indicates that this laser absorption contains more than one hyperfine component. For the most intense transition in figure 5 the total fluorescence increases by

13SOl A 31](11 v=19.J=4-3

i I I I L I i I 15'0 14"8 146 14"4

GHz

Figure 5. Rapid scan (3 MHz s 1) showing microwave transitions in the A all(l) state of IC1. The upper trace shows the total fluorescence signal (the time constant is 0-3 s).

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1224 S . G . Hansen et al.

26 per cent ; this figure would be even higher if a single, rather than the modu- lated, microwave f requency were used.

By tuning to various fluorescence lines and observing other microwave transitions in the A state it was possible to make an assignment. This was done by looking for c o m m o n differences between these frequencies, by using the ground state assignments for the fluorescence lines and by considering the hyperf ine s tructure of the fluorescence spectrum. Virtually every allowed transit ion between the J ' - - 4 and J ' = 3 hyperf ine levels was observed although some lines were obscured by overlap. Accurate measurements were made by scanning slowly both backward and forward through the transit ion and averaging the results.

T h e precision of the f requency measurement and the signal-to-noise ratio were such that line posit ions accurate to + 0.1 M H z should have been obtainable for non-over lapped transitions. Unfortunately, this limit was not reached because of several complications. T h e pr imary problem was that the electric quadrupole splitting due to the C1 nucleus was either unresolved or only partially resolved. Th i s led to some strange, asymmetr ic line shapes f rom which a line centre was difficult to estimate. T h e complete s t ructure due to the C1 nucleus could not be resolved because of both transit t ime broadening and power broadening ; at a molecular velocity of 5 × 104 cm s -1 and a laser beam width of a few tenths of a mill imetre the transit t ime broadening should amount to a few megahertz . At tempts to use an unfocused laser beam led to much lower M O D R signals, p resumably because the optical transit ion was fur ther f rom saturation. Line broadening due to excessive microwave power was generally less than that caused by the unresolved Cl s tructure and the transit t ime. For strong transitions though (those with A F = A J) extra s tructure in the form of wings was observed at high power levels in the M O D R spec t rum

Table 2. Observed hyperfine components associated with the J = 4 - 3 transition of ICI A 31I(1)v= 19. The five parameters at the bottom were determined by a weighted least squares fit to the data ; errors signify one standard deviation.

Observed (Observed- Observed (Observed- frequency/ calculated)/ frequency/ calculated)/

Line MHz MHz Line MHz MHz

½-~--~!e 14904.7(20) -2 .7 ~-~e6 3 15211.4(8) 0.0 ½-~-½-~e 14976.0(10) -0 .7 ~-~e3 3 14933.3(25) 1.1

911 14847.6(25) -2 .3 31 15193.0(8) -0 .3 ~--~-e ~--~e

11 ~ 14976.7(10) 1.1 ½3_½1 f 14911.0(10) -0 .8 ~- -28

a_92 ~e 14850.2(10) 1-5 ½!_1~f 14520.4(8) 0.1 ~-~e79 14600.5(15) 3.7 -~--~ ~/ 14993.3(15) 0.2 9 7 15070"4(10) -0"6 9 9 ~-~f 14751.5(10) -0 .7 ~-~-e

~-~e7 7 14818.2(20) -0 .8 ~-~f~ 9 14647.8(10) 0.6 ~-~e5 ~ 14515.9(10) - 1.4 ~-~f° 7 15058-1(8) 0.8 ~-~e7 5 15161.2(15) 0.1 ~-~f7 ~ 14951.7(8) -0 .5 ~-~e5 5 14859.1(12) -0 .3 ~-~f3 3 15146.6(25) 1.4

R.m.s. error=l .3 MHz, a2=1.12, B=1874.073(34) MHz, q~=1.007(66) MHz, eQq o = 202.8(34) MHz, eQq2 -- 2704.1(63) MHz, a ' = 759.5(12) MHz.

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Laser spectroscopy and MODR of ICI 1225

[18]. The line shapes were also dependent on the microwave modulation scheme used. The minimum line widths we measured were 4 MHz for J = 3-2 transitions in the X state and 6 MHz for J = 4-3 transitions in the A state.

Positions for 22 hyperfine components of the J = 4 - 3 transition in IC1 A ~H(1) v = 1 9 are given in table 2. The estimated uncertainties take into account the difficulties in determining the line centres. Thirteen of these transitions are between e-levels and nine are between f-levels.

4. CALCULATIONS

The hamiltonian needed to describe the hyperfine structure we resolve in rotational transitions of IC1 A 31I(1) is of the

H = Hrot+ HQ+ where

Hro t = (B _+ ½qa)[J(J+ 1)-- 1]

f o r m

H mad,

-D[J(J+ 1 ) - 1] 2

gives the energy of the ~-doubled e and f rotational levels in the absence of hyperfine interactions

HQ = T2(VE). T2(Q)

gives the quadrupole interaction energy and is the product of second rank tensor operators describing the molecular electric field gradient and iodine nuclear quadrupole moment, and

Hma~=a ' I . L

gives the magnetic hyperfine energy which results from the nuclear spin-orbit interaction. (For a more thorough discussion of the hyperfine hamiltonian see the Appendix of [19].) Because all the microwave lines observed belonged to a single rotational transition, the centrifugal distortion constant D could not be determined. Centrifugal distortion does however have a noticeable effect on the microwave transitions, so D was constrained at the optically determined value of 2-022 x 10 -7 cm -1 [3].

The hamiltonian was diagonalized using a Hund's case (a) basis set [A, Z, J, I, F> which included all possible J values (1-9) for the F levels of interest (½_½3). The five parameters which were obtained in the calculation, B, qn, eQqo, eQq2 and a', are discussed below. They were initially guessed and eventually determined when the iterative solution of H gave the best weighted least squares fit to the microwave lines. The line positions were weighted by the inverse squares of their estimated errors. The deviation of the calculated line positions from the measured, as well as the five parameters determined in the fit, are given in table 2. The variance of the fit, ~2= 1.12, is reasonable, indicating that the basis set and hamiltonian used were sufficient for describing the hyperfine interactions to within experimental error.

In the course of the diagonalization procedure, one obtains energies for all v ' = 19 A state hyperfine levels with F = 1_½_~. Combining this information with the known [17] hyperfine levels structure in the ground electronic state, allows the fluorescence spectrum to be calculated. This is shown in figure 2 (b), with the individual hyperfine line assignments given in table 1. The intensities for the various components were estimated using tabulated functions

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1226 S . G . Hansen et al.

[15] for hyperf ine intensities and assuming a rotational temperature of 3 K. As can be seen by comparison with figure 2 (a), agreement is good, thus providing a check on the accuracy of the assignment and the calculation.

5. Discussion

The value given for B in table 2, 1874-073(34) MHz, represents the average of the rotational constants for the levels of e and f designation and qn= 1.007(66) M H z is the t~-doubling parameter which describes the splitting. An analysis of 220 optical lines for this vibronic level gave B / = 1873.412(27) MH z and q n = 0 - 8 1 2 ( 3 0 ) M H z . (These numbers converted to M H z using c = 2.997 924 58 × 10 TM cm s -1. They are given in [3] f rom an analysis of the data in [4].) A number comparable to the B determined here can be obtained from Bi+½qn= 1873 .818(40)MHz; all of these error limits are one standard devia- tion.

The agreement between the present and previously determined values for B and qa is not particularly good. We at tempted to fit the microwave lines constraining B and qn to their optically determined values, but this resulted in an RMS error of 4"4 M H z and a variance of cr 2= 16.8 for the f i t ; obviously, the optical values are not consistent with the present data. The reason for this situation is not clear. The major assumption that is made in our calculation is the J ( J + l ) dependence of the t l-doubling. This assumption is generally considered to be good for a aI[ 1 molecule [15] and its validity at high J has been demonstra ted for the A state of IC1 [4]. Nevertheless, any departure from this dependence could lead to an error in the coefficient we determine. Th e only logical source of error in the optical work comes from neglecting the effects of the unresolved hyperfine structure. Subtle shifts in line centres due to un- accounted for hyperfine interactions could lead to slight errors in the fit con- stants but it seems unlikely that this is adequate to account for the observed discrepancy. It would be interesting to obtain microwave spectra involving other rotational transitions in this vibronic state so that a centrifugal distortion constant and the J dependence of the t~-doubling could be directly determined.

Also obtained in our calculation are two previously unmeasured electric quadrupole coupling constants for the iodine nucleus in the ~4 state. Whereas in the X 1E+ and B all(0+) states of 1C1 a single constant, eQqo, is sufficient, in the A aFl(1) state a second constant, eQq2, is required. It originates from the interactions of states which differ in A by two ; in the present case A = +_ 1 states are mixed. The coupling constants are given by [19]

eQqo=eQ(A = + ll2ToZ(VE) IA = + 1),

eQq2=eQ<A = + I ]2v%T+zZ(VE)IA= -T- 1),

where 0 is the iodine nuclear quadrupole moment and T~2(VE) is the spherical tensor operator for a component of the electric field gradient and is given by £i(ei/r,a)(4rr/5) l'e Y~(O;¢;). Our measurements for these constants are epqo= 202.8(34) M H z and eQqe =2704.1(63 ) MHz.

It is interesting to compare this value for e~q o with the similar quantities determined in the lowest vibrational levels of the X 1E÷, eOq o = -2 9 2 7 .9 MH z [17], and the B all(0+) states, eOqo= - 6 6 4 MH z [11]. The difference between

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these values in the iN and all states can be rationalized from simple electron configuration considerations. The 1)2+ state has a valence shell configuration of a 2 rr ~ rr .4, which to the I nucleus appears similar to the atomic configuration p,~p:2p~. The all orbital occupation is ~o rr 4 7r,a ~, which to the I nucleus approximates p,~puaS2p,a% The expression giving the electric field gradient due to p electrons along the z axis is [20]

( n'~+nu ) qz = - 2 n~ k

where n~ is the population of the p; orbital and k is a constant. Substituting the effective populations into this expression one obtains q~(1Z+)/q~(aH)=4 which is in good qualitative agreement with the measured values for the X and B states.

This simple model predicts that the values for eQq o in the A aFl(1) and B alJ(0+) states will be identical. The fact that we experimentally measure them to be quite different, in fact of opposite sign, is probably attributable to coupling with other electronic states. For eQq o to become positive the I nucleus must see an increased population in the p~ orbital. This would be accomplished if the aII(1) state could acquire some a s ~r 4 rr .2 a *= character. A low-lying az-(1) of this electron configuration is present ; the positive value'for eQq o we measure can be rationalized assuming sufficient mixing between ' the aN-(1) and A al l ( l ) states.

Since IC1 A alI(1) is intermediate between a Hund's case (a) and a case (c) state, the magnetic hyperfine parameter we measure does not strictly correspond to any of the magnetic constants defined by Frosch and Foley [21]. The magnetic hyperfine hamiltonian can be given by [21]

Hmag = [aA + (b + c)X]/z

if small terms off diagonal in A are neglected. In the case (a) limit we have A = 1 and Z = 0 so that Hm~g=aAI. ~ and our measured constant, a '=759 .5 (12 )MHz, is analogous to a. However, in case (c) coupling, A and Y. are not well defined and the measured constant should be interpreted more appropriately as a.(A) + (b + c)<X>.

Figure 6 shows the level pattern for J = 3 of IC1 A afI(1) v=19 , and is illuminating because it graphically illustrates the relative importance of the hyperfine interactions. Starting on the left with the unperturbed rotational level and moving to the right, we see first the effect of the magnetic interaction. The splitting caused is large ; adding the eQq o term changes the pattern only slightly. For this low J level the ~)-doubling is also relatively insignificant. The eQq 2 term is the only first order interaction which affects the e and f levels antisymmetrically. Apart from the magnetic interaction, it is this off-diagonal (in A) electric quadrupole interaction which has the greatest effect on the level pattern. To fit the experimentally determined pattern, shown at far right in figure 6, it is necessary to include higher order effects, that is terms off diagonal in J. Since the levels are mixed to varying degrees, they move in an asymmetric fashion. For a low rotational level the mixing is important in determining the actual hyperfine pattern ; however these effects should become less noticeable with increasing J.

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1228 S . G . Hansen et al.

Figure 6.

ICl I 3TT(1) v=19 Hyperfine interactions

Rotation + Magnetic + eQq, 0 + o-doubling + eQq2 + Higher order terms

~ ½ e

100 MHz

Evolution of the J=3 hyperfine pattern as the number of interactions is in- creased.

6. CONCLUSIONS

The present technique, M O D R of supersonic expansions, appears to be very useful. By working at sub-Doppler resolution, higher signal-to-noise ratios in the M O D R spectrum can be obtained because of decreased overlap of hyperfine components in the fluorescence excitation spectrum. The merging of ap- proaches also benefits from the fact that the low J states generally preferred for microwave spectroscopy are produced in great abundance in the supersonic expansion. A disadvantage of the present technique is the relatively broad spectraI line width due to transit time effects. This problem may be reduced by using heavier carrier gases, although the line widths currently seen are comparable to those obtained using conventional M O D R [22].

Hyperfine structure in the A 31](1) state of IC1 has been examined. The level pattern and constants obtained provide the first description of hyperfine interactions in any 31I(1) state of a diatomic halogen or interhalogen. It would be enlightening to extend the present study to other vibrational levels, par- ticularly v '=28 , where the curves of the A and X states may cross [3], to examine the vibrational dependence and effect of perturbations on the hyper- fine parameters. It may also be possible to see electronic transitions induced by microwave radiation [23]. Transitions from the A state to the B state, high vibrational levels of the X state or some previously unobserved state such as the aII(2) may be observable.

We are grateful to Dr. J. M. Brown for the loan of the travelling wave tube amplifier. We thank Dr. J. A. Coxon for providing Franck-Condon factors.

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Laser spectroscopy and MODR o[ ICl 1229

REFERENCES

[1] COXON, J. A., 1972, Chemical Society Specialist Report on Molecular Spectroscopy, Vol. 1 (Chemical Society), Chap. 4.

[2] MULLIKEN, R. S., 1971, J . chem. Phys., 55, 288. [3] COXON, J. A., GORDON, R. M., and WICKRAMAARATCHI, M. A., 1980, y. molec.

Spectrosc., 79, 363. COXON, J. A., and WICKRAMAARATCHI, M. A., 1980, J. molec. Spectrosc., 79, 380.

[4] HULTHEN, E., J~RLSgTER, N., and KOFFMAN, L., 1960, Ark. Fys., 18, 479. [5] WILLIS, R. E., JR., and CLARK III , W. W., 1980, ft. chem. Phys., 72, 4946. LOVAS,

F. J., and TIEMANN, E., 1974, J. phys. Chem. Ref. Data, 3, 609. [6] HACKEL, L. A., CASLETON, K. H., KUKOLICH, S. G., and EZEKIEL, S., 1975, Phys.

Rev. Lett., 35, 568. [7] LEVENSON, M. D., and SCHAWLOW, A. L., 1972, Phys. Rev. A, 6, 10. FOTH, H. J.,

and SPIEWECK, F., 1979, Chem. Phys. Lett., 65, 347. [8] BETTIN, N., KN6CKEL, H., and TIEMANN, E., 1981, Chem. Phys. Lett., 80, 386. [9] ENG, R. S., and LA TOURETTE, J. T., 1974, J. molec. Spectrosc., 52, 269.

[10] KN6CKEL, H., and TIEMANN, E., 1979, Chem. Phys. Lett., 64, 593. [11] HANSEN, S. G., and HOWARD, B. J., 1982, Chem. Phys. Lett., 85, 249. [12] HANSEN, S. G., THOMPSON, J. D., KENNEDY, R. A., and HOWARD, B. J., 1982, ft.

chem. Soe. Faraday Trans. II, 78, 1293. [13] FIELD, R. W., ENGLISH, A. D., TANAKA, T., HARRIS, D. O., and JENNINGS, D. A.,

1973, J. chem. Phys., 59, 2191. [14] CoxoN, J. A., 1982 (private communication). [15] TOWNES, C. H., and SCHAWLOW, A. L., 1975, Microwave Spectroscopy (Dover Publi-

cations). [16] BROWN, J. M., HOUGEN, J. T., HUBER, K.-P., JOHNS, J. W. C., KoPP, ]., LEFEBVRE-

BRION, H., MERER, A. J., RAMSAY, D. A., ROSTAS, J., and ZARE, R. N., 1975, J. molec. Spectrosc., 55, 500,

[17] HERBST, E., and STEINMETZ, W., 1973, ft. chem. Phys., 56, 5342. [18] RAMSEY, N. F., 1956, Molecular Beams (Oxford University Press), p. 120. [19] WESTERN, C. M., LANGRIDGE-SMITH, P. R. R., HOWARD, B. J., and NovtcK, S. E.,

1981, Molec. Phys., 44, 145. [20] GORDY, W., and COOK, R. L., 1970, Microwave Molecular Spectra (John Wiley &

Sons). [21] FROSCH, R. A., and FOLEY, H. M., 1952, Phys. Rev., 88, 1337. [23] WORMSBECHER, R. F., HARRIS, D. O., and WICKE, B. G., 1977, J. molee. Spectrosc., 64,

86. [23] EVENSON, K. M., DUNN, J., and BROIDA, H. P., 1964, Phys. Rev., 136, 1566.

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