Argon ion laser excitation of supersonic seeded molecular beams of I2

cllLIllIL.II

I’h>wc

North-Holl.md

79 (19X3) 321-339

Puhlmhm!: CompJn>

ARGON ION LASER EXCITATION OF SUPERSONIC SEEDED NIOLECULAR

BEAIMS

OF II =

Exprrmxnts cm the laser ewlIJIIon (B + >o of seeded supcrsomr. h~.tm\ ol I, h> J L\\ Jr@on-lo” IJ\rrr 31 5115 rim 2r.z reporIed Msacurements consIsted of laser-Induced fluoreswnce Jnd 1, beam aIIsnuJIwnz and I, urns-of-fl+I dwrlhuunn. J. a fImcIIon of carnrr-gas pressure and nozzle 1emperJ1ure From the IJwr-rnducsd heJm lot. rhs dlre~r phoIodl\\cki~Ilon or,,.. sectIon Is found to be (2 4 +05)X 10-‘y cm’ A simple model has been formulntsd to ds~srnr~ne the fr~cnon of n~olecutc. II~JI Jre excited b> the laser ut~hung the above data base and a\JllJble specIro\copIc dJIJ From the lJ\sr poxttrr depcndsncr <>ithe lluorescenee the model also llelds the magmtudr of Ihe h>perhne-J\erJged EmsreIn H cosffIcwnI found IO be (19 r 10)X 10’” erg-’ cm’ s-? The fracIlonJ1 ewIIJIIon of fJ\1 cold bsJms of I2 1s much er~Jwr rhm for ilou or m~\~~~lh~n beams and dependenr (\~a Ihe Doppler effect) upon the ~nglr of m~er~cc~~on of Ihe IJ\er Jnd molecular beams U IIh 1 \\ pi her po\ber = 1% e’icnaIron can be achlexed ROIJIIO~~I ImIperJIurcr JIlJlned m Ihe wperwmc e\p~nsto~:x JTC deJuc.A from the fluorescence nnalysls The> compnre well \\lIh ~r.mskmon~l wmper.nures nteawred h\ ume-of-fhghr rJngmg from noule Iemprmtures do\\” to IO K

1. Introduction

The characteristtcs of high intensity and tunabrht> make lasers ideal sources for molecular excttation. The interfacmg of laser-molecular-beam techmques mahes posstble the preparation of molecules in certain well-defined states for use ds reagents in chemical reactions under collision-free condttions [I]. Examples include the preparation and reaction of molecules m spectftc vtbrational [2] and/or rotatronal [3] states The role of electronic excttatron m chemtcal reacttons using molecular beams has been studied in several cdscs.

* Supported by NSF GrJnIs CHE-SI-16386 and CHE-7711384 z Fulbnght Fellox\ of the M~IsI~?. of Um\ersItIcs Jnd Rrsearch of SpaIn Present address Departamento de Qtnnucd FISIC~,Umxrrszdad Complutense. Xladnd-3. Spdn * Present address. Gould LJboraIones Rolhng hisado\\> IL 60008 USA ++Present address Occldenlal Research Corp lnme CL\ 92713. USA

0301-0104/83/0000-0000/$03.00

0 North-Holland

grncrallv \\tth ewrted atoms [4] but m some c.tsss \\ith molecules [S-7]. A common rssue in all of these r~perunents IS ths need to esrun.rtc the frxtion of reagent molecules in the excited state In addition. tt 1s tmportanr to kno\\ how to mcre.tse rhts fractton b> _ (1) rnswnizmg the number of molecules whtch cdn resonantl> absorb the laser radiation and (2) fmdmg those condlttons \\hlch mnvmrze the promotion of these molecules to the excited state. E\penmenrs m rhrs laborator? on the rr3.rctton of 1: + Hg have rsqutred such an understJndins [S]. To etaluste the reactton cross sectton of the e\citrd-state relatt\c to the ground-state redctron requtres knoivledge of the fraction of electronicall> excited Iodine molecules The presenr paper summarizes d number of e\pcrmrents ~hrch probe the interactron of isolated I, molecules \\iirhthe 511.5 nm photons from an argon-ion laser IS] From these experiments the direct photodrssocrstton cross section and the Einstein B coeffrctsnt hd\c been detrrmmed. These results together \\tth the available spectroscopic data [9-IS] have been used

rn J model to estimate the fraction of wallable molecules (I e. those m the J” = 13 and 15 rotational levels of the ground wbratlonal state) that Jre electromcally excited (to the u’ = 43 level of the B state) This calculation, coupled wth the rxperm~ental dependence of fluorescence on carner-gJs pressure. yields the rotational temperature, T,,,. of the beam With the assumption of a Boltzmann rotational dlstrlbution at T,,,. the fraction of I, molecules m the J” = 13 and 15 rotational Ievels IF hno\\n (this frrlction has a maximum at T,,,, = 1 I.2 K) The two fractions multiphed give the o\erJll fraction of I, molecules in the t”’ = 0 level of the X state which are excited to the B Stdte

This study concludes the experlmental factors

with Jn

e\ammatlon

of

which influence tile extent of laser excitation. e-g beam type (1-e maxwellian versus supersonic). beam velocity (fast versus slow). and the angle of intersection bet\\een the laser beam and the molecular beam.

Fig I. SchematIc of the expenmental arrangement NZ IF rhe nozzle. SK Annmer. Cl CZ. C3 molecular beam colhmators defrmng the \ ITIS CH chopper. F beam flag C4 the cntmnce colhmxor for the quadrupole mass fdter The laser beam IS along the I ITIS, wnh ihe XJ plane horiznmal The PMT \w\\ along the z was The dashed arcle about the region of m~erzcc00x1 of the lacer and molecular beams represents the PhtT \uz\\mgaI-+a

for beam density and fluorescence measurements 400 Hz for time-of-flight (TOF) measurements). and colhmated once agam TOF analysis of the various I, (and H,) beams was routmely carried out as described in ref. [22] A cw argon-Ion laser (Spectra Physics model 171) was used to excite the Iodine beam. The maximum multimode output at 514 5 nm was 4 W with a bandwidth of = 6 GHz (as measured with a Spectra Physics 450-02 Interferometer). In a few experiments. an etalon (not thermally stabilized) was Inserted m the laser cavity in order to allow tuning over small regions of the laser gain curve. The laser beam enters and exits the vacuum chamber through long baffle arms onto which quartz Brewster-angle wmdows are attached. The exit baffle contains a Wood’s horn to collect scattered light from the exiting beam. There is negligible loss m laser power in going through the baffle arms (i.e. the power measured at the scattering center is that measured at the laser)_ The laser crosses the molecular beam at an angle of 135”. This angle was chosen because of geometrical constraints of the machine, and to provide for a good overlap between the laser gain profile and the hyperfme absorption band of the iodine molecules. It will be shown in section 4 that and

2. Description

of eqeriment

The experiments have been carried out m the crossed molecular beam apparatus “Tnxie” [S. 19.20]. The machme has undergone several changes in order to make It suitable for laser excitation and fluorescence detection experiments [8.21] Only those expenmental details associated with the characterlzatlon of the laser excltatlon of supersonic molecular beams of lodme are presented here. A schematlc of the laser-molecularbeam intersection region 1s shown m fig 1. The supersonic beams of lodme were produced essentially as descrtbed m ref. [22] Carrier gases used were He, Ar, and H,. the latter bemg employed for most of the present experiments. Only the results obtained using a 0.18 mm diameter capillary nozzle are presented here. As m the preVIOUS work, the velocity distributions and characteristlcs of the expansions could be changed by varying the carrier-gas pressure and/or the temperatures of the nozzle and iodine oven. Depending on the source conditions. velocltles from 0.8 to 2.6 km S-I could be obtained The seeded beam of Iodine was skimmed, coIhmated. chopped (80 Hz

the combmatlon of multmlode laser operation and a crossing angle of 135” IS nearly optunal for be&m excitation. The iodme fluorescence IS measured \\lth ,m EMI 9781B photomultipher tube (PMT) orlentsd perpendicularly above the plane formed by the molecular and laser beams The PMT is contained wthm ‘1 blackened, liquid-nitrogen-cooled housmg A system of three lenses. with the focal point at the scattering center. was used to Increase the collection of hght. A Schott (06590) color glass filter minimrzed the amount of scattered laser light reachmg the detector. A Kelthley lock-m amphfler wrfs used to detect the fluorescence signal in phase wth the modulated molecular beam. The PIMT dark current was < 0.1 pA. and the typlcal fluorescence from the I, beams ranged from 0.5 to 20 nA With the lens arrangement. as described above. only a narrow volume In the so-called scattermg zone was in the focal region so that a small correcnon IS reqwred to take Into account the relatwely long (= 3 ps) radlauve lifetime 7 of the I; rnolecules (Excited I2 molecules can leave the wewng region before radlatmg ) Whenever an experunent involved beams of different velocities (e.g. the fluorescence slgnal as a function of nozzle pressure) corrections for this effect were apphed so that the relative fluorescence signals could be compared The probabihty. P. that a molecule of velocity_ 1;. radiates wthin a viewing field. d. (of a PMT) is gwen by P = 1 - exp( -d/w) For an I, beam of velocity 1 km s- I and d = 0.9 cm. P = 0 95 (i e 95% of the 1: molecules radiate \tJthm the PMT wewmg region). For a given experiment (of fluorescence versus carrier-gas pressure) the maximum range of P values IS from 1.0 for the slo\\est to 0.7 for the fastest I, beams

3. Results The dependence of fluorescence yield on nozzle pressure (I e H, carrier-gas pressure) is plotted in the bottom panel of hg 2. Variation III the notie pressure also has the effect of changing the I2 beam intensity. This is tracked simultaneously wth the “monitor mass spectrometer” (middle panel).

D~~idmg the obssned fluorescence signal b> the relati\e beam number denstty. the reduced fluorescence (fluorescence per umt number densit?) 1s obtamed (top panel) This results in a smooth cur\e 151th J maxmlum at = 550 Torr. It is tempting to assocI&te the maximum of the reduced fluorescence \\ith the ma\irmztng of the populations in the proper “acceptor” rotational states. J” = 13 and 15 of the I, X( ‘I;)_ L”’ = 0 state This \*as pursued b> further euperimentatlon FJ~ 3 sho=s the reduced fluorescence for beams formed under the very same conditions ewept for the temperature of the no&e. r,,. The

&I . , , . , , , , \ 200

400 HYDROGEN

600 PRESSURE

600

IO00

(TORR)

FIN 3 Reduced fluorescence versus pressure (cf. lop panel of Irg 2) Top nozzle at 3Sj K (:ermed the “cold nozzle ) Bottom nozzle a~ 515 K (the “hot nozzle-3 Bolh reduced

tluorrscrncr tunes peak. 81 approximateI> the same hydrogen pressure but the fluorescence srgnal from the “cold nozzle’ IS = 3 trmes that of the

h hot nozzle‘ srgnal

general appearance of the curves and the positron of the maximum for both conditions are sirrular. However, the reduced fluorescence yield at T,, = 385 K (“cold nozzle”) 1s approximately three times that at T,, = 515 K (“hot nozzle”) Clearly, the maximum of the reduced fluorescence cannot be explained by assuming that it corresponds to an expansion yreldmg T,,, = 11 K. As will be seen later, the laser power dependences of the fluorescence at 5 14 5 nm for given I z beams are essential to the analysis of the present results. Fig 4 shows one of these curves (sohd points). where the onset of saturation IS evident Curves such as that have been recorded for a variety of I, beams (e.g., see fig. 13). In addition to these fluorescence and beam density measurements, another series of expenments were devised to gain further mformation on the extent of laser excitation of the beam. In

analogy to the work on Br, [23]. it was expected that the mteraction of the laser with the i, molecular beam would affect the observed 1: and I + mass-filter signals_ The signals at M/Z = 254 and 127 were recorded with the lock-in amphfter mphase with the chopped laser beam. A smal! decrease (phase shift of 180” corresponding to 10-3-10-” of the beam density) in the mass-filter signal was observed. Fig. 4 shows the power dependence of the 1; and I+ losses at 514.5 nm. Note that the losses are not hnear with power. Thus 1s indrcative of the fact that more than one process is occurring (of which one is resonant) namely predissociation and photodissociatton. The results are analyzed in sectron 4 and a further discussion on the beam losses can be found in ref. 1211 Frg 5 shows the wavelength dependence of the 1; beam losses The beam losses at 488 nm (2.54 eV) and 496.5 nm (2 50 eV) show a strict linear laser power dependence - clearly a dtrect photodtssoctation process. This is expected because the energy of the 4S8 nm and 496.5 nm photons puts the Iz molecule above the dissociatton energy (2.485 eV) of the B state [18,24]. The effects of an intracavrty etalon have also been experimentally examined. The upper graph of fig. 6 shows the fluorescence observed wtth multimode laser output and for the laser output

.FLUORESCENCE 0 I; 0 I+ 0

I

MASS MASS

2 LASER

POWER

0

FILTER ll_

FILTER 3

4

(W,

Frg 4. Laser power dependence (at 5145 nm) of Ia beam fluorescence and beam losses Sohd pomts denote fluorescence versus laser power (ngbt ordmate scale) Open ctrcles and squares refer to decreases in the signals (beam denstttes) of 1; and I+, respectwely Left ordmate scale absolute fractronal losses observed, due to the processes of dtrect photodtssocranon and predrssocratron

LASER

POWER

(WI

Ftg 5 Lacer pouer dependence of the reiarne decrease m 1: wgnal for stxeral -axelengths of the argon 1011 laser The dependence at 514.5 nm IS non-hnear For 488 0 nm and 496 5 mm onI> the process of direct photodIssocIation IS expected this 1s borne out h) the hncar power dependence

In and out of resonance_ When the laser IS tuned off resonance with the etalon no fluorescence is observed from the beam A gas cell contaming I2 vapor Inserted in the laser path fluoresced strongly (which suggests the importance of Doppler effects). The lower graph of fig. 6 shows the 1: beam losses with the etalon tuned on and off resonance Note that off-resonance beam losses are still observed and that the power dependence is linear. Thts suggests that the process responsible for the beam losses is only direct photodrssocuttion. These results ~111 be exploited in section 4 to determine the direct photodrssoctatton cross sectton.

LASER

POWER (Wt

tuned

4. Analysis

I_ A

SER

P 0 W E R ( ‘.V)

Fl_p 6 Effect of mwscatn~ etslon on I, fluorescence and 1: beam losses a1 514 5 nm Lpper figure open cmzlss tnanglss and square shot\ respcctltel> Ihe ohsencd fluorescence for mulrlmodc laser eralon runsd to resonance. and crslon tuned off-resonance Sore rhe rtnrhcr onset of sa~urstmn for the resonam case and the zero ~aluc for the off-resonant e\pcnmem Bottom figure rel.m~s decrease of 1: slgnal t\lth rhe etalon tuned on (Inangles) and off (>quares) resonance The hnear po~cr dependence of rhe non-resonam beam losses are exploncd 1~1!~eld the direct phorodlssoclauon cross secuon for I 2 rll 5 14 5 nm. see rear

of the results

The main goal of thts study IS to determme the extent of electronic excttatton achteved in a molecular beam irradiated with the multimode output of a cw laser, and the optimum condttions for such excitation. Although thts work is restrtcted to the case of an I, supersonic beam and the 514.5 nm lure of a cw argon-ion laser. the methodology developed could be extended to other systems The expertmental results of the preceding sectton (fluorescence and beam losses versus pressure). do not dtrectly provide a means of determming the extent of excitation. i.e. the fraction of I, beam

molecules that can be promoted to the B state. It m&t seem that \\rthout a detailed LIF study [ZS] the fraction of acceptor molecules could not be ascertained From the dependence of reduced fluo-

rescence on the carrter-gas pressure one can. of course. determme optrmal excitation condittons. On the other hand. the laser power dcpendencc curves show that saturation is attained at low porkers_ In addition. the curves have different shapes depending on the I2 beam veloctty distributions and other charactenstics of the expansion. Thus a realistic model for the excitation of a

molecular beam is required which can make use of the known spectroscopic data and explain the experimental results. Such a model IS described below which takes into account the role of inhomogeneous DoppIer broadening of the hyperfme lines and their interaction with the multimode laser gain curve 4. I Fracrranal e_xcrtariort tttodel When a molecule IS irradiated several competmg processes may take place simultaneously [26]. Processes other than resonant induced absorptron and emisston or spontaneous emtsston also occur [27]. For example, in the case of 1,. the crossmg of the bound B(.311,) state with the repulsive ‘II,” state gtves rise to a natural predtssociatton (thus depleting the vibrattonal levels of the B state via a non-radiative process) [ 131. The natural predtssociation can be thought of as a two-step process mvolving radtative excitation B + X followed by a non-radtatrve decay lu - B [ 131 Brojer et al [ 151 demonstrated the existence of a hyperfme predtssoctation m the I, B state. Thus the total decay rate of a particular IZ rovibrattonal level 1s composed of several terms. wrth each hgperfme level contributing a different rate. In addition to the process of resonant absorption followed by spontaneous predissociation. direct photodissociation is known to occur [lo- 131. The transition is ‘II, - ‘x; and can be considered a non-resonant absorptton to the contmuum. This has been observed in the present work Any kmettc model which 1s developed to characterize the excitation of a collision-free beam of I, must take into account all of these processes_ Ftg. 7 shows the kinetic scheme for a two-level system. In principle. 1 (ground) and 2 (exctted) may represent two rovibrational levels of an electronic transition; alternatively, two hyperfme levels characterized by u, J and F (total angular momentum, including the nuclear spin) quantum numbers. In the case of the I1 B(u’ = 43. J’ = 12.16) + X(u” = 0, J” = 13,15) transition, 42 hyperfme 1eveIs are invoIved, since the nuclear spin is 5/2. These were resolved by Ezekiel and COworkers 193, who reported the posittons and rela-

1;

0 AZ1 w21

/i

wl2

a-

-I+=

I

4 21

a,

12

Rg 7 SchematIc representation of :he No-Ieke qstem wed to model the euztauon of a molecular beam of I2 v.lth Inscr radldtron at 514 5 nm Hi, and H;2 are the rate constants for stlmulated emlsslon and absorption respectwely. Al, that for spontaneous emlsslon from lebel 2 bath to the ongmal lebel. whereas A?, are the different coefftcients for the transmon from level 1 to dlfferent \Ibratlonal levels/ (the total r.idlatne decay rate constant gnen b) A, =X,/A?,) K,, the rate constant of predlssocIatlon and @PO,,that of dwxt photodtssoclanon (see text)

tive intensities of the lures as well as the spectroscopic parameters. The total number of I, molecules m enher of these states at time I will be n(t)=n,(z)+~z,(t) Of course, in the absence of radiation II = ttI = no (the initial number density of molecules) and tt2 = 0.

The equations that govern the absorptiondeactivatton, m the absence of collisions are dti,/dr= dtl./dr

-W,,ti,

+ UI,ttr,+A,,trI-

= IVl,tt2 - W2,n,-A,tyKpdtt,,

@,a,ti,.(la) (lb)

where IV,, and I?& are the induced absorption and emission rate constants respectively, AZ, is the Einstein coefficient, A, is the inverse of the radiative lifetime, so that A, = l/~,,~ = C,A7,_ Here K,, 1s the predtssociation rate constant from the excited electronic state. The rate of direct (non-resonant) photofragmentation from the ground level to the contmuum is given by @u,n,, where @ is the photon flux (i.e. the number of photons per second per unit area) and a, 1s the photofragmentation cross sectton. @ is given by @ = I/hvA where A is the laser beam area and I the laser power. The analytic solution of the system of dtfferen-

ti,ll equations (1) is given m appendix A. The final solution can be written in terms of /(I) = II ,/Iz,,. the fraction of the molecules excited by the laser ‘1s a function of the exposure time. /(I)

= H,(f )/no

=

H’,, = B,zP,,,S(‘iJ-

C(k*--A) (X_- D)(k+--A)

BC-

a.

(e

I

-eh-1).

(2)

llhere A. B. C, D. k,. and X-_ dre simple time-independent functions of the absorptlon-deactwation rates of eqs. (la) and (lb). Included in appendlx A are numerous expressions commonI> found in the literature which dre shown to be hmiting cases of the present general solution. It should be noted eq (2) does not give the total fraction of molecules that are excited in a beam. but only the fraction of molecules m the parrrcuh rovibrdtion level that can be exctted. The relation between W12 and Blz_ the Einstein B coefflclent is [28.29] IV,? = B,+(v)

(s-‘),

(3)

where B,, is the coefflclent for induced absorption in units of erg-’ cm3 s-’ and p(v) the radiation density per unit of volume and unit of frequency interval (erg crne3 s). Eq (3) is valid only if the width of the excitation source is much broader than that of the linewidth of the transition. In the most general case, however. the induced absorption rate IS given by [30] Ik,, = B,?

= P(z’)g(“)d”=B,ZR(I~). J -2

(4)

where g(v) is the normahzed Imeshape. 1.e. %‘ g(Y)dv= / -*

1.

respect to the hyperfme lines. as \xell as the ShdpeS .q( v) and P(Y) Of course if P(V) is essentially constant. cq. (3) IS recovered If the light source 1s quasi-iiioiiochromlltic dt frequency z*”

of

(5)

in general. g(v) is the convolution of the natural lmeshape wth the inhomogenous Doppler broadening arising from the distribution of velocities and angular divergence of a molecular beam. Ref [21] discusses the analytic expressions for g(v) which take into account these evperlmental effects R(V) represents the overlap (integral) of the radiation density of the laser and the lineshape of the transition It contains informatlon regardmg the relative position of the laser gain profile wth

(6)

\\here p,,, IS the energy per unit volume [30]. Eq (6) cdn be applied directly to the problem of exciting a single hbperfme transition with a \er_v narro\\ band ewitation source (e.g. the smgle-mode output of a laser)_ If the ewltatlon source IS the multimode output of a laser each of the 42 hyperfme levels c&n be excited One can consider the transitlon “as a whole”. using for the lmeshape:

u here c, = Il,/Uz,_ h, the relative line strength with the summation extended o\er all of rhe hbperfme levels. (If ever) g,( ~1,) 1s normalized. g(y) nil1 be normahzed also) Substltutmg the g(v) from eq. (7) into eq (4) R(P) can be calculared One can also consider the ewtation of each indi\tdual hlperfmr line separatel? Eq. (4) then becomes (If’*,),=

(B,,),r,(a).

(S)

1~here the Index I refers to rhe I th hbperfme transltion. The coefficient (B,,), can be expressed as (B,?),

= ~,~h,,/lr.

(9)

where g,J is an --aXeraged_‘ B,, corfflcienr. h, 1s the relatl\e strength of the I th h>perfme line. and h the axerage value of the strengths_ The term r,( I’) IS gnen by (10) Mhere g,(a*) 1s rhs normalized lmcshapc of the I th hyperfme hne. Xssuming that the lifetimes and rates for each of the hyperfme lines are known and by using eq. (S). each fractional e\cltation.f,. can be calculated via eq (2) The overall fraction u hich is excited IS gilen by the average fractionf= x.,f,/t~ LXhrre PI= 42 is the number of hyperfme levels. and it has been assumed that all hyperfme levels of

the ground state are equally populated. Although the 43-O transition is one of the best studied Iz transmons, such detalled information as to the indwidual hyperfine decay rates is not yet available. Here an average total decay rate (A, + K,, in eq. (lb)) of 5 X lo5 s-* is assumed [31]. (It was noted that changes of _+2 x lo5 s-l in the total decay rate affected the fmal results very little.) The form of g,(v) is taken as the natural lineshape convoluted with the mhomogenous broadening due to the velocity distribution of the I, molecules in the beam and the angular dtvergence of the beam. The relative spacing bet\\een the hyperfme lines and the relative hne strengths are from ref. [17]. A discussion on the calculation of the g,(v) can be found m ref. [21] In the top panel of ftg. 8 the displacement of the 42 hyperfme hnes with respect to the argon-ion laser gain profile (514.5 nm) is shown The laser gain curve 1s the experimentally determined envelope of the laser mode structure. It can be represented by Z(V) = (P/AY?i ‘I?) exp[ - ( v/~v)‘],

(1’)

where Z(V) IS the power in watt per urut of frequency at a frequency Y, P is the laser power in watt, and dv is the laser bandwidth (In calculatlons where the laser mode structure can be important (cf. fig. 16) a pseudo-random mode structure wth the gaussian envelope described was used [21].) The spectral power density is obtained by dtvlding I(V) by A, the laser beam cross-sectional area; for 1 W power, at the maxtmum of the gain profile, it is 0 02 W cme2 MHz-‘. The radiation density is p(v)=

[Z(v)/cA]

X

IO’

(ergscmm3).

Fig 8 Top panel- Doppler-free I, hyperfine structure for the 514 5 nm trans~on as reported m ref. [9] The gaussian tune IS the experunental emelope of the free-runnrng multimode argon Ion laser output The relative displacement of the hyperfme Imes from the center of the laser gam profile (tahen as Y = 0) IS from ref. [9], the rellawe heights and posxtlons of the hncs are from ref 1171 Mlddle panel Doppler dtsplacement of the hyperfine structure wrh respect to the laser gam profile for an I2 beam nlth o,= 1.4 hm S-I crossmg the laser beam at an angle of 135” Bottom panel Convolution of the natural hyperfine lmeshapes (tahen as delta functions) wth the velocity and angular (beam dlrergenee) dlstnbutions of the beam calculated assummg a speed ratm for the I, beam of 11 and a beam dnergence of 0 So (fuhm) The overall effect ts the dlsplacement rn frequency and mhomogenous Doppler broadening

(12)

The middle panel depicts the Doppler frequency sluft for an Iz molecule whose velocity vector of 1.4 km s-l is mtersected by the laser at an angle of 135”. However, the molecular beam has a dlstribution of velocities and an angular divergence. Summing over the individual g,(v)s which have been convoluted over these expenmental conditions (as described UI ref. 1211) yields the overall hyperfme shape shown in the bottom panel of frg. 8. In the litrut of zero angular divergence and monovelocity

the structure shown m the middle panel is attained This can explain the observation of fluorescence in an Iz gas cell and lack of fluorescence from the molecular beam (see sectIon 3) In the former case there was overlap between the laser modes and hyperfme structure whtle m the latter there was not. For a very narrow beam velocity distribution individual hyperfme lines are recovered (fig. 9). For the reduced fluorescence curve of fig. 3

,l’ / /

-\ ,\

termed -‘cold nozzle” curves \xere measured

V~=15kms-’

distribution labeled 1 corresponds to the h~ghc\t pressure (900 Torr). 4 the lowest (300 Torr) In cases where the expenrnental TOF dlstrlhutIon\ are hnown the corresponding stream velo~itw\. t,. .md thu\ the and speed r‘~tlos. 5 . are determined

A=11

:

(7;,, = 3% K). four TOF (fg. 10 .tnd t,lhlc 1) The

:

beam \elocit> dlstrlbutlons. These dlstrlbutwn~ together \\tth the beam angular dl\rrgencr g~xt: rise to the lmeshapes. y(v). shonn in fig 11 A\\ can be seen. increasmg the beam \eloclt> &lfta the “out of overlap” xxith the laser g.t~n lineshapes curve. (This shift occurs because the l,tw- intersects the molecular beam at an angle other rhan 90”. e.g. in the present \\oorh IS”.) To calculate the fractIona cxltation of J bwm of iz x\ith the model (eq. (3)) txxo quantltles aire still needed: the Einstein B cocffv5snt and the direct photodlssoclatlon rate. 4 Z

__

---h--

__ FRf&J

Fig 9 Calculated effect of speed ratlo on hyperfine swucwre (laser-molecular-beam mtersectlon angle. 135O) The assumed beam condltmns are I,, = 14 hm s-’ and speed ratlo S. from top IO bottom 11.42.63 and S4 The hjperfme su-ucture becomes resohed as the \elocq dlstrlbutlons ndrrou

Table 1 Translanonal Source

and rotational

condmon

cold nozzle (T_,, = 3S5 K)

hot nozzle (T,, = 515 K) hot nozzle-hot oven (7,, = 480 K)

DetermmanotI of a, ami B,,

The direct photodlssociatlon raw 1s obramrd from the experimental results presented m flp. 6. The beam losses at resonance are due to both predlssoclation and photodlssociatlon Off resonance there is no fluorescence bur beam losses are snll obsened. This signal 1s due to direct photodlssociatlon (the linear po\xer behallor confirms this) The beam losses are related to photodlssoclation cross sectIon via 131)

temperatures PHz (Torr)

u,(lms-‘)

T.(K)

r,,., (Kj (c~unu~ed

295 495 703 900

15 20 24 25

290 z 50 35.~1 25=5 11x1

2-l-10-‘70 Z-50 1-L 16 11-12

307 517 900

15 20 26

165 IT 50 13st 15 3525

350-500 135-165 ;3-u

660 855 1000

1.5 19 1.9

190+75 6OrS JOI5

150-lb0 6Y-Sb 41-5-l

r.mgc)

T,;

TIME

= 385K

(psec)

Fig 10 Expenmmral I, TOF dlsrnbuuons for the “cold noble’ a: four Hz pressures 900 (= 1). 703 (~2) Torr correspondmg to r, = 2 5.2 4.2 0. and 1 5 hm s- ’ mlth 5 = 1 IO 71 42 and 11 rrspecrnsi>

Vs =l.5

V,

i

=2Okms-’

8=42

OE-

N

Vg

=24kmr’

B

=71

V,

=25kms-1

9

= 110

J 3c

FREQUENCY

(GHz)

.md 295 (=4)

where CDis the photon flux. a, the photodtssociation cross section, yo a geometrrc factor relating the portion of the beam exctted by the laser to that sampled by the mass filter (here yo = O-954) and t the mteractron ttme At 1.5 W, @= 1.94 X 10” s-’ cm-‘, r = 2 x lo-’ s (given a beam velocity of 1 km s-t and excitation region of 0.2 cm) which via eq (13) results in a ad of (2.38 i 0 5) x lo-l9 cm’ [21] This can be compared to 1 x IO-I9 cm’ reported for Br, at the same wavelength [23] With the knowledge of the drrect photodissocration rate, it 1s posstble to subtract the contributton due to direct photodissociation from the beam losses (fig 12). The net result 1s beam loss due to predtssociatron. As menttoned earher thts is a two-step process, the first being the absorptton of a photon to the bound B state This suggests that the laser power dependence of the beam losses (corrected for photodtssoctation) should be proportional to the fluorescence signal. The upper left hand panel

kmr’

A=11

-

495 (~3)

Fig 11. Calculated hyperfine structure of beams 1 thou 4 top (based on TOFs from fig IO) Maximum overlap occurs for the slowst beam (4)

I

. TOTAL IO -

1

1

BEAM

0 CORRECTED

LOSSES BEAM LOSSES

. m

3

2

1

LASER

4

IW)

POWER

Fl_e 12 Contnbutlonr to the obscned If bwm lo\sr\ Cm_le\ c~perlmentall~ obsened beam lossec (from fig 4) Loner sohd

Ime. cnlculated contnburmn to this signal from dtrect photodts\OCIHIO~ (see text) Squares difference betueen the ohsened ygn.d and :he calculated photodiscoclatlon sqgal. due prnnartI> to the predlssoclatlon of I, (thus proportIona to the fluorescence sIgnal. cf fig 13 top left panel) The dashed hne through the squares IS calculated \~a rq (2) usmg the Emstrm B,? coefftclent as the on11 fittmg parameter B,, 1s found to be (3 9i 1 0)X 1Ol6 erg-’ cm’ se2_

of fig. 13 shows thts to be the case. The Einstein B coeffictent for the transition can be estrmated mdrrectly from tuo hterature sources By extrapolattng the Fran&-Condon factors and r centroids of ref. [16] to the present case tt can be estimated that the matrix element of the transition dipole moment. ]M(r)]‘. IS approximately 0.7 D’. This value of IA’(r)]’ leads to a value of B,, of 1.2 X 10lh era-’ cm3 s-’ [38] If a value of IAl(r = 0.91 D’ f:r the 510 nm transition 1s used (as reported in ref [l 11). B,, = 1.6 x 10’” erg- ’ cm’ In an older work, Ezekiel and Weiss [9] S --‘_ reported the osctllator strength, f,,. for a single I, hyperfme transttion at 514.5 nm. Using their value of 3.8 X lo-” for f2,_ B,, = 7.8 X 10” erg-’ cm’ -2 s . Since an average value of B for the entire transttion or for the transitton of mterest is apparently not known. rt was decrded to use the fractional excttatron model (eq. (2)) with B mttiallv a fttttng parameter. Thus the corrected beam ~OSSOS. proportional to fluorescence. usmg eq (2) wtth B adjustable. was 4.9 x 1O’6 erg-’ cm3 s-‘.

fig. 13 were ftt The best value of B with an uncertainty of

of = 20%. Onb B wds .rJtu\tcd to oht.un the best ftt: no other terms ( Up_ I -1 A, . t‘tc ) \\ere .tdjustcd. Thrs value of B,, I< m “.tveraged” caefftcicnt (B,,) for the et~r~~etransrtron ,tt 51-M nm and not for an tndt\tdual h>perf~nt: tr,m\ttron. The COIIststrncy of the model c.m be ~~m~mrd by compartng thts value of B,, to that reported for .i single hyperfme transrtton in rrf. [9] This IS done by using eq (9) for r,~ch of the h>perftne ltnsb B,, 7 r,mges from 3 3 X 10”’ to S 2 2: IO”’ erg-’ cmi s--. The Lalue 7 S x 10”. calcuktrsd ~bo\c. clr.trlv falls ~~ithm thts range Thus d complete model (I c. cq (2)) I\ a\.ul.tblc for the anal>s~s of thr ~~prrunrsnt.d rrwlts. The model requtrrs 0111~ the kno~~led~e of thcz br‘un veloctty and its dtstrtbuttnn and nd.e~ use of HO further adJustable paranister~

To test the model a numbrr of fluorsscsncc po\\er dependenctss for I, beams of different \eloctties and source condtttons \\ere measured. These are presented m fig 13 Each cur~c \\ds s~tmk~red (not fit) b> the model usmg the experimentall> determmrd beam ~sloctt~ dwrtbutton The model ts seen to bc succssful in accounting for the e~perunentally obscrl cd fluorescence and beam loss stgnals (tncludmg the sJturatton effect in the on-resonance po\\cr dependence curves of ftgs 5 and 6). The orrSma1 problem of esttmatmg the fractional rwttatton of J beam of I, can no\\ bs appro‘tched The reduced fluorescence cur\e (fig. 3) for the “cold nozzle” IS dtscusssd ftrst Fig 10 shows the TOF dtstributtons corrcspondmS to four nozzle pressures co~ertng the range of ftg 3. The fracttonal ewttatron model (~.e. eq_ (2)) 1s used to determme the fraction of the acceptor molecules (those in states L*” = 0. J’ = 13.15) that are excited to the B state at etch pressure using the clpcrtmental I. beam Lelocit) distributtons. The result is cur\e _4- in the top panel of ftg 14. The left ordinate scale (labelled fraction excited) gives the absolute fractton of acceptor molecules that are excited The maximum ewitatton is at = 200 Torr. The points on the solid curve dre from a more

I

1

1

10 -

t3-

h

= 224-c

TO” = 73-c “5 0 LQSER POKER 1

I

I

2

= 1 3 Lrn s-1 3

4

IWI

0

-i

Fig 13 Laser power dependence of I, fluorescence for VII-IOUSbeams Pomts. expenmental. curves calculated from the model Upper left panel show that the corrected beam losses (squares) are proporttonal to the fluorescence (circles) Note that as the beam \slocit> Increases the obscned CUIWSapproach lmeanry The model uses onI> rhe expenmenrally detcrmmed xelocny and speed rano for each beam

sophtstrcated program [21] whrch treats the laser gam profile not as a smooth gaussian curve but as a pseudo-random mode structure with that average (gausslan)

profile

The

results

obtamed

by

both

calculatrons are esentially the same. The

reduced

fluorescence

of fig

3 maxlmlzes

at

Torr while the fractional excitation of target molecules (curve A of fig. 14) does not_ Clearly, there is another important contributton to the total excitation. This factor is the rotational cooling m the supersonic expansion [25] which alters the relative populations in the acceptor states. It is well known that the relaxation of the rotattonal degrees of freedom is quite effrctent [32], and the present data confirm this. The change in population in the rotational levels = 550

J” = 13,15 as a function of pressure can be obtained by dividing the reduced fluorescence tune of fig. 3 by the fractional excitation curve (A) of fig. 14. The result is curve B of ftg. 14. The ordinate is proportional to the J” = 13,15 population. Note that the absolute population of these states 1s not obtained by this method, rather only the relative population (thus the “arbitrary units” on the right hand ordmate scale)_ However, absolute fractions can be assigned to curve B if a Boltzmann rotational distribution obtains over the entire pressure range. Such a distribution has a maximum in the population in the J” = 13.15 rotational levels at T,, = 11.2 K. Associating the maxtmum of curve B with this T,,, and assuming a Boltzmann rotational dtstnbutron, one calculates

This Tr,,, for the othrr prescures rotational temperature asslgmnents scales

in fig.

14. The

Boltzmann

leads to the on the upper dtstrtbutlon

to-

gether with

the deriled T,.,, valuescan be used to calculate the absolute fraction of 1. molecules in the J” = 13.15 states. The reduced fluorescence curxe of fig 3 (bottom) for the “hot nozzle” IS analyzed m the same manner. Eq. (2) is used to calcul,ne the fraction of dvailable molecules that dre excited. The result is curve A m the middle panel of fig 14. Dividmg the reduced fluorescence of fig 3 (bottom) by tune A yelds curve B. the relawe change of 1, In this CdSe curxe 6 population m J” = 13.15 shons no clear mawmum so that rotational temperatures cannot he assigned as aboLe. To overcome this obstacle. use IS made of the expertmentall> determined ratio of reduced fluorescence intensitles. Smce the reduced fluorescence at an> given pressure IS proportIons to the product of the values @en b> Curies A and B at that prebsure. It follo\xs that the ram. Sd> /?_of the reduced fluorescence 1 leld of the *_hot nozz.le” to the -‘cold nozzle” should equal the ratto of th:s product (A x B) for the -‘hot” to ‘-cold” nozzles:

ahere the subscrtpts 1 and 2 refer to the cold and hot nozzles rcspectnel~. In eq. (l-l) onl! B,. the in J” = 13.15 for the fracnon of I2 molecules -‘hot” nozzle. is not knox\n absolutely. Subsntutins the Lno\\n values at SO0 Torr m eq. (14). It IS found that the xslue of B, corresponds to T,,,, = 50

Fig 14 Top Panel Contnbutlons to the reduced fluorescence stgnal for the cold noble (data from ftg 3 top) Left ordmxe swle- the sohd hne (A) through the pomts IS the frxtmn of molecules of the beam already m the “proper*‘ states (u”= 0 and J” = 13.15) that can be excned b> the laser. cAxlatsd b\ the present model The pomts are the results from a more sophlstlcated program uhxh stmulates the multimode ourpur of the free-runnmg argon-Ion laser (see text) Cune (B) IS the population of the acceptor states xersus pressure (right ordmatc

SC&?) THIS cuns IZ obratned b? dnxdmg the ‘-redtked fluore+ cence (fig 3) b> the fracnon cxclted from ct.ne _A Bec~u.e the populatlon graph she\\>I mA\lmum LI LZpolslbls to ns,tpn rot~tlonal rsmpcr.irure~ IO the cnnrc curxe The arrow\, en rhs &scl,>a mdlcats pres,ure> of H, for u hxh TOF dlstrtbutwn. wre obwncd (fig IO) The rotxuxtal tempsrxure ranges from 250 10 10 K (upper scale) Sllddlr panel Contrlbutlons to the reduced fluorescence for the hor nozzle (data of fig 3 bortom) Slgmflcmce of the CUIICS and pomtl sAmc as m top pm?] Asstgnment of rot.tt:onal tcmperxures sxpkunrd m rhe te\t ROI.UIO~A~temperatures not as IOU as for the cold notie case

Bottom

panel-

Contnbutlons

to the rsduccd

fluorescence

for J

13 much poorer than for d hot nozzle due to the hIsher I2 mole frdctlon sore

hot olen-hot

nozzle

In this case the c\p.tnsion

sgnlficantl~ htghcr rotattonal temper.tturss

K. Once agam assummg a Boltzmann population distribution over the entire experimental range the rotatlonal temperature scale shown was deduced. A slmllar procedure apphed to the “hot oven” data yields the results shown m the bottom panel of f1.g 14 It IS mlphcltly assumed (see sectlon 5) that vlbrational coohng plays a mmor role (m comparison to the effect of rotationai coohng) upon the :tbsolure fraction of target molecules. (A laser-induced fluorescence study such as that of ref [25] \\ould be required to determme vibratlonal temperatures. T, ,,,. and thereby populations as a function of carrier-gas pressure.) This is dlscussed m sectlon 5. In addltlon. the procedure described above results in rotational fractions 1~hlch are consistent with the present data under \arlous expansion conditions

5. Discussion The asslgnmsnt of rotstlonal temperatures. T,,,,. and thereby absolute populdttons to the curves m fog 14 deserves some discusslon. The overall trend m the figures is reasonable. The data mdlcate that 10 K is attamed (at 900 Torr) with the cold nozzle (385 K); heating the nozzle to 515 K (at 900 Torr) yields a beam with T,,, = 35 K. The lowest T,,, reached in the case of the “hot oven” (where expansion is expected to be even poorer) 1s 45 K It 1s conflrmed [21] that the ratio of the total fraction of molecules excited for any two beam conditions yields essenually the same value as the ratlo of the experimentally determmed reduced fluorescence signals. It 1s known that m supersomc expansions rotational to translattonal energy transfer IS rapld and rotational temperatures follow the translatlonal temperatures [32] Via the TOF technique it is possible to extract the translational temperatue, T,, = Ts, of the beam directly. Here T, = mat/2k where a, IS the width parameter in the supersonic speed distribution [22], IPI the Iz mass, and k the Boltzmann constant. Results are presented m fig. If. The smooth bands represent T,,, as a function of pressure for the three different. specified expansion conditions. The corresponding solid symbols

0

200

400 600 600 HYDROGEN PRESSURE

1000

Fig 15 The \nnauon of rotatmnal tempem~ures wth h>drogen pressure for the three experlmrntal source condmons mdxared (dsfincd m fig 13) The bands mdlcate the esumatsd upper .md loucr bounds for the rotatlonal temperature at each pressure The pomts ulth error bars denots translational trmperaturss derlred from the TOF analyes of the same beams

are the T, calculated from the experlmental TOFs at the indicated pressures. The overall agreement between rotational and translational temperatures IS wlthin experlmental error. It has been assumed that the vibrational temperature, T, ,b, remains essentially constant over the pressure range covered, since vibrational relaxation is known to be a much less efficient process than rotatlonal relaxation [33]. At the lowest pressure, for the cold nozzle (T,, = 385 K), the fraction of molecules in u” = 0 is 0.55. For the highest pressure expansion It is estimated that Tv,b = 150 K (extrapolating from ref. [25]) for which the u” = 0 fraction is 0.87. The correspond-

populations are f,,, = 0.009 (for T,,,, = L 1 and f,,, = 0.110 (for T,,, = I 1 K) respectively. Thus although the vartation in the fraction of “acceptor” molecules (curve B) is not due entrrriy to changes m population in the proper rotatlonal level. It serves as a reasonable first apmg rotational

F t

proGnatton (in the absence of further informatlon. such as LIF). This assumption would force T,,, to be lower than tt actually is However. the maxtmum m fig 14 would still remam and thus the ~sstgnment of T,,, = 11.2 K at that pressure -_ lmphctt m the present analysts is the assumption of a pure Boltzmann rotattonal dtstrrbution over the entire pressure range. However, there is some ekpenmental evidence suggestmg non-Boltzmann rotational dtstrtbuttons m supersonic expanded beams -==_ It IS of Interest to maxrmtze the fractional ewitation and to determine the combmatron of elperrmental varrables (u,, laser-molecular-beam angle of mtersectton. etc.) whtch will yield the maximum fracttonal excitatton. Extensive calculattons ha\e been carrred out to determine the role of the angle of intersection between the laser and (vanous) I, beams upon the fractional excrtatton. some results are presented m fig 16. The free-runnmg multimode operatton of the argon-ion laser \\as simulated by averaging the contributtons from 55 pseudo-randomly generated laser mode structures [21] Curves A and B represent supersonic beams wtth us = 2 4 and 0.95 km s-t and speed ratto 5 = 85 and 8 respectwely. Curve C is for the spectfted max\\elhan beam. Included in the total fraction IS the estimate of the u” = 0 fractton: for the supersonic beams. these are taken to be 0% (T, ,,, = 150 K) and 0.59 (T, ,b = 350 K) for cases A and B respectively (extrapolating from ref. [25])

_ B~rnng other conslderatlons the procedure adapted here \sould be more accurate for molecular s>sterns such 8s h0 or CO for \rhlch 99 6 and 99 S% of rhe moleuile~ dre &eadJ XI ths V” = 0 ~mte at 500 K. + For N2 [34] and I-t2 [351 rhc rotntlonnl popul~l~on~ under cerlam erpans~on condmons are not go\emed b> A SW$ Bollunann For poly~om~cs the results nrc COnfllCtln_g De\latlon from a sm_ele Boltzrnann hake been mdlcated for NO, 1361 OCS 1371 md CO2 [3S]. although some eiperlmenIs sho\x A Boltzmann dlsrnburlon [39-411

lOdo

I

30 LASER-MOLECULAR

$0

& BEAh

120 CROSSING

I;0 ANGLE

180 tdeg)

Ftg 16 C.dculated irxuon of 1, beam moleculec eu~ted b\ rhe 5145 nm laser hne JI 1 U Guns A (9) 1s for d fast supersomc beam L, = 21 hm s-’ 5 = S5 curxc B (0) for ~1 SIC\\\ super,omc beam L, = 0 95 Lm s- ‘_ 5 = 8 and cun e C (A) for A max\xelhan beam T = 175 K The fx\hm angular dlxcrgenre 1s 0 S” for the ~up~rsomc hwm~ (A and B) and I 5” for the m~xx\elhan beam (Cl The fracrlan of excunon represenr, the ab>olurs fr~c11on lahmg m10 accaunl rhs frxtlon of molccules m the proper ro\lbratlonal Ie\els and the frxnon of [heart mols~uls~ affected b? rhs laser radlarmn See 1~x1

and 0.553 (Tllh = T,, = 3% K) for the ma\\\ellian case From frg 14. the fractton of acceptor molecules is 0.115 (T,,, = 11 K) and 0.0117 (T,,, = 300 K) for beams A and B respectively. For the rna~\\ellian beam it 1s 0.0092 correspondmg to T,,,, = 375 K (i.e. T,,). Also included 1s a geometrical factor \\hrch r&es mto account the fact that the drameter of the laser at the ewitarion zone is srn~ller than the beam drdmeter (0.765 and 0 642 for the supersomc and ma\\\ellran beams rcspectimely). Thus ftg 16 presents the total fractron of I, molecules in the respective beams that can be ewited to the B state with 514.5 nm photons (at 1 W).

336

In the present experunents (laser-molecularbeam angle of mtersection = 135O) the maximum overall fraction of I2 molecules excited IS 2 x IO-“. for bedm A Fig 16 shows that, under optlmdl conditions = 1% of the I, molecules could have been excited (for an angle of lOSo) A number of improved laser excltatlon conflgurations are possible. The first is to arrange a mirror system about the molecular beam whtch reflects the laser beam back through the molecular beam several times (= 9). A multlpass arrangement has been tested m the present work. The 15 beam losses were Increased thereby a factor of = 2 5 The other is to direct the laser parallel to :he molecular beam. In this Instance many more molecules could be excited (I.e. the absolute number); however there are obvious problems with this scheme (e.g. the radlatlve decay loss and the low fractIona e\citatlon. cf. beam A at 180” m fig 16) Fig 16 Indicates the advantage of a cool supersome beam in maxmilzing the fraction of molecules evxted. due mainly to the increased fraction of I, molecules in the low-lymg u” = 0. J” = 13.15 states (purely a consequence of the partition funcnon) However. the angle at w hlch the laser crosses the molecular beam must be optimized (cf. the sensltlve angular dependence for curve A)_ This stems from the large Doppler shift due to the large I, beam velocity. At very low angles of intersection the laser radlatlon is too far red-shlfted. while at large angles it IS shtfted too far into the blue for absorption to occur. Tfus can be compensated for hy usmg slo\\er supersonic beams, e.g _ curve B However. the general result is to obtain a lower total fractIona excltatlon due to the higher Tr’,,,_ Carrier gases other than Hz_ such as Ar, provlde slo\\er beams with fairly good expansion characteristics. This results in a good fractional excltatlon due to good overlap bet\\een the laser gain curve and IZ hyperfme structure and low rotatIona temperature Although this has been confnmed experimentally [21], Ar carriers were not pursued since I, beams an order of magnitude more intense were produced with Hz as the carrier gas (due to the higher throughput for HZ) [42] Fig. 16 shows that the poorest fractional excltation of a beam of I, is obtained with a maxwelhan

beam The contribution from the overlap of the hyperfme structure with the laser gain profIle 1s excellent but the fraction of molecules in the proper rotatIona states is quite low. Indeed. for e\cttatton at 90” the mode structure of the laser becomes very critical in this case (especially if well-collimated thermal beams are used) Z The hmitmg factor m all cases is essentially the rotational partition function. At best one can hope to force only 11% of the I, molecules into the acceptor states (assummg a Boltzmann dlstnbution) *-. For reactive scattermg the number density of 1; molecules tl* = fn,?. ISimportant. not f alone (the fraction of IZ molecules electronically excited) The reduced fluorescence curves (fig. 3) are directly proportional to f so that the best f is achieved at the maximum The quantity )I*. however. is proportional to the fluorescence: thus a maximum m the fluorescence curve gives the maxnnum II*_ To maximize II* it is necessary to produce intense beams. In practice this requires high partial pressures of I, in the expansion mixture which results in a higher T,,,. The net effect is lower f but larger II*. A larger f can be achieved in a supersomc expansion than m a gas cell (f= 10P5), but the net number density II* of 1; 1s lower. These results may shed some light on efforts to observe the mfluence of electromc excltatlon on the chermcal reactlvlty of If. In literature reports where laser excitation experiments were performed under molecular-beam (smgle-colhslon) conditions c The “dip

present m curves B and C at 90” IS due 10 the dlsappearance of the broadening effect of Ihe keloclty dlzrnbuuon Only the broadening due to the angular driergence remams Smce the hneshapes are narrower the overlap mtegrals, R(v), are smaller and the e~cltatmn decre.ws Homeber at very hlgb velocnies (and hlgb 5) as m cur\e A the mam comrlbunon to the broadrnmg of the lmeshapes 1s the beam angular dtvergence (smce it IS proporrlondl to the ~eloclty 1211) The hlperfine hneshapes remam essentially the same ober the angular range 85-95” and rhus no “dip” 1s observed If the contmuous laser garn curve of eq (11) had been used, these “dips” Hould not appear. The case for the excltatlon of atonuc species is very differem Under the appropriate condmons II has been reported possible IO elecrromcally excne 30% of all Na atoms m a beam [43] Thus accords with the present ewmaIe for 1, If one sets jroJurb = 1.

337

there appears to be no evidence for laser-induced reactton However, the I2 beams were prepared as thermal-maxwellian beams (smlilar to curve C of fog. 16). The present results suggest that d factor of IO’ to 10’ increase in the fractional ewitatton of I, molecules can be obtained under suitable expansion and excttatton condittons.

this \\ork. FJ.4 ackno\\ ledges the support provided by the IMmistry of Unwerstttes and Research of Spam and the Council of International Exchange of Scholars.

Appendi\

A. Solution

of the kinetic

equations

Eqs. (1 d) and (1 b) are of the form 6. Concluding

remark

dtr,/dr

= /~Jz, -I- Ba,.

(A-l)

Appreciable electronic excitation of I2 under colhsion-free condttions with the Ar’ laser 514.5 nm line is dtfftcult due to the small populatron of the appropriate u. J states m the beam molecules at a given temperature. Experimental condttions can, however. be adJusted to maximize the relattve

dlr,/dr

= C~I, i Dn2_

(A.2)

B=

(g,/sz)B,,R(v)‘=iz,.

population m these u. J states using the techmque of supersonic expanston which cools the internal degrees of freedom. In the present conftguratton. the maxtmum fraction of an 1, beam excited by the 1 W multlmode output of an argon ion laser at 5 14.5 nm was = 3 x 10m3 (From mode1 calculations thts frac-

C=

B,,R(

tion could be increased by a factor of = 3 by optimtzmg the angle of intersection of the laser beam with the molecular beam.) The present work has also added some addttional information to the already note\\orthy collection of data available on the I, molecule Speciftcally, at 514.5 nm, the I2 direct photodissociatton cross sectton \\as found to be (2 4 f 0 5) x IO-l9 cm’ and the Einstein B coefficient to be (4.9 * 1.0) X IO’” erg-’ cm’ s-‘.

il. B. C. and D are

where the coefftcrents rl = -

[B,,R(+@u~].

v).

D = - [(gi&)B,zRW

-aqt

(A-3)

- h’,,].

(All symbols ha\e been defined in section 4.) Here R(P) represents the o\+rlap of the energ! densit! profile of the ewttatron source and the h>perfme lineshape The procedure for soiling the lmear system (A 1) and (X2) IS standard. The general solution is: eh_’ + n’-~ &I_ iz, =(Y (1) I I (II A-3 + &(21 eA_’ II-.=Q> e 2 where &! ‘r drrl constants soluttons of the quadrdtlc

k’-(_4~D)k

(.X4) (_Q) and k _ and equation

X-_ dre the

T(.4~-~C)=0.

(-4.6)

narnrl~ r41=+f The authors wish to acknowledge the early contributions of Dr. M-A. McMahan (details of 1~hich are reported in ref. [S]). FJA and MM0 ackno\tledge many fruitful discussions on various aspects of the excitation problem wtth D W Squire. The data pertaining to the hyperfme lines of iodine \sere provided by Professor S. Ezehtel of MIT whose cooperatton IS deeply appreciated. Thanks are due to Professor B. Garetz of the Polj tschmc Institute of NY for the loan of the etalon used in

+ D)i$_&D]2wc]1

‘_

(X.7)

The &I(j) can be e\pressed m terms of the mtegrJtton constants C,. C,. and the coefftclents (X.3) such tha: (X.1) and (A.5) become 11, = [B/(X_-_A)]

e<-‘+

[C&_-D]/C]

I+‘. (_4-S)

II z=C,e Imposing

&_I+ C &I_ 2 the boundar>

(X.9) conditions

(I = 0. trl = no

AOK et al / Laser excuafmi of supersonrc seeded nroIecuIarheanls of I2

FJ

338

and tr2 = 0). the fmal expression is gtven by

f=

tlJtlo =

C(k+-A) (k__

BC_

h*I_

D)(k+_

A)

(e

Since R(v) is proportional to the laser power. (A.14) predtcts a linear increase with the power. e’-‘)

(b) For very long excitation conditions)

(A-10) Special

When the direct photogfragmentation rate can be neglected and the fraction of molecules excited IS small, the overall number denstty of molecules tI = tl , + tt z can be considered constant. The same could be applied when predtssoctation is negligible factor favors and A, = A,, (the Fran&-Condon the return to the original ground vibratronal state) In this case eq (2) can be written as = {tt - [(g,

dtr,/dr

B,,R(u) g, f= E<

cases.

+ g,)/g,]tt,}B,,R(z~)

+ gz)/g,]&,R(V)

2416

or in terms of the fraction of exctted molecules df/dr

I71 CT.

- ($d+A,

(A-12)

)I-

&R(V) f= Kg, +gg,Vg&WW

X(1-w[-4

-

+ (K,, +A, )

[
K,,]I>-

(A-13)

When there is no predrssoctatton and the hfetime 1s long (B,,R(v)=+ A,, ). eq (A 13) can be stmphfted to f=

Cg,/(g,

i- g,)l

X(1 - exp[-

[(g, + gl)/gzlR(~)B12~])r (A-14)

providing that at equilibrium before number of molecules in level 2, tJl, Eq. (A 14) has been used to esumate vibrational excitation of a molecular

excrtatton the is negligible. the extent of beam of HCl

(11. Two limits are apparent from eq. (A-13): (a) For very short excitation times, f=

B,2R(~)r.

PI

(A-15)

and Y-T Lee, J Chem Phys 73 (1980) 5122 D Lubman and RN Zare DIscussIons Fara-

day Sot 62 (1977) 317 Retuner, L WBste and RN Zare. Chem Phbs 5S (1981) 371 M A McMahan Ph D. Theses Department of Chemlsny.

Columbia

Solving eq. (A 12) it can be found that

(~-16)

[I ] R B Bernstem, Chemical dynamics via molecular beam and laser techmques (Oxford Unn Press. London, 1982) [2] A Gupta DS Perry and RN Zare J Chem Phys 72 (19SO) 6237.6250. [3] H H Dlspert. M W. Gels and P R Broohs J Chem Phys 70 (1979) 5317 [4] CT Retmer and R N Zarc, J Chem Php 77 (1962) [S] CC Kahler Is1 R C Estler.

= (1 - [(g, + gz)/g&P,zR(v)

+ K,, + A,. -

References

(A.1 1)

-&,+A,)tJ,,

times (steady-state

Uruverslty, New York

NY (1981)

[91 S Ezekiel and R Weiss, Phys Rev Letters 20 (1968) 91 J. Chem Phys 56 (1972) ilO1 L Breuer and J Telhnghmsen. 3929 J Chem Phys 58 (1973) 2821 [Ill J Tellmghuisen I121 A ChuIJlan. J Chem Phys 51 (1969) 5414, A ChulJian and T_A James. J. Chem Phys 51 (1969) 1242 J. Chem Phys 57 (1972) 2397. 1131 J Telhnghmsen. J Chem Phys 62 [I41 J. Vrgue. M Brayer and J C. Lehmann (1975) 4941. 1151M. Brayer. J VI@ and J C Lehmann J Chem Phys 63 (1975) 5428. 64 (1967) 4793 J. Quant Spectry Radratne Transfer 19 iI61 J Telhnghursen. (1978) 149 S G Kukohch, LA Hacker. D G YoukI171 D J Reuben. mans and S Ezekiel Chem Phys Letters 22 (1973) 326 1181 RS Mulhken. J Chem Phys 55 (1971) 288. Bemsrem, Rev. SCI Instr 41 iI91 R W. Brckes Jr and RB (1970)

[20] TM

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Mayer, B E Wdcomb and R B Bernstem, Phjs 67 (1977) 3507. J.A Haberman. Ph D Thesrs. Deoartment of University of &consm Madrson: WI (1975). BE Wtlcomb. Ph D Thesis, Department of Universny of Texas, A&tm. TX (1976). Ph D Thesis, Department of I211 M M Oprysko, Columbia University, New York, NY (1983) and [=I M M Oprysko. F.J. Aorz., M A McMahan stem, J. Chem Phys 78 (1983) 3816

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339

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I-331 E Weltz and G W Flynn _L\nn Ret. Phys Chem 25 (1974) 275 1341 D Coe. F Robben L T&bat and R Cat~ohca Phys Flmds 23 (1950) 706 [35] J Verberne, I Ozrcr L Z.mdee dnd J Reucs hlol PhLs 35(197S) 1649 (361 R E Smalley L \\ hxron and D H Leq. J. Chem Phys 63 (1975) 4977 [37] S G. Kuhohch D E Gates and J H WanS J Chem Phys 61 (1974) 4686 [3S] S P Venhatehan S B K\JII .md J B Fenn J Chem Phys 77 (198’)2599 1391 T E Cough. R E Uller .md G Stoles J Chem Phys 69 (1975) 1x? (401 I F Sd\crJ and F Tomm~suu Phys Rev Letters 37 (1976) 136 1411 DN Tr.1~15 J C XlcGurl, D llcKeo\rn and RG Dennmg Chem Phyc Letters 45 (1977) 257 [42] A Roth Vacuum wchnology (horth-Holland. Amsrerdam 1976) [43] Xl Vernon and k .T Lee pruare commumcauon (1957)