Phase- and energy-changing collisions in iodine gas: Studies by optical multiple-pulse spectroscopy

Volume 110, number 6

PHASE- AND ENERGYCHANGING STUDIES

CHE_MiCAL. PHYSICS LETI-ERS

COLLISIONS

BY OPTICAL MULTIPLE-PULSE

19 October

1984

IN IODINE GAS:

SPECTROSCOPY

Edward T. SLEVA and Ahrned H. ZEWAIL l Arthur Amos Noyes Laboratory of Chemical Physics 2, California Institute of Technology, Pasadena, California 91125, USA Received 21 June 1984

Using phase-coherent optical multiple-pulse spectroscopy, we report the measurement of phase- and energy-changing coIlisiona1 cross sections in I2 gas. WC obtained the following cross sections: ophase = 590 -C110 AZ and oenergy = 227 f 12 A2. At 30 mTorr, 40% of the homogeneous is due to phase-changing collisions, and the total Iinewidth therefore does not give the lifetime directly.

1. Introduction

In a series of papers from this laboratory [ 11, we have described the technique of (phase-coherent) opticalmultiple-pulse spectroscopy and some of its potential applications. Basically, the technique involves optical pulse trains in which the phase of each pulse relative to the other pulses is specified. To achieve these sequences of multiple and phase-coherent pulses (optical analogues of NMR sequences), we have acoustooptically modulated a continuous-wave laser; this approach, developed by Zewail and Orlowski, permits one to measure the coherence of an ensemble of molecules while detecting only incoherent fluorescence [2]. The advantages of this method are discussed elsewhere [ 121. In this Letter, we report the use of this technique to measure phase- and energy-changing collisional cross sections in I2 gas. These were obtained from measurement of the coherence and fluorescetrce decays as a function of pressure. We also improved on our earlier measurement [l] at a f=ed pressure in order to assess limitations of the technique and to achieve optimum signal-to-noise ratio. The signal-tonoise of the photon echo obtained here is at least 20, and the echo is back ground-free. For Ia, we obtained ’ Camille and fienry Dreyfus Foundation Teacher-Scholar. 2 Contribution # 7042. 582

the following cross sections: upphase = 590 I 110 A2 and *energy = 227 i 12 R2. These values are consistent with previous measurements and demonstrate the large difference in the cross sections for these types of collisions.

2. Experimental In these experiments we used a single-mode ring dye laser (Spectra Physics model 38OA), pumped by an argon-ion laser. The laser is equipped with several tuning elements. A birefringent filter serves to introduce losses which become larger as one moves away from the frequency of interest. A 900 GHz etalon further restricts the number of available modes, and a 75 GHz etalon is used to select a particular mode from the few remaining. The peak of the 75 GHz etalon is electronically locked to the cavity mode in order to prevent mode hops. Laser mode structure was monitored with a Spectra Physics model 470 scanning interferometer and the wavelength of interest was determined with a Jarrell-Ash monochromator. Coherent visible radiation at 589.7 run from the ring dye laser was focused into a Harris model 190 acousto-optic modulator. The modulator was driven to 70% diffraction efficiency by 500 mW of a 480 MHz electrical signal and displayed a pulse risetirne of 0 009-2614/84/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

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CHEMICAL PHYSICS LETTERS

rection of laser beam propagation_ In this scheme, only incoherent emission is detected_ The signal was preamplified and processed by an EG & G model $65 gated integrator and a model 162 boxcar averager. The rf quadrature section that was built to produce the required phase-coherent radiofrequency pulses is now described. A frequency synthesizer was used as a stable source of 38.4 MHz cw signal at 17 mW. Two

=4 ns. The first-order diffraction peak was spatially filtered from the rest of the diffraction pattern and collimated prior to passage through the sample cell. The optical pulses were detected after passage through the sample cell by a fast photodiode and were displayed on an oscilloscope throughout the experiment_ A photomultip~er tube was used to detect the fluorescence emitted in a direction perpendicular to the di-

I

Frequency

Fig. 1. Schematic diagram of the radioficquency modulation

of the (single-mode)

synthesizer

quadrature

19 October 1984

H

Filter

H

section used for generation

of multiple-pulse

trains by acousto-optic

laser beam.

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CHEMICAL PHYSICS LETTERS

frequency doublers were used in series to raise the signal frequency to 133.6 MHz. The 133.6 MHz signal was amplified with a simple transistor circuit and then filtered. The filtered signal was fed into a series of two broadband amplifiers; the output was filtered once more and then sent to a power splitter/combiner. One component of the split signal was fed directIy into tfte local oscillator input of a mixer and the other component was frequency doubled and filtered before being sent to the intermediate frequency input of the smc mixer. The mixer yields a frequency output of 461 MHz, which is filtcrcd prior to further amplification. This rf signal is fed to the quadrature section proper, whiclt consists of a quadrature hybrid, two 2way I SO” power splittcrlcombiners, four rf switches and a 4-way O* splittcr/combincr. The co~~~po~uxrtsarc configured as in fig. 1, The original signal is split into IWO phase COII~IOIICII~S,which arc switched 011or off by the rf switches prior to recombination. Variable resistors and capacitors arc used for fine twcaki:l~ of relative ail~l~litudes and phases with a vector voltmeter. The rfswitchcs itrc TTL-triggcrcd dcviccs. Thcrclbrc, csccution of :I given rf pulse sequcncc reduces to the trivial problem oft;cncratingan appropriate TTL switching sccpci~cc. Scanning of the pulses may be achieved by tri~~eriti~ from the boxcar. as this device hns a coI~vei~ieil1 scanning mode. The S:IIU~ICcell consistsofa glass bulb with Bruwstct windows ~~IKIiI teflnn stopcock. Prior to salnl>lc l>rcp;lr;ltion, lllC Cdl Wits bilht Olll with IlCillill& IillIC while iIt*

19 October

1984

tached toa vacuum manifold until a vacuum of =:1 X 10m8 Torr was achieved. iodine was then introduced by distillation at O°C into a side arm of the sample cell. This side arm was also used during the experiments to immerse the iodine crystals in various low-tcmpcrature baths in order to control the vapor pressure. The dcpendcncc of iodine vapor pressure upon temperature is given by an equation of Giauque [3].

3. Results and discussion The pulse scqucnce

J-YJYL_

used hcrc is:

*...*

JY-LFL

The XXX scqt~c~~ceis comprised of three l~~lscs that arc in pliusc with oiic imuthcr, while in the XXX scqucncc, the third pulse is phase-shifted by 180° from the first two. The XXX sequence signal serves as n bascline for the XXA? sequence, so that the pure echo shapt: isobtuincd from the diffcrcncc between the first (XXX) and the second (XX%). Prior to taking 1’2 nmsurcIllCIIlS, ill1 CC110StlilpC for il lNlrticuliir VillUC Of T WilS rccordcd in order to ascertain that the siynul observed for T = 7’ would in fact be the aitil~litudc of the dcc:tying echo. A typical echo for grtscous ioditlc is shown in fig . 3-, and an C&O &XXY is SIIOWII io fig. 3. A Slcrn-Volmcr plot of 7)-J, the rcciproool lluorcsccncc lifctimc. versus prcssurc is displuycd in fig. 4

iJig. 2. ‘rypicalccho forguseolls iodioc III 30 m’l‘orr, obtained with ll~cscqucncc XTXT’X . .. XTXT’~; T wus fiscd and T’ WDSvaried. Note Ihat, us c.\pectcd, lhc who m;hmmll occurs 121 when T f 7’. Now also thnt the bnckgound on the echo is csscntiully zero, yielding ;I kg11 S/N ratio.

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CHEMICAL

PHYSICS

LETTERS

z-. C In

5

E

-

-

T, = 947

?I7 ns Rote

(/A’)

_.-.’

;

T,;’

100

200

400

300

Time

./”

X/H

*

__--

__---

500

(ns)

Fig. 3. Echo dccuy Tar gnscous iodine ut 9 rn’l’orr. obtuincd by using thr scqucrlcc in fig .2 but varying t (in this cusc r = 7’). I’hc three pubc ussd lwc n width ol’ 100 11s. Diacusslon ot. the rcliltionsliip of puhc duration to the appcurcncc of inhon~ogcncous broadcninp clfccts can bc found hi ref. [ 11.

, '0

!

20

Pressure (mTorr)

togctlicr witlt tltc T! I! mcasurcmcnts mudc by Orlowski ct al [4]. Tlu? Stern-Volmer plot is lincur over tlrc prcssurc range used in our cxpcriincnts. TIE fluorcsccttcc lifctitnc Ibr gsscous 1, is dictated by two proccsscs, llic first of wlriclr is loss of population by spontaneous ciiiissioii, im.! tiic second loss tltrouglt collisiottW!uccd qttcnclting. T!IC Iifctitnu of

I2 mcnsurct!ttt zero prcssurc (ix. r~mtsurcdin tt bctttn) is 1.3 ps [4]. From tllc results in fig. 4, wc dcducc the rc!otions!tip IIT,, = 0.824 + 0.0164~ /JS- ,

(1)

wlrcrc p is tltc prcssurc in nrliwr. From cq. (I), the C%tlYl!~O!titCd zero-!xessurc T, e is 1.22 MS,wlticlt is in good ogrccmcnt witlt tltc bcum voluc. Tlw error involved in cq. (1) is cxanplified by the uncertainty drawn in fig. 4. Because of collisions, it can bc shown that tire slope, b, of cc!. (1) may bc related to tlrc non-radiative collisionul quenching cross section u by the expression

iSI* 0 = akT/v )

(3

*Note that the (I reportedin ref. [S] isu cross-sectional nrca (as opposed to D collisional distance).

Pig. 4. The Iluorcsconcc decay (I’tc) nud rohcrcncc dcca) (Tz) rutcs plotted us u function of prcssux. Tlic Tz dnti~indicutcd by 11trhnt;lu corrcspond to tits in which long-thnc dut:~ (tukn uftcr tha onset of transit-time sffccts) IIWC been used. wldk dntu indicutcd by n circb corrcspond to fits in which datu which dsviatus from tllc liner fit hove been discudcd. Also rhown uro ‘I’, u dstu us P function of prcssurc along with the T,, rssults of rsf. 141. Our nwsurcuwnts of Tt, uro in ugrocnirnt with those ol‘rcf. 14 1: the two tines dnl\vn uround tho ‘1‘1, uuxsurcmcnts rcprcscnt tllc limits of c’rror on Tt OS‘111~circle ut zero prcssurc indiwtcs rhc rptc obtuiucd in a alolccuhr bwm.

wl~c k is the Boltzmann constant, I’tl~e tcmpcraturc, and 0 the thcmxt! rclativc velocity for tltc collisiott pair. At room tcmpcmturc, u‘= 2.24 X lo2 m/s. Knowing b from the data of fig. 4, the value obtained for the energy-changing collisional cross section uE = 227* 12G. Sim!!arly. T2 was measured for iodine in a bulb as n function of pressure. (See figs. 3 and 4; the slight dcviation of tlic plot from linearity at long times in fig. 3 is due to transit-time effects.) T!lc plot of Ti_’ versus pressure (fig. 4) e.x!tibits the anticipated linearity, and evidently TF1 < ?‘i’ at zero pressure. From the data of fig. 4. we deduce the following relationship for Tztype (coherent) processes:

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110, number

6

CHEhlICAL

l/T2 = 0.42 + 0.06~ /.Ls-~ . For two levels interacting

PHYSICS

(3) with a bath [6],

(4) where Tie and Tls are the excited- and ground-state* decay times, respectively. Ti is the pure dephasing time constant. Two points must be noted here. First, the cross section for phase-interrupting collisions can be obtained provided Til is known. Second, at zero pressure, @;)-I + 0 and TIWgl+ 0 (ignoring radiative emission); we therefore expect that

T-,(zero pressure) = 2TIc E 27fluoresccnce _

(5)

In some cases it is assumed that TI e = Ti 6, and under this condition [from eq. (411, T2 = T, ,.~The results of TI e and T, measurements near zero pressure constitute a cruc~l test ofthe validity of this assumption. Near zero pressure, a rovibronic state in the ground manifold of I, (Z state) can only relax by spontaneous radiative decay, which occurs on a relatively long timescale. The upper state (B), on the other hand, can relax by the radiative decay (Tie) whichis responsible for the visible emission. In contrast, at finite pressures both the Z and B rovibronic states can relax through vibrational/rotational channels; if this energy-changing collisional quenching is efficient on the timescale of T; e, then it may be reasonable to assume that TI e = Tls_ Our data extrapolated to zero pressure indicate that T, > Tie, and not that T2 = T1,. In fact, T2 is almost twice T,. This is consistent with the above picture, although exact quantification is not available because of limitations on the S/N ratio as we approached the zero-pressure limit (very low gas density). At moderate pressures, we invoke the assumption that Tl e Z=Tls (for the reasons mentioned above), and from the results displayed in fig. 4 we obtain oV = 590 2 110 A2. Clearly, oP, thecrosssectiotr forphasecitattgitg collisiotts. is tmch larger that1 0,. the cross section for energy-changing collisions_ The values obtained by this technique are in reasonable agreement with the other measurements made with fluorescence decay time arises from collisional population transfer from the rovibronic level that is pumped by the laser to other vibrational and rotitional levels of the ground (electronic) manifold.

* Thcgroundstatc

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LETTERS

19 October

1984

quenching and two-pulse photon echoes [7-9 J. Why is oV > uE? This question cannot be answered without taking into consideration the detailed nature of the potential surface for collisions. However, it is instructive to consider that a T1 process (a~ cross section) involves transitions from the initial i to the final f state and l/T1 0~ IVif 12~ according to the Golden rule. On theotherhand, l/T> 0: ~I’, which represents [ 101 the dispatity in the collisional perturbations of the initial and final states. This disparity is “easier” to achieve through collisions (even long-range collisions) than the transfer Vif process. Hence CQ,is expected to be larger than Q, which in turn is expected to be on the order of the hard-sphere cross section. Accordingly, homogeneous broadenings could be dominated by cr.+,-type interactions and not lifetime effects. This brings to focus the important point regarding the relationship between linewidth and lifetime measurements: l7zey do tool correspond unless up processes are frozen out and the systetn is IWOlevel it2 nature. To illustrate our above points, we examine the contributions of the different relaxation mechanisms to the homogeneous linewidth of the transition. For ex-

ample, at 30 mTorr, the total homogeneous broadening is 700 kHz. The T1 contribution to this is 60%, while pure dephasing, where the population remains unchanged (the elastic-collision contribution), is 40%. The total homogeneous contribution to the width of the rovibronic transition is much less than the inhomogeneous broadening, which is DopplerJimited in this case (400 MHz). Therefore, measurement of the apparent inhomogeneous width will not give the lifetime of the state. Neither, in this case, would the measurement of the totalhomogeneous width give the lifetime or T1 contribution directly_ Only by direct time resolution would one be able to disentangle the dynamical channels that contribute differently to the broadening [l I]. This point is very important to the interpretation of many reported values of lifetimes (or predissociation rates) obtained from linewidth measurements. We are currently completing measurements of T1 e and T,, as a function of pressure [ 121. Acknowledgement This work is supported by a grant from the National Science Foundation (Grant #DMR 8105034).

Volume 110, number 6

CHEMICAL PHYSICS LETTERS

References (11 W.S. Warren and A.H. Zcwail, J. Chem. Phys. 75 (1981) 5956; 78 (1983) 227992298.3583. 121 A.H. Zewail. TX. Orlowki, K.E. Jones and D.E. Godar. Chcm. Phys. Letters48 (1977) 256; T.E. Orlowski. K.E. Jones and AM. Zcwail. Chem. Phys. Letters 54 (1978) 197. 131 W.F. Giauque, J. Am. Chem. Sot. 53 (1981) 507. I41 A.H. Zewail. T.E. Orlowski. R-R. Shah and K-E. Jones. Chem. Phys: Letters 49 (19!‘7) 520. I51 \V_Demtrijder, Laser spectroscopy (Springer, Berlin, 1982) p_ 593. 161 A. Schcnzlc and R.G. Brewer, Phys. Rev. Al4 (1976) 1756; hl. Bums, IV. Liu and A.H. Zewail, in: Modern problems

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1984

(71 J.I. Steinfeld. JILA information

Center Report No. 24, University of Colorado, Boulder (1984). [ 81 R.G. Brewer and S.S. Kane. in: Nonlinear behaviour of molecules, atoms and ions in electric, magnetic or electromagnetic fields. ed. L. Niel (Elsevier, Amsterdam. 1979) pp. 45-54. [9 ] R.G. Brewer and A-2. Genack, Phys. Rev_ Letters 36 (1979) 959. IlO] I(.E. Jonesand A.H. Zewail, in: Advances in laser chemistry, ed. A.H. Zewail (Springer, Berlin, 1978) pp. J 96-222. [ 111 P.M. Felker and A.H. Zewail, Chem. Phys. Letters 108 (1984) 303. [I?-] E.T. Sleva, W.S. Warren and -4.H. Zcwail, work in progress.

in solid state physics. Vol. 20 (North-Holland, Amsterdam, 1982). p. 301.

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