A measurement of the lambda-type doubling spectrum of the CH radical by microwave-optical double resonance: further characterization of the A'A state

C t i u ~ s r o ~ t i ~ n R . BRAZIER' A N D JOHN M. BROWN' The D~,/~trrtttlet~t r!f Chetnistry, Sorcthtrttq~tor~ Utli~~ersity. So~rthtrtrrptotl, Et~glotltl SOY j N H

Rcccivcd July 17, 1984

Scvcral lincs in thc lambda-doubling spcctrum of thc CH radical in its ground 'I1 statchavc bccn rccordcd by thc tcchniquc of microw;~vc-optical doublc rcsonancc. Individual lincs in thc (0.0) band of thc A'II - x'II systcm at 43 1 nni wcrc pumpcd with a dyc lascr and thc absorption of microwavc radiation was dctcctcd as an incrcasc in thc lcvcl of tluorcsccncc. Thc rnicrowavc transition frcqucncics wcrc mcasurcd to an accuracy of 0.1 MHz and thc rcsults wcrc uscd to dctcrminc valucs for thc lambda-doubling paramctcrs in thc rnolccular cffcctivc Hamiltonian. Scvclxl lincs in thc (0.0) band of thc A -X systcm wcrc also rccordcd with sub-Dopplcr linc widths using thc saturation tcchniquc of intcrniodulatcd tluorcsccncc. Thc proton hypcrfinc structurc was casily rcsolvcd. Thc vcry small cffccts of lambda-doubling in thc A'A statc wcrc also dctcctcd for thc highcr rotational lcvcls by prccisc mcasurcmcnt of thc lascr induccd tluorcsccncc spcctrum. Thc valucs obtaincd for thc paramctcrs that dcscribcd thcsc cffccts in thc rnolccular Hamiltonian arc discussed.

On a cnrcgistrC plusicurs raics du spcctrc dc dCdoublcmcnt lanibda du radical CH dans son Ctat fondamcntal '11. cn utilisant la tcchniquc dc doublc rdsonancc optiquc micro-ondc. Dcs raics individucllcs dans la bandc (0 .0) du systcmc A'A - ~ ' 1 1 :I

431 nm ont CtC pompdcs avcc un lascr i colorant, ct I'absorption du rayonncnicnt micro-ondc a Ctd ddtcctdc conimc uric

augmcntation d u dcgrC dc fluorcsccncc. Lcs frCqucnccs dc transition micro-ondc ont dtC mcsurCcs avcc unc prdcision dc 0 , I MHz ct Ics rCsultats ont CtC utilisCs pour dktcrmincr dcs valcurs dcs paramctrcs dc dCdoublcmcnt lambda dans I'hamiltonicn molCculairc cffcctif. Plusicurs raics dans la bandc (0 .0 ) du systcnic A -X ont aussi dtC cnrcgistrkcs avcc unc largcur infcricurc i~ la largcur Dopplcr, cn utilisant la tcchniquc dc saturation dc tluorcsccncc intcrmodulcc. La structurc hypcrfinc tlu proton a CtC aisCmcnt rCsoluc. Lcs trcs pctits cffcts dc dCdoublcmcnt lanibda dans I'Ctat A'A ont aussi CtC dctcctds pour Ics nivcaux rotationncls plus ClcvCs. au nioycn dc mcsurcs prdciscs du spcctrc dc tluorcsccncc induit par Ic rayonncnicnt lascr. Lcs valcurs obtcnucs pour Ics paranictrcs qui dkcrivcnt ccs cffcts dans I'hamiltonicn mol6culairc sont discutdcs.

[Traduit par Ic journal]

Can J Phya . 62. 1563 (19x4)

1 . Introduction The CH free radical was first identified in 1918 ( I ) .

Since then it has been an object of much interest. for a variety of reasons. The emission spectrum in the visible and near-ultraviolet played an important part around 1930 in advancing our understanding of the energy levels of diatomic molecules in doublet states (2). Somewhat later, it was realized that the breaking-off of the rotational structure in the B ' C - - X ' n system was an early example of thc phenomenon of predissociation (3). At about the sanle time. CH was one of thc first lnolecules to be identified in the interstellar medium (4). Only a single line, R2(1) , was observed in the A'A - X ' n system, which was correctly interpreted as an indication of the very low temperatures of such clouds ( 5 , 6 ) . In the meantime, CH had been recognized by those studying reaction kinetics as an important constituent of flames. particularly in combustion pro- cesses (7).

' ~ r c s c n t addrcss: Thc Dcpartnicnt of Chcmistry. Univcrsity of Arizona, Tucson. AZ 85721, U.S.A.

'Prcscnt addrcss: Thc Physical Chcmistl-y Laboratory, Oxford Univcrsity, South Parks Road, Oxford. England OX1 3 4 2 .

Following the identification of the OH radical in the interstellar gas clouds through the observation of lines in its lambda-doubling spectrum at microwave fre- quencies (8), radio astronomers were eager to detect CH in the sanle way. However, although the relevant frequencies for OH had been measured previously in the laboratory (9). the same was not true for CH. The microwave spgtrum of CH eluded detection (10, 1 I ) despite the efforts of many different groups, most of which are not .recorded in the literature. The optical spectrum remained the only source of information on the energy levels of CH in its ground 'll state ( 12, 13) and considerable effort was expended in attempting to refine the lambda-doubling intervals for the lowest rota- tional level, J = 4 (14-16). Some high quality rrb itlitio calculations were also performed with a similar objective (17).

A significant step forward was taken in 1971 with the detection of a rotational transition in CH at far infrared wavelengths (1 8 ) by laser magnetic resonance (LMR) . However, the particular transition detected ( J = 34 +

2; at 118.6 pm) did not contain direct information on the lambda-doubling frequencies for the J = 4 level. Before further work could be done on the laboratory spectrum, the radio astronomers achieved a great coup

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1564 C A N . J . PHYS. VOL. 62. 1084

with the detection of three hyperfine components of the J = transition at 3.3 GHz for CH in extraterrestrial sources (19. 20). The same transitions were sub- sequently used to map the distribution of CH in the interstellar niediuni. In certain instances, the signals were seen in emission with abnormal relative intensities and froni regions in space that suggested that they had been amplified by maser action (19). The need for fur- ther spectroscopic information remained, however. both to aid astrophysical searches for CH in excited rotational levels and to characterize the energy levels of the CH radical. Such information was largely provided by further work on the far infrared LMR spectrum. The development of optically pumped, far infrared lasers made a very thorough study of CH possible (21. 22). An important aspect of these experiments was that they allowed the coniparison of different methods of gener- ating CH in the laboratory, pointing strongly to the F + CH, flame as the best source investigated.

With the help of predictions based on the analysis of the far infrared LMR spectra (23), and the benefit of experience in the generation of CH froni the same studies, we have been able to detect several low-J tran- sitions in the lambda-doubling spectrum by microwave- optical double resonance (MODR). A preliminary ac- count of this work has already been published (24); the present paper is a full description of our results, including an analysis and interpretation. In the process, we have niade very precise measurements of the posi- tions of lines in the (0.0) band of the A'A -X'II system by laser induced fluorescence and have been able to detect the small effects of lambda-doubling for CH in the A'A state. We have also recorded sections of the (0,O) band of the A'A - X'n transitions at sub-Doppler resolution using saturation techniques. These obser- vations have allowed us to measure the proton hyper- fine splittings for CH in its A'A state for the first time.

At about the same time as we were making our obser- . . . . vations, Bogey and co-workers at the Univesity of Lille

alsosucceeded in detecting lambda-doubling transitions in CH. They performed a conventional niicrowave ex- periment, passing the radiation through an extended radio frequency (r.f.) discharge in CH, and other gases (25). To achieve the requisite sensitivity. they had to use higher frequencies (>44 GHz) and so their obser- vations involve larger J values than do ours. We have included their measurements in our fit of the lanibda- doubling spectrum.

2. Experimental details The CH radicals were generated continuously in a

discharge-flow system by the reaction between fluo- rine atoms and methane at a total pressure of a few tenths of a Torr ( I Torr = 133 Pa). The fluorine atoms were generated by passing a 2% mixture of F, in helium

through a microwave discharge. The products of this discharge were reacted with methane in a mixing cell. niade of quartz to permit the passage of microwave radiation through its walls. Extremely low flow rates of methane were required for optimum conditions. which corresponded to a milky blue cheniiluniinescence. The conditions were optiriiized by eye for the strongest lines. On occasions, CF, was passed through the dis- charge as an alternative-source of F atoms. The CH signals produced in this way were of comparable in- tensity but overlapping bands from other species that were produced made i t a less convenient source.

The optical transition used in this work was the (0.0) band of the A'A-x'I-I system at 431 nni. The radiation source was a Coherent Radiation 599-21 standing wave dye laser pumped with 2 W of ~~ltraviolet ( U V ) output (all lines) of a Spectra Physics argon ion laser. Using stilbene-3 in the dye laser, a typical output power of 40 to 60 niW was obtained. Although i t was possible to scan the laser in stabilized, single-mode operation over 30 GHz, the range was often reduced to maintain maximum power and stability. The frequency jitter was somewhat greater than for the red dyes (about 4 MHz root-mean-square (RMS)), but this was not a limitation to the present work since the lowest line widths achieved were 20 MHz full width at half max- imum (FWHM). All the experiments described in this paper involved the excitation of fluorescence from the CH molecules. In our apparatus. part of the fluo- rescence was collected with a cylindrical lens and focussed through a 70-nm band-pass filter centred at 450 nni onto a photomultiplier tube (RCA IP28). The excitation spectrum of the (0.0) band of the A -X sys- tem of CH, recorded with an experimental resolution of about I cni- ' , is shown in Fig. I .

The absolute frequency of the laser radiation was established by comparison with the spectrum of lx'Te,, which was,recorded sirnultaneously. An atlas of the frequencies of selected lines of this niolecule between 17 500 and.23 800 cni-' has recently been published (26). The spectra were recorded in absorption with the sample in a cell heated to 500°C, conditions that corre- spond to those used for the atlas. Deposition of solid on the cell windows was avoided by the use of double glazing, the region between the two layers being evac- uated. The average density of measured lines in the Te, atlas is 2 lines/cniC' (the comparable figure for the iodine atlas (27) is 4.5 lines/cm-I) and consequently, there was often only one calibration line within a given scan. We have, therefore, used the markers from a 75-MHz free-spectral range (FSR) etalon to interpolate between the CH line to be measured and the reference line. The data were recorded and calibrated with the aid of a microcomputer. An example of a typical recording of a line in the Doppler-limited excitation spcctrum of

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BRAZIER A N D BROWN

wavenumber (cm-'1

FIG. I . Thc (0,O) band of the A'A-x'H system of thc CH radical, recorded at a rcsolution of about I cm ' by opcrating the dye laser broad band and tuning the bircfringcnt filter. The base linc is a mcasurc of the scattered light level. I t slopes and indeed falls away completely at the high-frequency end bccausc of thc variation in the output power of the laser.

CH 1s shown in Fig. 2. Spectra of most of the stronger l ~ n e s In the (0,O) band

of the A - X system were recorded at sub-Doppler reso- lution by the techn~que ot ~ntermodulated fluorescence (28). The laser beam was s p l ~ t Into two beams of ap- proxinlately equal Intensity. which were then chopped at different frequencies (356 and 499 Hz) before being focussed and passed in opposite directions through the sample cell. The two beams were l a d on top of each other to maxim~ze sensitivity. Feedback to the laser was suppressed by rotation of the plane of polar~zation w ~ t h - in the ring of counter propagating beanis and the insertion of a plane polarizer outside to block the re- turning light. The nonlinear response of the molecules to the rad~ation serves to mix the two modulation fre- quencies. and signals were detected at the sum with zero Doppler l ~ n e broaden~ng with a photonlultiplier tube and lock-in amplifier system. The separation be- tween lines was measured with the aid of the trans- mission fringes from the 75-MHz FSR etalon. The line widths obtained for CH were about 30 MHz FWHM working at a total pressure of 0 4 Torr. This is much broader than the natural line wldth for CH In the A'A state, estimated to be only 0.30 MHz from the measured rad~at lve lifetime of 0 .53 p s (29). There were experi-

mental indications that the line widths had significant contributions from collisional and power broadening.

The lambda-doubling transitions of CH in its ground '11 state were recorded by the technique of niicrowave- optical double resonance (30). The laser frequency was t~lned to pump (and partially saturate) an optical transi- tion that involved one of the lambda doublet con]- ponents, and the resultant fluorescence was monitored as the microwa-?e frequency was swept across the region of interest: Amplitude modulation of the micro- wave radiation and phase-sensitive detection of the sig- nal at about 2 kHz were used to improve the sensitivity of the experiment. The pressure was kept at about 2.5 x 10-I Torr, somewhat lower than for the other mea- surements. Above this pressure. the lines showed sig- nificant collisional broadening, whereas below it. the fluorescence signal died away quite rapidly. The micro- wave radiation was supplied either by a klystron or a backward wave oscillator, amplified where possible with a Hughes 10-W travelling wave tube amplifier. It was applied to the CH molecules from the end of an open waveguide, in some cases with the aid of a micro- wave horn. Despite this relatively crude arrangement, i t was quite easy to saturate the signals. The power levels were lowered considerably (by a factor of at least ten)

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CAN. J . PHYS. VOL. 62. 1984

R2,(6> 23 393. 5699

FIG. 2. The R2,.(6) linc of the (0.0) band of the A ' A - ~ ' 1 1 system of CH recorded by computer. Thc thrcc channels displayed arc ( i ) the CH cxcitation signal. which contains only onc linc R2,.(6), ( i i ) thc absolute-frequency calibration spectrum of ""Tc2, which contains one rncasurcd linc, and ( i i i ) thc 75-MHz fringes, which allow thc interpolation bctwccn thc tellurium and CH spcctra. Thc linc ccntres werc idcntificd by the computcr and markcd as shown. Thc frcqucncy of thc CH linc was also cornputcd.

for the stronger lines to reduce power broadening. Accurate measurements of the transition frequencies

were made by mixing a snlall portion of the radiation with a known, low-frequency reference signal, which was stabilized to 1 kHz by a Microwave Systems MOS- 5'.frequency stabilizer. Beat signals at 30 MHz werc detected with a Microwave Systems PLS-30 syn- chronizer. The reference signal was adjusted so that one of the two beat signals occurrecl close to the centrc of the line to be measured. Such measurements had a precision of 50 kHz, but an accuracy that was two to three times higher. It would have been comparatively easy to improve these figures significantly by further investment of time and money.

3. Measurements and analysis 311. Latnbckz-~loublit~~q sl)ec.tr-lrt?l ,for. t h ~ X 2 1 1 .state

A total of 18 transitions. involving five lambda dou- blets in the N = 2, 3, and 4 rotational levels of CH, has been measured by MODR, as described in the previous

section. Proton hyperfine structure causes four lines to be associated with each lambda-doubling transition, two strong lines in the centre with A F = 0 flanked by weaker, s5tellite lines ( A F = 2 I ) as shown in Fig. 3. A typical .example of this pattern is shown in Fig. 4 (see also ref. 24). The satellite lines appear much stron- ger than expected relative to the central pair because high nlicrowave power was used to record these spec- tra. causing power broadening of the main lines. The satellite lines fall so much closer to the main lines for transitions in the F, manifold that it was not possible to resolve them for the N = 2 level. The experimental measurements are given with their assignments in Table I . In all cases the transitions were observed close enough to the predictions of Brown and Evenson (23) , to render the task of making assignments quite trivial. There did, however. appear to be a systematic trend of the predicted frequencies away from the measured values as N increased. This was partly attributable to a rnisassignment in the far infrared LMK spectrum on

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BRAZIER A N D BROWN

L a m b d a - d o u b l i n g t r a n s i t i o n s I I

FIG. 3. Diagram showing the four hyperfine components associated w~th each rotational transition ~n the lambda- doubling spectrum of CH. The two main lines obey the selec- tion rule 4 F = 4 J = A N = 0. The signals for th~s transition have been shown in Fig. I of ref. 24.

which the predictions of Brown and Evenson (23) are based. More de ta~ ls of the revised assignment are glven below.

The observed trans~tion frequencies con ta~n informa- tion only on the lambda-doubl~ng and hyperf~ne param- eters. It is, theretore, necessary to constrain the rota- tional and fine structure parameten in a fit of these data. For this purpose, we have used the values determined by the LMR measurements (22). While the work was in progress, we learned of the observation of several higher N lambda-doubling transitions by Bogey et a/ . (25). We have Incorporated their measurements in our fit, together with the frequencies measured by the r a d ~ o astronomers (20, 3 1 ). The effective Hamiltonian for the molecule in a 'n state was taken in the N' formulation (32). Because A 2 B for CH In ~ t s ground state, the electron spin coupling is very close to the Hund's case b l i m ~ t . Parameter combinations appropriate to this limit (for example, p and (1) were, therefore, deter- mined. The data were welghted in the f ~ t according to the inverse square of the experimental error. as glven In Table I .

During the course of our fit of the lambda-doubling frequencies, it was discovered that there was a mis- assignment in the far infrared LMR spectrum of CH recorded at 70.5 k n ~ (22). The correct assignments are

Frequency (GHz) FIG. 4. The N = 3, J = 3; lambda-doubling transition of

the CH radical in its X"1 state, recorded by the technique of MODR with an output time constant of 300 ms. The proton hyperfine structure is labeled by the values of the quantum number F involved. The hyperfine splittings in the F , levels are smaller than in the F Z levels so that the satellite lines are not clearly resolved (see Fig. I of ref. 24 for comparison).

given in the footnote below.' Although these represent a fairly small change, they do nevertheless require a slight adjustment of the molecular parameters. Since the lambda-doubling and proton hyperfine parameters are determined-more precisely by the microwave data. the LMR measorements were refitted with these param- eters constrained to the values from the microwave fit. The lambda-doubling measurements were refitted in turn by using the revised LMR parameters. At this stage, the changes in the parameter values were so small that the iterative process could be considered to have converged. The parameter values obtained in this man-

.'The corrected assignments for lines in the 70.5-km spec- trum of CH ( F z . J = 4i + F!. J = 34) Lire

(MI = -4, \ respectively)

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C A N J . PtlYS. VOL 62. 1084

TABLE I. Experimental values for lambda-doubling frequencies of the CH rad- ical in its ground state

F, J F' F" V/ (MHz) 0bs.-Calc./(kHz) Rcf.

"The superscripts indicate the parities of thc upper and lower states involved. "Estimated cxpcrimcnral unccrtainty, in units of thc last dccimal place. 'Calculated frequency obtaincd using parametcr valucs in Tablc 2. "L. M. Ziurys, B . E. Turner, and R. I. Saykally. manusclipt in preparation. 'Prcscnt work.

ner are given in Table 2. Although i t was possible to trifugal distortion correction to the Frosch and Foley determine almost all of the fine structure and rotational parameter d (34), which governs the splitting between parameters, the sextic centrifugal distortion parameter the two main hyperfine lines and so is very reliably H was constrained to a calculated value because the determined. The standard deviation of the fit of the LMR observations did not go to sufficiently high N LMR data relative to the experimental precision is 0.94, values to allow i t to be determined (see ref. 22 for while that for the n~icrowave data is 0.79. The quality details). of f i t relative to experimental error is about the same for

I t can be seen from Table 2 that six lambda-doubling each of the three sets of microwave data (refs. 3 1, 25, parameters ( p . p,,, PH. q , ( /D , and qH) are required to fit and the present work). ,

the measurements to the experimental precision. It was When our fit was completed, we learned of the first also necessary to include some higher order hyperfine astrophysical observation of CH in an excited rotational terms, the origins of which have been discussed by level.' The two main A F = 0 components of the N = Brown el (11. (33) in a study of the OH radical. Two of the possible five parameters, Cj' and rill, are deter- ' L. M . Ziurys. B. E. Turncr, and K. J . Saykally. manu- minable for CH. The latter parameter represents a cen- script in preparation.

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BRAZIER A N D BROWN 1569

TABLE 2. Molccular paramctcrs for the CH radical in thc v = 0 lcvcl of thc x'II statc"

Dctcrmincd from LMR data

A,, =843 817.57(69)" g l = I .000879(5) B,, =425 476.852(73) g.7 = 2.0020' Dl, = 43.8255(32) I?gl = 0.1275(57)

IO'H,, = 0.350' 10-g, = 0.2820(19) , = -771.1 l(26) = 0.1182' Y D U 0.158(24) 10 '~: ' = -0.2724'

Dctcrmincd from microwavc data

p = 1003 9957(23) a = 54 28(14) Pn = -0 27335(28) h, = -57 67(20)

lo"pl, = 0 326(49) c = 5717(17) q = 11596830(12) r l = 43 5 167(40) (71) = -0 457479(47) IOdlJ -0 1601(52)

1O4ql1 = 0 9632(51) 1O'C; = 0 56(17)

"Vdluc In mcgahcrt7 whcrc dpp~opr~atc "The f~gures In parcnthcscs r e p r c ~ n t one standard dev~atlon ot the

least squares f ~ r , In units of the last quoted dcc~mal placc 'Parameter constra~ncd to thls value tor both least squares f1 t3

I , J = l f lambda-doubling transition at about 700 MHz were detected in an HI1 region (W5 I ) with the 300-ni dish at Arecibo. Puerto Rico. The assignment was con- firmed by comparison with the frequencies calculated with the parameters derived in the present work. The discrepancies between the obscrved and calculated fre- quencies were only 8 and 3 kHz for the two lines (the estimated experimental precision is 7 kHz). The new astrophysical frequencies were included in a final fit of the microwave data, but because they were so close to the predicted values, they niadc little difference to the parameter values apart froni increasing the precision with which they were determined.

Similar fits to that reported in Tables I and 2 have been niade by Bogey et ~ l l . (25) and also by Lubic and Amano (35). who have recently detected lines in the (1, 0 ) vibration-rotation band of CH with a tunable difference frequency laser. Although the parameters obtained are generally similar to those given in Table 2, the present fit must be considered superior since it in- corporates the far infrared data, whereas the other two fits d o not.

30. Rem~cr.s~rrernent ofthe (0. 0) Dcrizd qf'the A'd -X217 systetn of' CH and cleter-rnirzatiot~ of I~rtrlDd~l- douDliizg f i r . the A'A stclte

Although the A-X system of CH must have been recorded by a large number of different groups in recent years, it came as something of a surprise to discover that the best available measurements in the literature were still those made by Gero in 1941 (12) with an accuracy of about 0.05 cm-I. Since this figure is coni-

parable with the Doppler line width for CH at 300 K (2.4 GHz FWHM), it is clear that such measurements can be markedly iniproved with modern techniques. Furthermore, certain parameters such as the spin-orbit coupling constant A produce rather small splittings in the spectrum and so can be much better determined with iniproved measurements. In particular, the effects of lambda-doubling in the-A'A state have not thus far been detected. Indeed, it is very hard to find any examples of lambda-doubling in diatomic molecules in 'A states. Using theoretical estimates of the parameters involved (see below), we calculated that the lambda-doubling causes a splitting of the order of 100 MHz in the level with N = 10 for CH in the A'A state.

We have, therefore, niade careful measurements of some 40 lines in the (0,O) band of the A -X system of CH at Doppler-limited resolution. The lines are distrib- uted uniformly throughout the different branches but we have tended to concentrate on high N transitions since these are the most likely to reveal the effects of lanibda- doubling. The lines were measured by interpolation froni the nearest Te, line(s) with the fringes from the 75-MHz FSR etalon. as described in Sect. 2 (see also Fig. 2). The measurement error in this procedure was estimated to be 30 MHz. Two overlapping lines, Q I 1 ( 7 ) and Q2/ (7) , were deconvoluted by fitting 2 Gaussian profile to each. The frequencies of these Dopplcr- limited observations and their estimated errors are given in Table 3.

Because the lambda-doubling splittings of CH in the A'A state are much smaller than in the X'11 state. they are not so amenable to s t ~ ~ d y by MODR tech- niques. However, the spin-rotation splittings for the A statc fall in the convenient microwave region. We have done some preliminary work on the detection of the J = 5; + 64 transitions for the N = 6 level at about 12.65 GHz. Although it was possible to detect a signal. careful measurevents were not made at that time. We intend to make a m o r e detailed study of the A'A state of CH by MODR iri the near future.

The data in Table 3 were used to determine values for the niolecular parameters of CH in the A'A state. The effective Hamiltonian was cast in the same N' form (32) used for the 'n state. The lambda-doubling (LD) terms for the 'A state were described by

[ I ] % , , , = ; c l ~ ( J : + J J ) - ! ( / ) J + ~ L / J )

x C J : S , + J ~ S - )

where it is understood that the terms in J : connect basis states with AA = -4 and so on. This formulation is a natural extension of that accepted for I1 states (see for example. ref. 36). It can be seen that the lambda- doubling intervals depend on two parameters, q, and (pJ + 4 q J ) for Hund's case a coupling or p, and el, for

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TABLE 3. Measu red wavenumbers ( c m I ) o f lines in the (0,O) band o f the A'A-x'II transition o f the CH radical

N R I Q I P I "P. , R2 Q. Pz

"The figures in parentheses are the estimated errors of measurement, in units of the last quoled decimal placc. "There arc two entries for each rotational transition. The first corresponds to the transition from the P parity component of the lower levcl involved, the second to

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BRAZIER AND BROWN 157 1

TABLE 4. Matrix representation of thc cffectivc Hamiltonian for a moleculc with given J value in a 'A statc

I J , 512) 1 J , 312)

A + f y + y,, + B ( z + 2) - ~ ( z ' + 5z + 4)

+ H ( z 3 + 9 z 2 + 22z + 8)

NOTL. Thc upper and lower algn choiccs rctcr to and f lcvcls rc\pcctivcly. z = ( J + +)' - 4 = ( J - 3 / 2 ) ( J + 517) R ( F ) = F ( F + I ) - J ( J + I ) -- l ( 1 + I )

TABLE 5 . Molccular parameters for the CH radical In thc v = 0 level of thc A'A state (in cm I)

"Numbcrs in parenthcscs rcprcscnt onc standard deviation crror estimates, in units of the last quoted decimal placc.

Hund's case b coupling. The matrix representation of the effective Hamiltonian for a given J value in a Hund's case a basis set. as used in our calculations, is given in Table 4 .

The frequencies of the 'A-'11 transitions in Table 3 were fitted as such with the parameters for the lower '11 state constrained to thc values obtained earlier (see Table 2). Since the measurements were Doppler- limited, the effects of proton hyperfine structure were not included. There was a considerable variation in the accuracies of the measured frequencies and so a weighted least squares fit was performed, with each line being weighted according to the inverse square of its overall measurement error as given in Table 3 . The parameter values determined after a few lincs with large errors had been omitted are given in Table 5 . The stan- dard deviation of the fit relative to experimental error was 1.23. The values obtained for A. B, and D are consistent with those determined earlier ( 12, 14), but are much more preclse. A number ot other paranieters for the A'A state are also determinable but it can be seen that only one of the two lambda-doubling parameters, qA, is properly deterni~ned in the flt.

T o appreciate better the slre and variation ot the lambda-doubling w ~ t h N, we have deternilned the lambda-doubllng Intervals for the 'A state by sub- tracting the corresponding ~ntervals for the 'n state from the observed spl~ttings In the spectrum. Fortu-

TABLE 6. Lambda-doubling intervals for CH in the A'A statc

Splittings (MHz)

Lcvel Observcd Calculated Obs. -Calc.

nately, the niicrowave measurements have been made up to quite high N values. and it was possible to extrap- olate them with confidence to the limit required ( N = I I ) . Thc results of this calculation are shown in Table 6. In most cases, the value given is an average from P-, Q-, and?-branch lines. The rather wild tluctu- ations in the "observed" values, which are a man- ifestation of measurement error, tend to mask the expected rapid increase in the splittings with N. The calculated values show this trend more clearly. The splittings are of a similar magnitude for the two spin components ( F , and F 2 ) , as expected from the esti- mated values for the parameters pA and 4,.

3 . . Me~~s~lt.eruetzt L I ~ I L ~ ~1 t1~1 j~~ i . s of' tlze prototz h\y)et;fi'tze splittitzg qf' CH itz the A'd st~lte bjl srrtllratiotz s j ~ ~ 2 ( ~ t t ~ o s ( ~ o j ~ ~ (irztertnod~ll~~t'e~l fl~loresc.etlce)

The strongest lines in the ( 0 . 0 ) band of the A -X transition of CH were also recorded at sub-Doppler resolution by the technique of intermodulated fluo- rescence. as descr~bed in Sect. 2 . These lines were associated with the first four transitions in the Q- and R-branches. Allowing for the effects of spin- and

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CAN. J . PHYS. VOL. 67. 1'184

FIG 5 The proton hypcrflne structure on thc Q1,(3) llnc of the (0.0) band ot thc A"-XX'II transltlon ot CH, recorded by thc techn~que of ~nterrnodulatcd fluorcsccnce The lines arc labeled by the values of the quantum numbcr F lnvolved Thc observed spllttlng arlses prlmarlly from the hypertlne Inter- action In the A'A statc The relatlvc lntenslty of thc two llncs allows an unarnblguous asslgnmcnt ot thc quantum numbcrs

lambda-doubling. we obtained 32 lines all together, of which 28 were measured in the present work. The signal-to-noise ratio was never particularly high, ranging from 50: 1 at best down to 5 : I , all recorded with a I-s output time constant. The widths of the lines depended on the pressure at which the recordings were made. The best figure achieved was 20 MHz FWHM at 3 x lo-' Tors total pressure, although some transitions were recorded with a line width of about 50 MHz.

For transitions between the higher rotational levels, the spectrum consisted ofjust two lines separated by the proton hyperfine splitting. A typical example, in- volving the Q,,(3) line, is shown in Fig. 5. The differ- ing intensities of the two lines allow an i~nambiguous assignment of the F quantum numbers involved (which in turn means that the signs of the hyperfine parameters are deterrilined). The splitting observed in the spectrum is a combination of ground and excited state splittings. Since the ground state hyperfine structure is well char- acterized bv the microwave and LMR measurements. it is straightforward to remove this contribution to the observed splittings and determine the splitting for the 'A state alone.

The spectra associated with the first two lines in the R-branch were more complicated in structure. In addi- tion to the two main hyperfine co~iiponents (with A F =

+ I ) . they also showed weak satellite lines ( A F = 0) and strong crossover signals (37). The latter are two- photon transitions. which occur at the mean frequency of a pair oftransitions with a common upper (or lower) level. The sub-Doppler spectrum associated with the

- Frequency L 5 w ~ z ,,r

FIG. 6. The proton hypcrfinc structure on thc R, ( I ) l~nes of the (0.0) band of the A'A-~'11 transition of the CH radical, recorded by the tcchniquc of intermodulated fluoresccncc. The lines arc labeled by thc values of the quantum nurnbcr F involved. For the R, , ( I ) transition, thc weak F = I + I satellite line is also visible; thc corresponding line is not resolved for the R2,.(1) transition. Crossovcr signals between two one-photon transitions with a common lowcr lcvcl arc mr?rked with asterisks.

R 2 ( I ) transitions is shown in Fig. 6. For the R2,(1) component, the F = 1 + I transition can be seen as a weak feature between the other lines. but for the R,,.(i) line, i t is overlapped by the stronger F = 1 + 0 com- ponent. In both cases, the crossover signal involving the I + I and the stronger 2 + I line is clearly visible and is marked with an asterisk. The observation of such features would be useful to break the experimental cor- relation between the hyperfine splittings in the upper and lower levels had the microwave information on the ground gate splittings not been available.

The hyperfine splittings measured in this way are listed in.Table 7 with the estimated errors of mea- surement. In the final column of this table, the ground state contribution to the splitting has been removed to give values for the splittings of the levels in the A'A state alone. It can be seen that the splittings are large, particularly for the Fl levels where they start at about 450 MHz and fall to 350 MHz by N = 5. For the F2 levels, the splittings increase with N, from 150 MHz up to about 220 MHz. The splittings for the e andfcom- ponents of the 'A levels are the same to within experi- mental error.

The splittings in Table 7 were used to determine the three magnetic hyperfine parameters for a niolecule in a 'A state, ci, 0 , and c in the notation of Frosch and Foley (34). The fourth parameter, r l , does not affect the hyperfine splitting' in first order. In higher orders, i t

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BRAZIER A N D B R O W N 1573

TABLE 7. Proton hyperfine splittings for lines in the (0.0) band of the A'A-x'II transition in CH, measured by inter-

modulated fluorescence

Line

Observed Measured value splttttng (MHz)

3 2 - 2 I 463 8(10)" ( 3 - 2 + ) - ( 2 - 1 ' ) 441.6(30) (4 - 3 ) ( 3 2 406 5(19) (5' -4-) -(4' -3 ) 404.7(30) ( 5 - 4 - 4 3 383.8(15) 6 - 5 ) - ( 5 - 4 ) 394.9(15) 6 5 5 4 ) 376.1(23) (3 -3')-(2 -2') 480.8(12) ( 3 - 3 ) - ( 2 - 2 ) 464.3(12) (4+-4 )-(3'-3 ) 437.5(14) ( 4 - 4 + ) - ( 3 -3') 415.4(20) (6 -6')-(5 -5') 381.3(20) ( I - 0 - ( 2 - I ) 173.9(40) ( I 0 ( 2 - I ) 226.9(40) 2 I - 3 2 ) 232 3(14) ( 2 - I - - 2 257.2(14) (3--2+)-(4 -3') 247 7(11)

Observed - ground

state

"Figures in parentheses represent the estimated measurement error, in units of the last quoted decimal place.

would cause a difference in the splittings for e and f levels, but such effects are too small to be significant with the present precision of measurement. The matrix elements diagonal in J for the three hyperfine ternis required are given in Table 4. Because of the relatively large spin-rotation splittings for CH in the 'A state, the matrix elements off-diagonal in J have only a very small effect, which was ignored in the present work. In the least squares fit, the rotational and fine-structure parani- eters were constrained to the values previously deter- mined and given in Table 5 . The obsei-ved splittings in Table 7 were reduced to a set of eight splittings for the N = 2 to 5 levels of the F, and F? components given in Table 8. The three hyperfine parameters in Table 4 were fitted to these eight splittings in an unweighted least squares fit, the results of which are also given in Table 8 . The standard deviation of the fit is 2.7 MHz, in con~plete accord with the estimated errors of mea- surement given in Table 7. All three hyperfine parame-

TABLE 8. Results of the fi t of the proton hypcrfine splittings for CH in the A'A state

Splittings (MHz)

Level Observed

F l N = 2 448.0 F , N = 3 401.4 F I N = 4 369.2 F l N = 5 359.2 F ? N = 2 159.6 F z N = 3 183.6 F ' N = 4 203.5 F z N = 5 216.7

Calculated

NOTE: Parameters determined: tr = 57.26(85)MHz; 1) = 563.6(34) MHz; c = 61.4(80) MHz. Standard devia(ion of fit = 3.7 MHz.

ters are wcll determined. I t can be seen that the large hyperfine splittings arise predominantly from the pa- rameter b (in essence, the Fermi contact interaction at the proton).

4. Discussion 40. The rlerertt~itlatiot~ c!f'Itrttlhtltr-do~rbli11g itlter1~rl.s I7y

LMR We have described the measurement of lambda-

doubling intervals in the CH radical in its ground state by MODR. Quite apart from their intrinsic value, these observations demonstrate an impressive sensitivity for such a measurement. Admittedly, all the various factors seem to work in favour of this particular experiment: the niolecule is light with a large rotational partitim func- tion; the optical transition is very strong so it is readily saturated and accompanied by a strong tluorescence (visible by eye at a wavelength where the retina is a rather insensitive detector); the microwave transitions are strong (dipole moment = 1.46 Debye, ref. (38)) and even if they wipe not, high power levels are available in this region of the spectrum. Consequently. the signal-to-noise .ratios recorded in the pfesent work are much higher than those usually achieved in MODR experiments. It is certainly not unrealistic to suggest that even more elusive species, such as molecular ions, might be studied in the same way. One obvious candi- date for such a study is N H i . which is iso-electronic with CH (39).

The measurements on CH have extended our knowl- edge of the lambda-doubling frequencies to all the excited levels that are likely to be of interest to radio astronomers. Indeed, as we have rncntioned earlier, transitions in the first excited rotational level ( J = 14, F , ) at about 700 MHz have recently been observed4and are confirmed by reference to our frequencies. The level involved is only 18.9 cm- ' above the lowest. J =

level. The next level up is the J = 14, F? component,

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1574 C A N . J PHYS. VOL. 62. I984

which lies 67 cni-' above J = $. The microwave fre- The dominant configuration for CH in its ground 'II quency in this case is around 7.3 GHz (see Table I ). state is I u '2u23u ' I T', where the 3 u and I .ir molecu-

46. Ir~terpretation of rnoleclikir pclrameter:s for CH in the X 2 1 1 stclte

The molecular parameters for CH in its ground state have been collected in Table 2. The values for the rotational and fine structure parameters have been im- proved slightly by refitting the far infrared LMR data, but the changes are so small that the interpretation of these parameters as presented in ref. 22 is unaffected. The main achievement of the present work is a consid- erable refinement of the lambda-doubling and proton hyperfine parameters. Both types of parameter contain information on the electronic wavefunction.

lar orbitals are primarily carbon 2 p u and 2p.ir atomic orbitals. The lowest excitation from the ground state involves promotion of an electron from the 3 u to the I .ir orbital, l u ' 2 u 2 3 u ' I v'. Four electronic states arise from this configuration, (I"%-, A'A, BIZ-, and C'Z I ,

all of which have been observed (40). although very little is known about the "Z- state. The lambda- doubling parameters p and q measure the contamination of the 'II state by 'Z ' and 'Z- states through sp~n-orbit coupling and Coriolis effects. Such mixing can be treated by perturbation theory and, to second order (4 I) , we have

[2] p = -2 C { ( ' ~ l l l ~ ~ s o ~ r ~ ' ~ 1 1 2 ) ( r 1 2 ~ 1 1 2 ~ - B ~ l 1'11-112) + ( ' I 1 1 , 2 ( - B ~ , 1rz2Zl12) ,2

x (~12Z- l12J~so(2n- l l?) ) / (~ l l - EL) and

In the evaluation of these expressions, it is necessary to use spin-orbitals that are antisymmetric with respect to permutation of any pair of electrons and that also be- have correctly on interchange of pairs of orbitally equivalent electrons. The determinantal wavefunctions for the various electronic states involved are given in the upper part of Table 9. The experimental values for p and q can be tolerably well reproduced by a very simple calculation in which the valence orbitals 3u and I T are represented by carbon 2p, and 2p, , p,, orbitals respectively (41, 42). The matrix elements required, evaluated with this approximation, are given in the lower part of Table 9. Their substitution in the expres- sions for the lambda-doubling parameters gives

[5] q = 2{B2/(EIl - E x + ) - 3B2/ (EI l - Ex-)}

Taking B = Bo for theX'Il state (14.19 cm-') , ( = 27.5 cm-' for a carbon 2p orbital (431, (E l l - El - ) = -25 697 cm-' , and ( E l l - E x + ) = -3 1 777 cm-' gives p = 1654 MHz and y = 1030 MHz. These values compare quite well with the experimental ones in Table 2 ( p = 1004 MHz, q = 1160 MHz), particularly the value for q. Obviously the pure precession approx- imation is rather severe, but the value for p may also reflect neglected contributions from other electronic states, notably the u J C - state, which lies only 6000 cm-' above the X'II state (44).

Full ub initio calculations of the lambda-doubling

parameters of CH have been made by Richards and co-workers (17, 42). The best result quoted in ref. 42 givesp = 1037 MHz and q = 1136 MHz, in very good agreement with the experimental results. Rather re- markably, the value for ( p + 2q) , which governs the lambda-doubling in the lowest J = 4 level, is calculated to be 331 1 MHz, in almost perfect agreement with the experimental value of 3324 MHz.

The higher order lambda-doubling parameters are harder to evaluate theoretically. However, it is worth noting that the approximate formulae given by Veseth (45) for p, and q,, viz.,

[6] p~ < - 2 p D I B and q, = -4qD/B appear to be quite reliable in this instance. The expres- sions in [6] give p, = -0.206 MHz and q, = -0.476 MHz, compared with the experimental values -0.2735 MHz and -0.4575 MHz respectively.

Of the other parameters in Table 2, the spin-rotation parameter y can be estimated in a fashion similar to that used for p and q. This parameter is a measure of the admixture of both 'C and 'A states,

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BRAZIER AND BROWN 1575

TABLE 9. Results for the estimation of parameters in the effective molecular Hamiltonian for CH

Spin-orbital representations of low-lying states of CH

Matrix elements

( I ) Spin-orbit coupling HSO = 2 <,1;s,

( 2 ) Rotational Coriolis mixing H,,,, = - B( J+L- + J - L + )

NOTE: The approximate equality in each expression corresponds to the agsumptlon of the pure precession hypothesis: ( 2 , > ~ , ( 1 , 12pu) = [ / ( I + I ) - I .0]"' = a.

Substituting the pure precession results from Table 9 , we obtain

[8] y = -B{{- l / (E l l - E l + ) + l / ( E l l - El )

- ~ / ( E I I -

Taking ( E l l - E A ) = -23 217 cm-I, y is estimated to be -920 MHz, again in quite good agreement with the experimental value of -771 MHz. It should be noted in [8] that the contributions to y from the '2' and '2- states cancel almost exactly. The experimental value reflects primarily the mixing with the A'A state (the calculated contributions from the ' x i , ' 2 - , and 'A states are -368, +455, and - 1007 MHz respectively). It should also be remembered that the experimental value refers to an effective parameter that has absorbed

a contribution from the spin-orbit parameter A" (46), so that exact agreement with a calculated value for y is not to be expected anyway. The two contributions to y can be separated by a study of the far infrared LMR spec- trum of CD; this is in progress (22).

The four first-order hyperfine parameters for the pro- ton in CH have been determined in a fit of the micro- wave data. The values have not changed much from those determined in the earlier fit of the LMR data (22), but are now about an order of magnitude more precise. Levy and Hinze ( 1 I ) calculated values for a , b (= b, - ;c) and c by ab itzitio methods while constraining the only hyperfine parameter then known, d, to the value determined from the astrophysical data. Their values are 58.5 + 4.5, -72 + 10, and 57 + 4 MHz, re-

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1576 CAN. J . PHYS. VOL. 02. 1984

spectively, which agree reasonably well with the ex- perimentally determined values of 54.3, -76.7, and 57.2 MHz. As is well known (34), the parameter a is a measure of the coupling with the electron orbital angu- lar momentum, whereas c and d involve the electron spin angular momentum. Both interactions depend on the average value of l / r3 , where r is the distance of the unpaired electron from the nucleus. The values in Table 2 are consistent with

( 1 /r3)sPin = 1 . 1.5 ( 1 /r.')c,rb,, a result that is very similar to that for the radical OH in its ground 'n state (47). The values for the higher order hyperfine parameters for CH, d, = -0.016 MHz and C ; = 0.006 MHz, are also quite similar to the values determined for OH of -0.0228 and 0.0065 MHz re- spectively (33).

4c. I~zterpretation c?f' molecular parclmeters .for C H in the A'A state

Tables 5 and 8 give the values of eleven molecular parameters required to describe the energy levels of CH in t h e ~ ' A state. The spin-orbit coupling constant ( - I. I cm- ' ) is very small compared with the value for the ground state of 28 c n - ' . The fine structure splitting in this case arises from the two electrons in the In orbital, and because their spins are paired, the two individual contributions largely cancel out.

Three rotational parameters, B, D , and H , are re- quired to describe the observed transitions. The calcu- lated value for H,. Ho is 0.77 x cm-' (22), compared with the experimental value of 1 .O1 x cm-' . This discrepancy reflects the combined effects of deviations from the calculated values for CH in both the

X'n and A'A states, as the calculated value for the X state (Table 2) has been used throughout in our analysis. The difference is not large enough to suggest that the value assumed for the ground state is not valid.

The spin-rotation parameter y for the A'A state may be estimated in the same way as for the X'n state described earlier. For this state, the parameter describes the admixture of 'n and states. The main con- tribution, which arises from the mixing of the X'n state, has already been calculated in the previous sec- tion as 1007 MHz (the sign has been changed because the order of the two states involved is reversed). How- ever, there is also a contribution from the next higher 'n state, the D 2 n state, which arises from the config- uration I u 2 2 u ' 1 IT.' (13). The spin-orbitals required and the matrix elements involved in this state have also been given in Table 9. Taking (E, - El , ) as -35 764 cm-' , the extra contribution to y is calculated to be 668 MHz, giving a total value of 1676 MHz. This is to be cornpired kith the experimental value of 1264(16) MHz. The agreement is fairly good. As for the ground state, the theoretical estimate is larger in magnitude. Again, the experimental value has an undetermined contribution from the spin-orbit parameter A[,.

Table 5 also reports the partly successful attempt to determine the lambda-doubling parameter for CH in its A2A state. The splittings are produced through inter- action with remote 'C states through the intermediary of 'n states. Such effects are expected to be very small since they arise only in the fourth order of perturbation theory. Adopting the definition of the lambda-doubling parameters given earlier in [ I ] , it can be shown that

Making the pure precession hypothesis, we are thus in x cm-' and q, = 1.547) X lo-" cm-' with l u a position to make an estimate of these two parameters. error estimates in parentheses. The two sets of values Using the expressions given in Table 9 and taking the are in fair agreement, sufficient at least to give one 'n state to be the ground state, we obtain p, = -3.34 confidence in the somewhat marginal experimental x cm-' and q~ = 3.29 x cm-' . For com- data. It is nevertheless clear that rather better mea- parison, the two experimental values are p, = 10.(12) surements are needed to test the model for the lambda-

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BRAZIER AN[> BROWN 1577

doubling more thoroughly. It should be possible to make such measurements by studying the spin-rotation splittings for the A'A state by MODR, as we have men- tioned earlier.

Three proton hyperfine parameters, a. b, and c, have been determined for CH in the A'A state (Table 8). As is well known (34), they provide information on the distributions of the open:shell electrons:

[I 11 a / H z = CLoI4rh C ~CLB~NCLN( 1 /I.,')

in the usual notation (48). The expectation values In these equations are evaluated over the spin-orbltals for the 'A state, as given in Table 9 for the configurat~on 1 cr'2cr'3w1 I r ' . Since the orbital angular momentum is carried by the electrons in the I r orbital, only they contribute to the parameter a. On the other hand, the two electrons in the 1r orbital have their spins opposed, so they do not contribute to the spin-dependent pararn- eters bt and c .

Let us first consider the nuclear spin electron orblt interaction a. The spin-orbital wavefunctions in Table 9 suggest that the interaction in CH in the A'A state should be identical to that in the X'n state (both arise from electrons in the I r orbital). T h ~ s suggestion is well supported by the experimental results X'n: a = 54.3(3) MHz and A'A: a = 57.3(17) MHz (2cr error estimates in parentheses).

Next we examine the Fermi contact interaction br. As can be seen in Table 8, the data were fitted to the Frosch and Foley parameter b since this is the quantlty that determines the hyperfine splitting for large N values. Since the dipolar parameter c was also determined, b, is readily calculated,

I br- = b + 3" = 584(9) MHz

This value is strikingly large and corresponds to an electron density at the nucleus q(0) ' of 0.883 X lo3" m-3. The expectation value in [I21 is evaluated over the 3 u orbital. So far, we have represented this orbital reasonably satisfactorily by a carbon 2p, orbital. The electron density at the proton may be estimated by writing the 2pcr wavefunction as a Slater-typc orbital. The resultant contribution to b, is 78.9 MHz, very much less than the value above. The explanation for this dis- crepancy is that only a small amount of hydrogen I s character is required in the 3 u orbital to explain the

observed value of bl:. If the 3cr orbital is represented by

where 4, is the carbon 217, orbital and 6' is the hydro- gen I s orbita!, the experimental value for qrl,,(0)' cos- responds to c; = 0.82, ci = 0.18 (neglecting overlap in the normalization of [14]). Such a contamination of the 3 u orbital is consistent with the at) irlitio calculations of Cade and Huo (49).

Finally, we consider the dipolar hyperfine parameter c , [ I 31. We require the expectation value of the operator (3 cos' 18 - I ) / r 3 . evaluated over the orbital 3cr. For the linear combination [14], only the carbon 2p orbital gives a nonzero contribution. It can be estimated by the method of McConnell and Strathdee (50), with a sub- sequent correction (5 1 ) to take account of the singu- larity at the proton. Using a Slater orbital for the C2p orbital, we obtain

On substitution in [I31 with c f = 0.82, we estimate the value of c to be 135 MHz. This is somewhat larger than the experimental result of 6 l(16) MHz. However, the calculated value is quite sensitive to the involvement of the carbon 2s orbital in [I41 and very sensitive to dis- tortion of the hydrogen I s orbital by electrons in the C-H bond. In view of this. the agreement with the experimental value is satisfactory.

4d. Flirther work Further work on the A2A state of CH is required to

characterize the lambda-doubling and hyperfine inter- actions better. We have already alluded to the possi- bility that such information can be obtained by MODR.

We have also done some preliminary work on the analogous molecule SiH (52). Silicon has a fairly large cosmic abundance and there is quite a high probability that SiH is a coastituent of the interstellar gas clouds. However, i t has not yet been detected by the radio astronomers, at least partly because the lambda- doubling spectrum has not yet been recorded in the laboratory. The A'A-X'II transition of SiH is at slightly shorter wavelengths (410 nm), which is a more difficult region for the operation of a dye laser. Further- more, there is good evidence that thc dipolc moment is very small (53). However, this should not bc a serious limitation for the MODR experiment since such high microwave powers are available.

Acknowledgments We would like to express our gratitude to Dr.

Timothy Steimle, who taught us both how to perform successful MODR experiments. We also thank Dr. Brian Howard for the loan of some microwave equip- ment. We are grateful to the Royal Society and the

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1578 CAN. J . I'HYS. V O L . 61. 1')S-l

Science and Engineering Research Council, Great Britain, for equipment grants and the financial support of one of us (C .R.B. ) .

1 . T . HEURLINGER and E. HULTHEN. Z. Wiss. Photogr. Photophys. Photochcm. 18. 241 (1919).

2. R. S. MULLIKEN. Phys. Rcv. 30, 785 (1927). 3. 1'. SHII)EI. Jpn. J. Phys. 11, 23 (1936). 4. T. DUNHAM and W. S. ADAMS. Publ. Astron. Soc. Pac.

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