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Relaxation and spectroscopy of CaCl in seeded supersonic beams
Chemxal
Physics
Norrh-Holland
77 (1983)
Pubhshing
RELAXATION
U. BUCK,
201-212
201
Compaq
AND
J. KESPER,
H-H. KUGE
Alal-- Planch - Insrrrrrr ftirSrr~nturlgsforsciltmg 4 November
RecelLed
1982
formula
fluorescence
IS given uhlch
SUPERSONIC
BEAMS
and D. OnEN 3400 Gorrmqm
F~vit~uI Repuhhc of Gem~am
m final form 4 March 1983
The rotational and rtbratlonal by laser-Induced
OF CaCl IN SEEDED
SPECTROSCOPY
relaxaLlon of a calcwn-monochlonde The rotaIlona1 dlstnbutlons cannot
represents
the measured
dlstrlbuttonr
bwm seeded m He. 4r and Kr has been mvestlgated be described b> L( cmgle !smpcr.wxe 4 tu*parameter
and uhxh
s characterized
b> local remperarures
K dependmg
on the rotational slates and [he expansion condlrions wth source remperarures of r, = 1320
The effectwe
coohng
increases
from He to Ar as tamer
gases. In contrast.
the xlbrxmnal
dtsrnbuuons
could be reprecenrcd
Boltzmann dlstnbutions with temperatures of 1400 10 569 K The order of wbrarional coohng goes from of the CaCl X-B spectrum hale been recorded unh hlgb resoluuon The artempl 10 Identlf> the measured best molecular
needed accuracy
from 30 to 200
K and T, = 1520
K bk
or c He c Kr Parts hnes reheals rhar rhe
for 0~s system do not reproduce all lrnes of Ca35CI and especlall~ not zho
constants
1. Introduction
Laser-induced fluorescence is a widely accepted method to study state-resolved vibrational and rotational distributions of diatomic molecules [ 11. If these investigations are performed m a supersonic nozzle beam [2] we have an attractive tool to study both the spectroscopy of the species m the beam and the kinetics of the collision processes that occur during the expansion. The spectroscopy is simplified appreciably because there is considerable rotational and vlbratlonal cooling of the molecules and there are nearly Doppler-free hnewidths. In addltlon, the extent of the coolmg by seeding the species in different diluents can be used to derive information on the rotational and vibrational relaxation of the molecules_ Investigations along these lines have been performed mainly on the alkali dimers Na, [3,4] and Rb, [S] and the halogen molecules I, [6-91 and Br2 [IO]. In the present paper we extend these studies to calcium monochloride. CaCl. The alkaline-earth monohalides have attracted a lot of interest in the past years since they represent an interesting class of ionic molecules with a single unpaired metalatom-centered valence electron The very dense 0301-0104/83/0000-0000/$03.00
from the electronic transitIons haxe been resolved on11 recently_ The spectra haxe been analysed by laser excltatlon and fluorescence spectroscop) [ II- 161. optical-optlcal double resonance [ 171. laser-rf double resonance [IS-2 I]. and rnicro\\a\e spectroscopy [Xl. Studies of the radiati\,e lifetime [23] and the electric deflection [24] complete the experimental informauon on these systems. We ha\e measured the ~~brauonal and rotational state distributions of CaCl in its eltctronic ground state b> mducing transinons to the B’S’ state with a smgle-mode cl\ dye laser and observmg transiuon from the excited state to the ground state. CaCl is formed in the source b> A chemical reaction and expanded from 0 7 or 0 3 mm diameter nozzles \\lth He. Ar. and Kr as carrier gases at temperatures of 1320 and 1520 K;. The completely resolved vibration-rotation spectra have been analysed in terms of the most recent constants from other laser-induced fluorescence experiments [ 13.15.171 and microwave spectra of the ground slate [22] Although rhe general features of the measured spectra are reproduced. there are still some discrepancies especially for Ca”C1. To demonstrate the precision of the present e\periment the spm-rotation constant is derived and spectra
0 1983 North-Holland
compared with the results of other expenments. For pressures of the carrier gases from 55 to 1500 mbar the populations of angle rotatton-vibratton levels have been obtamed. Whtle the rotational distributions were found to be extremely non-Boltzmann with an apprectable coolmg m the order He -Z Ar, the vibrattonal distributions could be represented by Boltzmann distributions. The cooling is only moderate and mcreases in the order Ar < He < Kr. The reversed order for Kr and studies with different nozzle diameters indtcate that an appreciable amount of the vtbrational relaxation for the heavier rare gases is due to other processes than pure collistonal relaxatton [8,25.26]. There are several recent studies of colhsional relaxation in seeded beams using other techniques_ Rotational relaxation has been investigated by Raman scattering (271, infrared spectroscopy with bolometric detection [28] and electron beam fluorescence [29,30] Vibrational relaxation was studted by electric resonance spectroscopy [31.32]. We will compare our more extensive data with these studies where it 1s appropriate. In section 2 we describe the experimental arrangement The spectroscopic results are given in section 3. Next. we present the relaxation data for rotation and vibratton and discuss the results m terms of simple relaxation models.
2. Experimental 2. I. Apparatus Fig 1 shows a schematic view of the apparatus_ It consists of three separately pumped chambers_ The source chamber is pumped by a 6000 Y/s diffusion pump backed by a roots-pump (500 m’/h) and a rotary pump (100 m3/h). During operation the pressure in the source chamber raises up to 3 x 10m4 mbar when He is used as carrier gas at a stagnation pressure of 1500 mbar. The molecular beam enters the second chamber through a skimmer heated to 900 K. After passing a chopper, a fluorescence detector and a Fizeau-type velocity selector, the beam enters the third chamber with the quadrupole mass filter as detection system. The pressure in the second chamber is
Ep
I
I
Laser t-3
I
I
Fig 1. Schematrc view of the apparatus (A) Beam source (B) shimmer. (C) beam chopper. (D) kisser l&t catcher. (E) velocity selector. (F) quadrupole mass filter delector. (G) fiber bundle to the photomultlpher. (H) single fiber from the laser
lower than 10mh mbar and m the detector chamber lower than 2 x 10-s mbar. 2 2. Laser excitatton and fluorescence
detectlou
A single ftbre leads the laser light to the fluorescence detector_ The laser light is produced by a tunable Spectra-Physics ring dye laser, model 380 A, pumped by a Spectra-Physics argon ion laser. model 171-03. The nng dye laser was operated in two modes of operation. In single-mode operation the typical output power was 350 mW at 593 nm, and the typical halfwidth of the unstabilized mode was 30 MHz. During the low-resolution expenments, the laser was used in multimode operation. In this case the halfwidth had to be increased from naturally 2 GHz to at least 25 GHz in order to maintain the tunability over several angstroms This halfwidth is achieved by directing a portion of the light reflected by the fibre entrance back mto the cavity. The multi-mode output power did not exceed 600 mW at 593 nm. Part of the laser hght was guided to several control instruments: A Spectra-Physics interferometer, model 450-4, FSR (free spectral range) 10 GHz, to observe the mode structure, a Burleigh RC 110 temperature-stabilized interferometer, FSR 1 GHz, finesse 70, to give frequency marks, a McPherson 1 m scanning monochromator to give the coarse wavelength determination and a low-pressure I,-absorption cell to achieve an absolute wavelength calibration. Due to Doppler broadening and the unresolved hyperfme structure
the residual full halfwtdth of the I,-absorption peaks was = 0.9 GHz. This hmits the absolute CaCl transition frequency determmation to within an error of kO.005 cm-’ or 0.0002 nm with respect to the I,-absorptton peaks. The fluorescent light emitted from the CaCl
Table 1
molecules was collected
4r
by a laser-stray-light
re-
ducing detector, and fed to an EMI 9816 QB multiplier by a fiber bundel. The signal was measured by a PAR model 128 lock-in amplifter. The fluorescence signal, the frequency marks, the laser power. the Iz-absorption peaks. and the CaCl quadrupole mass filter signal were recorded on strip chart recorders
The crucial point of the experiment in the generation of an intense and stable beam of CaCl which has to be produced in a reaction at high temperatures_ In two experimental series we used two different sources. For both ovens the principle of construction was the same there are two separately heated chambers, a bigger reservoir and a smaller unit containing the nozzle. In the first variant the oven conststed all over of stainless steel, Inconel 600, which limited the nozzle temperature to a maximum value of 1370 K In the second variant we made the nozzle chamber of tantalum. In this case the temperature was hnuted to 1720 K by our nozzle heating system The nozzle diameters. were 0.3 mm and 0.2 mm for the first and the second oven, respectively. To produce CaCl we used two reactions. during the first series of experiments. Ca + M&l,
+ CaCl + Mg + Cl,
(I)
during the second 1331. Ca + NaCI --, CaCl + Na.
(II)
Reaction (I) has the disadvantage that it leads to d rapid corrosion of the stainless steel probably due to the formation of atomic Cl. Reaction (II) produces an intense Na beam even at low oven temperatures. Almost all of the Na had to be removed before we could observe the fnst CaCl signal. Under these condttions the intensity of the CaCl beam was 1.5 x 10” particles/sr s, when seeded in
Ch.w.msnsuc
Garner gas
hwm
Pressure (mbar)
d.un -I’
Speedmu0
T(K) cdrrier
CKI
c.w-w _gas
72
15
66
145
40 30
-
90
-
103
-
.?F
Hrt Kr
750 600 500
CKI
=’ Rcacnon (I) source temprratur+137-O h nozzle dwnrrsr 03mm
500 mbar He. and 2 x lOI particles/sr s. Lxhen seeded in 300 mbar Kr. These Lalues haxe been obtained from the mass spectrometer signals calibrated by an effusive He beam. The recorded CaCl intensity decreased \\ith increasing mass of the carrier gas and. aside from He. \~iithmcreasmg carrier-gas pressure_ Both effects seem to reduce the reaction yield. Only He leads to an enhancement of the CaCl signal with increasing stagnation pressure up to a temperature-dependent mallmum. Raismg the pressure above this point decreases the CaCl signal rapidly. The ma\irnum p. D values for a detectable CaCl signal \xere found to be = 22 Torr cm \\iithhehum. 14 Torr cm with argon and 7 Torr cm with krypton. u herep, is the stagnation pressure and D the nozzle diameter. The CaCl mtenstty could be increased b> d factor of t\\o by raismg the nozzle temperature from 1570 to 1720 K. Unfortunately. the need of re.isortable hfctime for our nozzle heating s?stsm limited the attainable nozzle temperature to 1520 K for permanent operation The resenoir temperature was kept at 1050 K since raising the remperature above this value did not increase the beam intensity_ Typical beam data for different carrier gases are given in table 1. xxhhsreths translational temperature T and the speed ratio charactertze the expanston [2].
3. spectroscopy In order to investigate the rotAtiona rsla\atton m the beam WC hd\e to deal \\ith the CaCl spectrum in the \isible. Wtth a rhodamin 6G d,e laser
U Buck et al / Relax-arron and spectroscopy of CaCI m seeded superronrc
204
can conventently induce a transitton from the X ‘X+ state to the ftrst excited A21f or the second B’Z+ state. We have chosen transrtrons to the B ‘Z-I state because the spectrum IS less complex than in the A”TI case. Nevertheless the spectrum of the X ‘XC-B ‘Z+ transttton 1s very dense due to the stmilar potentials in the ground and excited states In addloon, the existence of the Ca7’C1 Isotope with a natural abundance of = 25% complicates the analysis. Since both states are ‘Z states four rotattonal branches, R,, R,, P,. P2 and wtth lower mtensittes the R, and Pa satellite branches can be observed Our denommatlon follows Herzberg [34] so that the R branch denotes a AJ = + 1 transmon, the P branch a AJ = - 1 and the indices 1 and 2 denote J = Iv -I- l/2 and J = N - l/2, respectively. From 592.98 to 593.32 nm we measured the absolute frequencies of = 230 rovtbronic CaCl B ‘2+-X ‘Z+ transittons. For the Isotope Ca”CI we have obtamed the R, and Rz branches of the Au = 0 sequence wtthm 0 < N” < 50 and Y” = 0. 1. 2 and 3 (see also table 2). A portion of this htgh-resolution spectrum is shown in fig. 2. The full wtdth at half maximum of the lutes caused by Doppler broadening due to the angular divergence of the beam was = 150 MHz with He as carrier
one
593 14
593 15
593 16
Laser
wavelength
hems
gas. and ‘t: 90 MHz wrth Ar as carrier gas. The dtfference is due to the different velocities of CaCl when seeded m different carrter gases. For a pure CaCl beam the linewidth would reduce to = 40 MHz which is the hmit caused by the hyperfme structure [21]. A high-resolutton spectrum recorded whtle seeding with Ar permitted the resolution of the very weak R, satellite branch. Our frequency calibration was given by the stmultaneously recorded I?-absorption spectrum. The wavenumbers of the todine lines were taken from Gerstenkorn and Luc [35] They give a stattstrcal error of *O-O005 cm- ’ and a possible systematic error due to their calibration with uranium lines of f 0 002 cm-‘. Our error in determmmg the absolute transition frequencies of CaCl was +O 005 cm-’ wtth respect to the iodine hnes. This error contains both the statistical and a possible systematic component. In order to identify our observed CaCI transitions we computed the CaCl transition frequencies usmg several sets of spectroscopic constants There are essentially three complete sets of constants available for the X “Z and the B’Z state. The set of Domatlle et al [ 171 IS dertved from a combined fit of the laser excitation spectrum of the X-B system. the microwave spectrum of the ground
593 17
593 18
lnm
Fag 2 Obsened fluorescence excnatlon spectrum of a CaCl beam seeded m 500 mbar He m the B’Z-X
‘2
bdnd system
state
and the optlcal-optical double resonance spectrum of the E-B system Since only the lowest vibrational states are involved in thts analysis (v” = 0. 1, 2). Telle [ 131 derrved a new set of constants
essentially based on the results of ref. [17] but also fttted to higher vtbrational states (up to u” = 12) of new measurements. Fmally there is a very detailed laser spectroscopic investrgation of the X-B system by Berg et al. 115). who used 1124 lures of the AL’= 0. + 1 sequences for A!” < 120 and Y” < 11 together with information from other transrttons. e g the X-A system 1141. for the ground state. Two very recent high-resolutton mvestigattons of the ground state complete the avarlable data. Moller et al. [22] measured the mtcrowa\e spectrum and obtained very precise rotational constants. Childs et al. [21] performed a molecular beam laser-rf double resonance expertment and determined the hyperfme-structure and spin-rotation constants to an extreme precision_ In both cases the vibrational and rotational dependence of
the spin-rotational data
constant is extracted
from the
The compartson of the observed lme positions of our measurements with calculations revealed that the constants of Domaille et al. [ 171 could not reproduce the measured frequencies within the derrved accuracy. Only the constants given by Telle [ 131 and Berg et al. [ 151 could be used to Identify the lines. Smce the line-to-line compartson did not show any anormal behavtor we used the normalized root-mean-square deviations (RMS) of every rotational branch as a measure of the devration from the predicted line positions
The results are hsted m table 2 A value smdller than 1 0 means that the predictions is consistent wrth the data within the stated error hmrts. Table 2 clearly shows that the improvement of the Telle set is remarkable compared to the Domaille set. Still, there are some larger discrepancies of the Telle constants for the R,(2.2) and R,(3.3) branches. The constants of Berg et al. [ 151 give. on the average, the best agreement with the data. with the largest deviations for the R,(2,2) and RJ2.2)
T&k
2
A’
L\“_c’
Ref [IS]
Rd [IS] + ref
Rcf
Ref
I131
1171
1X] RI
o-24
00
0 s5
100
0 75
27
R,
00 1.1
0 97
2’1
R, R, Rz R,
6-28 19-41 16-36 30-50
R2
2s-44
11 22 22 33 3.3
1 26 1 57 2 IS 0 93 075
I 10 1.77 1 75
065
RI
l-20 8-33
2 75 3 30 I 9’ 1 Y3
3 77 135 6 91 1 ss
1.1s
OYS 0 7,
69 39 14 s b5 ‘7 1 135
branch. In order to improve this result. \\e combined the precise rotatronal constants of the ground state of Moller et al [22] 111th the constants of Berg et al. for the vtbratron and the excited state. Unfortunately. this data set leads to an mcreased difference bet\\een measured and calculated transttton frequencies. very probably due to a correlation of the excited- and the ground-state constants of Berg rt al. [15]. The use of different carrier gases permits us to identify sixt>-four lmes of the C&Cl Isotope belonging to the R, and R, branches of the 1~ = 0 sequence for 2 Q N” G 23 and L”’ = 0. 1. Because of the much more enhanced rotational relaxation for Ar as carrier gas. small umdentifted lures of higher vibronic transitions vanished \\hrle loller vrbronic transitions of Ca”C1 increased in intensity proportronal to the mtensmes of the correlated C$‘Cl trdnsnions. The root-mean-square devrations for the measured and calculated transition frequencies for Ca”Cl are given in table 3. The calculated Lalues \\ere obtdmed b> multlply-
ing the Ca”Cl constants of Berg et al. 1151. and Telle 1131 by an appropriate poaer of the ratio p = ( p”‘/p37)l/2.
where p IS the reduced mass of the molecule [19]. Smce only a fm Ca’7Cl lines were rdenttfred we could not decide I\hether the relative strong deviation between calculated and measured frequencies is due to slightly incorrect Ca-“Cl constants or a breakdown of the mass-scalmg procedure. To demonstrate the accuracy of the measurement He determine the spin-rotation constants by
U Bud
206 Table 3 Root-mean-square
RI R2
R, R,
et al / Relaxarron and spectroscop)
0”
2-19 2-18 8-23 6-20
0.0 0.0 1.1 1.1
. I)’
Ref 1151
Ref [13]
19 23 30 30
17 19 22 IS
means of a least-squares fit from sixty-five lines for Ca-“Cl and twenty-eight hnes for Ca37C1 out of the data fields given above The vlbratlon-rotatlon-dependent value of the spin-rotation mteractlon strength is given by Y=Yoo+Y,o(U+~)+Yo,N(N+
1).
(1)
Using the ground-state values of ref. [22] we derive the values for the B’Z’ state The results are listed m table 4, together with values of Berg et al 1151. Our data are not sensitive to yo, because only lines with N” d 50 were measured. The magnitude of yoo compared to the ground-state value clearly indicates that the B’Z state 1s perturbed by the close-lying A’II state. Following the treatment of Zare et al. 1361 the spin-rotation constant of the B state is equal to the negative A-doubling constant p of the A state and is given m the unique perturber approximation by y = - 2AB(njL+la’)‘/ AE, where A is the spin-orblt interaction, B the rotational constant, L, the raising operator for the orbital angular momentum and AE the energy difference between the electronic states n, n’_ In a further approximation, van Vleck’s case of pure precession [37], it is assumed that the valence electrons have a well-defined angular momentum and the matrix element gives f(f + 1). Using the constants of ref. [14] for the A’IT state and I = 1
sphttmg
constantsof the CaCl B’X’
stale in cm-’
CzPCl
Yoo YIO
YOl
get y = -0 060 cm-’ which IS not too far away from the experimental value, but clearly outsrde the experlmental error. However. the experrmental value of p = 0.0642 (2) cm- ’ of the A state [ 141 is close to our experimental result for y. We conclude that the umque perturber model is a good descriptlon for rhe interaction of the states but they are not :n pure precession. The reason is a contribution of d wavefunctlons to the p character which IS slightly different for the two states [ 14,16.17]. rhe present results for Ca’SCl are in good agreement with the yoo and ylo reported by Berg et al. [15]. The yoo value agrees also well with yoo = - 0.0652 (2) obtained by Domallle et al [ 171 The spm-relation constants for Ca37C1 determmed in the same way are also hsted in table 4. The results are compared with predlctions based on the appropriate powers of the reduced mass ratio times the Ca3%1 constants of this work. The values agree within the error limits. The validity of the mass-scaling relation for the spin-rotation constant has also been found for the ground-state data [21,22]. None of the available sets of molecular constants fits all our measured line positions within the given experimental error. The constants of Berg et al. [15] are a good representation for the Ca3’Cl spectra except for the R, (2.2) and R2(2,2) branches. To decide whether these deviations are we
devmtrons Ca3’Cl
N
Table 4 Spm-roratlon
OJ CaCI IO weded srrperronrc heanls
due to erroneous constants or local perturbations we have to extend the measurements to larger N values. The rgreement wth Ca3’C1 IS worse. TO
improve the accuracy of the molecuIar constants for CaCl our measurements (possibly extended to a larger wavelength range) have to be evaluated m a simultaneous fit together with the precise microwave data of the ground state [22].
Numbers in parentheses refer to 20 unceriamtles m last dlglls Ca37Cl
thus work
ref 1151
this HOA
calculated a)
-0.06513(9) -3 9(3)X10_’ -
-006531(14) -40 (12)x10-4 1.36(12)x IO-’
- 0 0630(2) --44(17)X 10-4 -
- 0 6325(9) -3.7(3)x1o-J
*) Calcuiated from the Ca3%l constants of tis
uork and the appropriate power of the reduced mass ratios
4. Rotational
relaxation
Lure-intensities from high-resolution scans with the laser yield direct information about the relative number of molecules in a specrfrc vibrational and rotational state of the electronic ground state once the spectroscopic constants are known [ 11. in frg 3 the number of CaCl molecules m specific rotational levels is plotted against the rotational term value F. In thus measurement He was used as carrier gas at a stagnation pressure of 500 mbar. In fig. 3 the R, and R, branches of different vrbrational bands are marked by different symbols. All values are normalized to the strongest populated state m each branch. The different behaviour of the curves IS essentially due to the rotattonal states N measured in the different branches. The semilogarithmic plot illustrates directly the devratron from the Boltzmann distnbutron which should give a straight hne The deviations are largest for the small N values. A temperature determined by the slope of the number density versus the term energy curve 1s only meaningful in an infinitesimal sense as the derivative in one point and we like to call this quantity the local temperature d ln[n( F’)/(ZJ
T;‘(F)=k
+ I)]
dF
I-F
(2)
From fig 3 ue computed the local temperatures and plotted them against their term values. as shown in fig. 4. In ftg. 4 there is no normalization Despite a relatively large deviation of single points the general behaviour of all points could be represented by the formula
T,= T,[l
-eeup(-M-)1_
(3)
where F IS the rotational energq ‘_ From a leastsquares fit we obtamed the parameters T, and b_ As can be seen in ftg. 4 T, has the meaning of a “final rotational temperature”. which is reached at large F, whereas the “dynamic parameter” h determines the curvature or. m other words. ho\\ fast the final temperature TAis approached_ From fig. 4 it is also immedrately clear that there is no large difference in the rotational populattons of various spin states (R, and R,) and Larious \ibrattonal levels. because this aould produce different curvatures or at least different final temperatures for each vibratronal-rotattonal branch. With the assumptton that eq. (3) is Ldhd for all vibrational levels the number of molecules in specific rotdtional states is obtamed by integrating the Boltzmann distribution
-p( - F/X ?, )
~~=C(2J+1)~l_e\P(_bF)]I,1T,b-
(4)
with T, and b the same as before and the normahzation constant C_ For large bF values the expresston
approaches
a
Boltzmann
dlstnbution
with
T,.The solid lines in ftg 3 dre calculated using this expression ~11th the parameters derhed from the frt displaced In frg. 4 The various cumes for various branches differ only b! an additional constant which is used to shift them parallel to the-1 a& until they coincide with the points. It can be seen that within the experimental error the above expression represents the measured data Fig. 4. also shox\s that the local temperature T=
L 0
.
J 100
200 F(J I km-‘)
300
&OO
Fig 3 Measured rotatlonal-state populations of CaCl seeded m 500 mbar He as a function of the rotattonal energ F for a source temperature of r, = 1320 K and a nozz.Ie dumetsr of D = 0 3 mm The dlfferent branches are marked as follous- 0 R,(O.O).oR, (0.0). + R2(1.1).&R, (1.1) 0 Rl(OO). x R, (2.2). 0 Rz (3.3). v R, (3 3) The sohd hnes are calsulatcd dccordmg to eq (4) \hllh T_ = 243 K and b = 0 011 cm The pomts are normahzed to the largest values of each branch
+ In :he formula T, apprcuchcr zero as F approarhcs zero Thus bchaviour can be rsmoksd b> addmg a constant X&IS Ea IO F. But m our mxcbtlgauonz Ihc de\aatmn 13 30 small 1ha.r we could not deternuns the \.duc E, b> uhlch Ihc tune haz IO be shlfted to _e~\eA reahcrlc behaviour of T, near F= 0 as ought bc nccssssq m orher mxesclgarions of low-.X’ reialauon\
U Bud
208
er al / Relaxarron and specrroscop~ of CaCl IR seeded supersonrc beam
varies over more than one order of magnitude being smallest for low-N states and largest for large-N states. This result is also found in other hrgh-resolutton studies on I, [7], CO [28], Nz [29.30] and NO [38] and shows that low-N states relaxe much faster than high-N states because of the dtfferent energy gaps. However, It dtsagrees with several other investigations on I, [8,9] and Br, [lo], mostly performed with hmtted resolution and limited N-range. where the data could be described by a single temperature. In order to test the assumption of equal rotational population in different vibrational states, we have to compare dtfferent vibrational branches which have been measured for the same rotational levels. An example for such a comparison for the R,(2,2) and the R1(3,3) branches is shown in fig. 5. The N range investigated lies in a region of term values
greater
than
100 cm-’
where
the local
rotational temperature varies only slightly and can be approximated by one temperature. It is easily derived from the slope of the Boltzmann-type plot [In n/(2J + 1) versus F(J)] As can be seen from hg. 5 there is a small difference between the two branches of T, = 160 f 30 K and T, = 226 f 30 K Just outside the error bars. This seems to indicate a slightly different rotational population in different vibrational levels. However, in view of the errors involved. in the further course of the work. we will make the assumption of a nearly equal rotational population in various vibrational levels. Several high-resolution spectra were recorded wrth different carrier gases and stagnation pressures. Table 5 shows the final ftt parameters T, and b for the local-temperature expression at various source conditrons. For these measurements the nozzle temperature was kept at 1520 K with the nozzle diameter of 0.2 mm. With increasing stagnation pressure the “final temperature” T, decreases and the parameter b, the “dynamic parameter”, increases. This holds for both carrier species He and Ar although the relaxation is strongly enhanced by use of Ar. This result is a reflection of the larger cross sectrons for rotational relaxation of CaCl-Ar collisions. Sirmlar results have been found in several investigations [8-lo]. However, our detailed information on the rotattonal relaxation with a range of local rotational temperatures, makes it impossible to evaluate the data by means of a simple relaxation model [39], since this model a priori assumes the existence of one temperature to describe the relaxation process. Under the present experimental conditions where more
Table 5 Dara for rotatIona Camer
pdmbar)
POD (Torr cm)
T,(K)
b(cm)
500 750 1000 1250 300 500 750
7.6 114 15.2 19.0 46 76 11.4
243 217 127 111
0011 0015 0.02 1 0031 0031 0 037 0 042
gas He
I
I
200
100 F /J) km-’
I
I
300
)
fig 4 Measured local rotauonal temperatures derived from the data of fig. 3. For the ongn of the dtfferent pomls see also fig 3
Ar
relaxauon of CaCI a)
a) For the meanrng of the parameters D=OZmm
68 44 34
T. and b see eq (3)
c
-
=-a\
lo’-
R,
(3.3)
R2
(2.21
\
0
100
200
300
FIJJ Icti’l FIN 5 Measured rocat~onal populations of the Rz (3.3) and Rz (2.2) branch of CaCI as a function of the rotatIona The
straight lmes correspond
to rotational
energy F
temperatures
be fitted. would deviate from the value estimated from the pure rotational drstribution fits. In all cases the deviation was less than 10%. In fig. 6 two measured lo\\-resolution spectra are displayed_ The points represent the digitized measured spectrum whereas the solid line is the best-fit computer simulation of the spectrum. The resulting vibrational population is sho\vn in the inserts as a functton of the vtbrational quantum number. The difference of the spectra is due to the completely different rotational dtstributions. This leads, in the case of the Ar carrier gas \\ith a IOU T,_ to a nearly structureless spectrum. xxhereas for He the P-band heads are clearly seen. In all cases. the vibrational population could be represented by
of
226 -t 30 K and 160 + 30 K. respecwel,
than 100 rotational states are involved, the application of methods that assume a thermodynamic modellmg of the expansion with a kinetic description of the relaxation by use of state-to-state rates and the master equation [40,41] requires a prohibitively large amount of calculations.
03
02
5. Vibrational
01
relaxation
The small portions of the CaCl spectrum recorded with high resolution could not dehver information about the vibrational relaxation in the seeded beam. Therefore we changed to low resolution. that means to multi-mode laser operation. The spectra obtained in this way have been fitted by a least-squares fit in order to get the vibrational distribution This fit program mcluded the deviation of the rotational populatton from the Boltzmann distribution_ This population was held fixed during the ftt procedure with the parameters T, and b from the investigation of the rotational relaxation at the same stagnation pressure_ The dependence of the vibrational population on the dynamic parameter b is only small This is not surprismg because the deviation from an equilibrium rotational distribution is only noticeable for low N. In some test calculations we proved whether or not the fmal temperature. if allowed to
0 09 09 07
2
06
-ii
5 -
05 0‘
Wave
length I nm
Fig 6 Lou-resolunon spectra of a CaCl beam seeded m (a) 750 mbar He and (b) 500 mbar Ar al a source lcmpcrarurc of To = 1520 K and a nozzle dlamcrer of D = 0 2 mm The pnmrs represent the measured specu-um The sohd hnes are computer slmulaiions of the spectrum Hith !iired rorauonal dlsrnbuuons from rhs h&resolutlon
scans. The results for Ihe ubranonal-
state dxsrnbuuon are shoun in rhc mssrls The IUO spectra ..xe charactsnzed b! (a) TV,,. =965 K. T,=217 K 6=0015 cm and (b) T_,,, = 1170 K. TS = 4-I K h = 0.037 cm
210
U Buch ex al / Relaxanon
and specrroscopb
of CaCl m seeded supersonrc heamr
Table 6 Data for vtbrattonal relaxatton of CaCl T0=1320K.D=03mm
T0=1520K.D=02mm
Garner pas
He
Ar
&bar)
D r+orr cm)
TV,h (K)
PO (mbar)
POD (Torr cm)
T “,h (K)
500 750 1000 1250 1500 300 500 750
76 11.4 15 2 190 228 46 76 II 4
1130 965 890 sso 920 1400 1170 860
160 500 1000
3 65 114 22s
1132 811 791
46
1000
55 IO0 300 600 70 150 300 500
1.25 228 6 84 13 6S 1 60 3.42 6 S4 1140
1286 1279 1150 963 984 819 654 589
300
Kr
a Boltzmann-hke dtstributron function characterized by a single Mbrational temperature T,,*_ The results for two different sets of data, one obtained wrth To = 1520 K and D = 0 2 mm and one with T, = 1320 K and D = 0.3 mm are given in table 6. In order to compare the two results, frg 7 shows the reduced vibrational temperatures T,,JTe as a function of rr,D, where no is the source density and D the nozzle diameter. These results are characterized as follows- (1) The two data sets with different nozzle diameters coincide within then expenmental errors for He, Kr and low-pressure data for Ar. The points for Ar at rr,D = 5 X 2Ol6cmz doffer for the two data sets. (2) Besides this deviation the general order for the coohng efficiency of the vibrational degree of freedom is Ar < He < Kr. In order to denve quantrtattve relaxation cross secttons we have applied the method of Quah [39]. Given the classical relaxation equation and the isentropic Mach-number relations, the variation of the vibrational temperature Tvlb, with reduced distance from the nozzle X = L/D, is given by
d(T,,,/T,) = dX
B
1-
(T,lb/T,)Cl- i(K - w21
K’/zM[l
++(h._
1)@]‘(4
’
(5)
,
1
0
5
10
15
Dno 11016cm-*1 Fig 7. Measured reduced vibrational temperatures of a CaCl beam seeded in He (0. l), Ar (A. A). and Kr (a I) as a function of the product of the nozzle diameter D times the source density n, The open symbols refer to expanstons from D = 0 3 mm nozzle dtameters while the full symbols refer to expanston from D = 0 2 mm nozzle diameter The sohd hnes are calculated usmg the relaxation model of Quah [39]
where T, 1s the source temperature, K the specific heat ratio and M the Mach number. The parameter B is given by B = 4n,DQ,,,(
m/2np)“‘,
(6)
where PIo is the atomic number density, Q, ,b is the relaxation cross sectron, err the mass of the carrier gas and p the reduced mass of the atom-molecule system. Eq. (5) is numerically integrated using the known dependence of M on X for free-jet expansion until T\,,., is constant. The result is a curve which relates T,,,/T, to the dimensionless parameter B from which Qblh 1s obtained by a frt to the measured data. The solid lines in ftg 7 are calculated by this method based on the relaxation cross sections Q, ,b = 0.27 2 for He, 0.12 2 for Ar and 0.62 AZ for Kr. The fact that He is more effective than Ar in promoting vibrational relaxation is to be expected from any pure collisional relaxation model. The transition probability for the impulsive Landau-Teller model [42] gives p a exp( -afIE/ott).
(7)
where AE is the transferred energy, a the rangeparameter of the interaction potential and u the relative velocrty. Smce u is largest for He it should give the largest probability. This relation is confirmed by theoretical considerations on the complete coupled-channel equations [43] and also by solving these equations by exact methods 1441 Always the hghtest scattering partner is most efftcrent m producmg vrbrational transitions. Therefore the result for Kr cannot be explained by purely Impulsive collisional relaxatron. It might be possrble that complex formation due to orbiting collision or formatron of van der Waals complexes is responsible for the enhanced vibrational relauation. Similar conclusions have been derived in seeded beam studies of I, in the excited 126.451 and m the ground state [8] The process itself proceeds via the vibrational predissociation of the complex to the ground state and has been extensively discussed in the literature [25,46.47]. For Kr we expect, because of its deeper well with respect to CaCl, a higher probability for forming complexes than for He. The behaviour of Ar confirms thus conclusion. At low p10D values and for those data with the larger nozzle diameter Ar behaves
normal, the relaxatron 1s due to drrect collisions and less effectrve than for He. However. for the two values at hrgher noD obtamed with smaller nozzle diameters the relaxation vra complex formation starts and becomes more effectrxe than for He. Holding no D constant a smaller nozzle diameter D means that CaCl undergoes more termolecular (or even higher-order) collisions which favours the formation of van der Waals complexes. We conclude that in the case of He and most of the Ar points \ve have colhsional rela\atron nhereas for Kr the relaxation 1s enhanced by the vibrational predrssocration of van der Waals molecules or another process \vhich is more effective than a purely impulsive collision_ To investigate this quostion further a better relaxation model has to be applied which allo\vs the direct extraction of the state-to-state rates [41] The reversed order of heavier rare gases in quenching vibrationally e\cited molecules has also been found in ref. [32]_ Although the authors claim that the Landau-Teller transition probabilities explain their result. a careful inspection of therr fitted parameters sho\\s that then range parameters are unph>sically small and an addrtronal scaling parameter was mtroduced to reverse the order according to eq. (7) [S].
Acbno\\ledgement We are grateful to Dr. H Tells and Dr. H-L!. Schutze-Pnhlmann for pro\ idmg their results prior to publication The computations were performed at the GWD. Gottmgen.
References R N. Zare .md P_J D_qdlplm. Saxux 1% (1974) 739. J L Kmsq. Ann Ret. Ph>s Chsm ZS (1977) 349. J B Indcraon R P Andre and J B Fan _L\d\rtn Chsm Ph\s 10 (1966) 275 Xl P. Smhn. X Schultz .md R E Zare. J Chcm Ph>s SS ( 1973) 519 K Bsrgmzmn. b Hefter snd P Henng. J. Chsm Ph>s 65 (1976) -lSS. Chsm Ph>b 32 (197s) 329_ C D CaId\\sll. F Engeslhr snd H. Hags. Chcm Ph>s 51 (19SO) 21. P S H. Fitch L N’harton and D H Leq. Chcm Ph>s LCIbxS 38 (1977) 13’
212
U Buck ef al / Reluxarron and spec:roscop_s of CaCI m seeded supersonrc beams
[7] R E Smalley, D H Levy and L Wharton, J. Chem Phys 64(1976)3266 [8] G M McClelland, K L Saenger, J J Valentuu and D R Hcrschbach. J Phys Chem 83 (1979) 947 [9] A Amtrav. U Even and J Jortner, Chem Phys 51 (1980) 31 [IO] S J Bullmann, J W Farthmg and J C Whuehead. Mel Phys 44 (1981) 97 [I I] P J Domddle. T C Stelmle. N B Wong and D 0 Hams. J Mol Spectry 65 (1977) 354 [IZ] J M Brown, H Martm and F D Wayne. Chem Phys Letters 55 (I 978) 67 [ 131 H Telle. Thests. Umverslty of Cologne. Germany (1979). H H Telle and U Telle. Computer Phys Commun 28 (1982) I [ 141 L E Berg, L Klynnmg and H Martin, PhysIca Scrrpta 21 (1980) I73 I IS] L E Berg. L Klynnmg and H Marhn, Physuca Scripta 22 (1980) 216 116) R E Bernath. B Pmchemel and R W Field. J Chem Phys 74(1981)5508 [ 17) P J Domadle. T C Stermle and D 0 Hams. J Chem Phys 68 (1978)4977 [18] W J Childs. G L Goodman and L S Goodman. J Mel Specwy 86 (1981) 365 1191 W J Chdds. D R Cok. G L Goodman and L S Goodman, J. Chem Phys 75 (1981) 501 1201 W J Chdds. D R Cok. L S Goodman and 0 Paulson. Phys Rev Letters 47 (1981) 1389 [Zl] W J Chdds. D R Cok and L S Goodman. J Chem Phys 76(1982)3993 1221 K Mdller. H U Schiitze-Pahlmann. J Hoeft and T Tdmng. Chem Phys 68 (1982) 399 1231 P J Dagdlglan, H W Cruse and R N. Zare. J Chem Phys 60(1974)2330 [24] P J Dagdlman Chem Phys Letters 88 (1982) 225.
[ZS] G Ewmg, Chem Phys 29 (1978) 253 1261 J Tusa. M Sulkes and S A kce. J Chem Phys 70 (1979) 3136 [27] G Lqks. S St&e and J Reuss Chcm Phys 62 (1981) 217 [ZS] D Bassl. A Boschettl. S Marchetn, G Stoles and M Zen J. Chem Phys 74 (1981) 2221 [29] M Faubel and E R Werner. J Chem Phys 75 (1981) 641 [30] S P. Hernandez. P J Dagdlglan and J P. Doerrng. Chem Phys Letters 91 (1982) 409 1311 R P. Manella. S K Neoh, D R Herschbach and W. Klemperer. J Chem Phys 67 (1977) 2981. 1321 H G Bennewtz and G Buess. Chem Phys 28 (1978) I75 [33] P J Dagdlglan. Chem Phys 21 (1977) 453 1341 G. Herzberg, Spectra of dlalomic molecules (Van Nostrand. Pnncelon. 1980) (351 S Gerstenkorn and P. Luc, Atlas du spectre d’absorpuon de la molecule de I’lode entre 4800-20000 cm-’ (C N R S Parts. 1978). Rev Phys Appl I4 (1979) 791 1361 RN Zare. AL Schmehehopf W J Harrop and D L Albntton. J Mol Spectry 46 (1973) 37. [37] J H van Vleck. Phys Rev 33 (1929) 467 1381 H W Ldlf and P Andresen. 13th Symposmm on Rarefled Gas Dynamxs. Novoslbusk (1982) 1391 C G M Quah. Chem Phys Letters 63 (1975) I41 1401 H Rabne and S H Lam, J Chem Phys 63 (1975) 3532 1411 R E Mdler, Thesis. Unrversny of Waterloo, Canada (1980) 1421 D Rapp and T Kassal. Chem Rev 69 (1969) 61 143) R B Gerber. Chem Phys I6 (1976) I9 [44] G Drolshagen. Thesis. Umverslty of Gottmgen. Germany (1982) [45] T D Russel. B M DeKoven. J A Blazy and D H Levy. J Chem Phys 72 (1980) 3001 [46] J Jortner and A Beswck, Advan Chem Phys 47 (1981) 363 I471 G Ewing, Dlscusslons Faraday Sot 73 (1982) 325
Physics
Norrh-Holland
77 (1983)
Pubhshing
RELAXATION
U. BUCK,
201-212
201
Compaq
AND
J. KESPER,
H-H. KUGE
Alal-- Planch - Insrrrrrr ftirSrr~nturlgsforsciltmg 4 November
RecelLed
1982
formula
fluorescence
IS given uhlch
SUPERSONIC
BEAMS
and D. OnEN 3400 Gorrmqm
F~vit~uI Repuhhc of Gem~am
m final form 4 March 1983
The rotational and rtbratlonal by laser-Induced
OF CaCl IN SEEDED
SPECTROSCOPY
relaxaLlon of a calcwn-monochlonde The rotaIlona1 dlstnbutlons cannot
represents
the measured
dlstrlbuttonr
bwm seeded m He. 4r and Kr has been mvestlgated be described b> L( cmgle !smpcr.wxe 4 tu*parameter
and uhxh
s characterized
b> local remperarures
K dependmg
on the rotational slates and [he expansion condlrions wth source remperarures of r, = 1320
The effectwe
coohng
increases
from He to Ar as tamer
gases. In contrast.
the xlbrxmnal
dtsrnbuuons
could be reprecenrcd
Boltzmann dlstnbutions with temperatures of 1400 10 569 K The order of wbrarional coohng goes from of the CaCl X-B spectrum hale been recorded unh hlgb resoluuon The artempl 10 Identlf> the measured best molecular
needed accuracy
from 30 to 200
K and T, = 1520
K bk
or c He c Kr Parts hnes reheals rhar rhe
for 0~s system do not reproduce all lrnes of Ca35CI and especlall~ not zho
constants
1. Introduction
Laser-induced fluorescence is a widely accepted method to study state-resolved vibrational and rotational distributions of diatomic molecules [ 11. If these investigations are performed m a supersonic nozzle beam [2] we have an attractive tool to study both the spectroscopy of the species m the beam and the kinetics of the collision processes that occur during the expansion. The spectroscopy is simplified appreciably because there is considerable rotational and vlbratlonal cooling of the molecules and there are nearly Doppler-free hnewidths. In addltlon, the extent of the coolmg by seeding the species in different diluents can be used to derive information on the rotational and vibrational relaxation of the molecules_ Investigations along these lines have been performed mainly on the alkali dimers Na, [3,4] and Rb, [S] and the halogen molecules I, [6-91 and Br2 [IO]. In the present paper we extend these studies to calcium monochloride. CaCl. The alkaline-earth monohalides have attracted a lot of interest in the past years since they represent an interesting class of ionic molecules with a single unpaired metalatom-centered valence electron The very dense 0301-0104/83/0000-0000/$03.00
from the electronic transitIons haxe been resolved on11 recently_ The spectra haxe been analysed by laser excltatlon and fluorescence spectroscop) [ II- 161. optical-optlcal double resonance [ 171. laser-rf double resonance [IS-2 I]. and rnicro\\a\e spectroscopy [Xl. Studies of the radiati\,e lifetime [23] and the electric deflection [24] complete the experimental informauon on these systems. We ha\e measured the ~~brauonal and rotational state distributions of CaCl in its eltctronic ground state b> mducing transinons to the B’S’ state with a smgle-mode cl\ dye laser and observmg transiuon from the excited state to the ground state. CaCl is formed in the source b> A chemical reaction and expanded from 0 7 or 0 3 mm diameter nozzles \\lth He. Ar. and Kr as carrier gases at temperatures of 1320 and 1520 K;. The completely resolved vibration-rotation spectra have been analysed in terms of the most recent constants from other laser-induced fluorescence experiments [ 13.15.171 and microwave spectra of the ground slate [22] Although rhe general features of the measured spectra are reproduced. there are still some discrepancies especially for Ca”C1. To demonstrate the precision of the present e\periment the spm-rotation constant is derived and spectra
0 1983 North-Holland
compared with the results of other expenments. For pressures of the carrier gases from 55 to 1500 mbar the populations of angle rotatton-vibratton levels have been obtamed. Whtle the rotational distributions were found to be extremely non-Boltzmann with an apprectable coolmg m the order He -Z Ar, the vibrattonal distributions could be represented by Boltzmann distributions. The cooling is only moderate and mcreases in the order Ar < He < Kr. The reversed order for Kr and studies with different nozzle diameters indtcate that an appreciable amount of the vtbrational relaxation for the heavier rare gases is due to other processes than pure collistonal relaxatton [8,25.26]. There are several recent studies of colhsional relaxation in seeded beams using other techniques_ Rotational relaxation has been investigated by Raman scattering (271, infrared spectroscopy with bolometric detection [28] and electron beam fluorescence [29,30] Vibrational relaxation was studted by electric resonance spectroscopy [31.32]. We will compare our more extensive data with these studies where it 1s appropriate. In section 2 we describe the experimental arrangement The spectroscopic results are given in section 3. Next. we present the relaxation data for rotation and vibratton and discuss the results m terms of simple relaxation models.
2. Experimental 2. I. Apparatus Fig 1 shows a schematic view of the apparatus_ It consists of three separately pumped chambers_ The source chamber is pumped by a 6000 Y/s diffusion pump backed by a roots-pump (500 m’/h) and a rotary pump (100 m3/h). During operation the pressure in the source chamber raises up to 3 x 10m4 mbar when He is used as carrier gas at a stagnation pressure of 1500 mbar. The molecular beam enters the second chamber through a skimmer heated to 900 K. After passing a chopper, a fluorescence detector and a Fizeau-type velocity selector, the beam enters the third chamber with the quadrupole mass filter as detection system. The pressure in the second chamber is
Ep
I
I
Laser t-3
I
I
Fig 1. Schematrc view of the apparatus (A) Beam source (B) shimmer. (C) beam chopper. (D) kisser l&t catcher. (E) velocity selector. (F) quadrupole mass filter delector. (G) fiber bundle to the photomultlpher. (H) single fiber from the laser
lower than 10mh mbar and m the detector chamber lower than 2 x 10-s mbar. 2 2. Laser excitatton and fluorescence
detectlou
A single ftbre leads the laser light to the fluorescence detector_ The laser light is produced by a tunable Spectra-Physics ring dye laser, model 380 A, pumped by a Spectra-Physics argon ion laser. model 171-03. The nng dye laser was operated in two modes of operation. In single-mode operation the typical output power was 350 mW at 593 nm, and the typical halfwidth of the unstabilized mode was 30 MHz. During the low-resolution expenments, the laser was used in multimode operation. In this case the halfwidth had to be increased from naturally 2 GHz to at least 25 GHz in order to maintain the tunability over several angstroms This halfwidth is achieved by directing a portion of the light reflected by the fibre entrance back mto the cavity. The multi-mode output power did not exceed 600 mW at 593 nm. Part of the laser hght was guided to several control instruments: A Spectra-Physics interferometer, model 450-4, FSR (free spectral range) 10 GHz, to observe the mode structure, a Burleigh RC 110 temperature-stabilized interferometer, FSR 1 GHz, finesse 70, to give frequency marks, a McPherson 1 m scanning monochromator to give the coarse wavelength determination and a low-pressure I,-absorption cell to achieve an absolute wavelength calibration. Due to Doppler broadening and the unresolved hyperfme structure
the residual full halfwtdth of the I,-absorption peaks was = 0.9 GHz. This hmits the absolute CaCl transition frequency determmation to within an error of kO.005 cm-’ or 0.0002 nm with respect to the I,-absorptton peaks. The fluorescent light emitted from the CaCl
Table 1
molecules was collected
4r
by a laser-stray-light
re-
ducing detector, and fed to an EMI 9816 QB multiplier by a fiber bundel. The signal was measured by a PAR model 128 lock-in amplifter. The fluorescence signal, the frequency marks, the laser power. the Iz-absorption peaks. and the CaCl quadrupole mass filter signal were recorded on strip chart recorders
The crucial point of the experiment in the generation of an intense and stable beam of CaCl which has to be produced in a reaction at high temperatures_ In two experimental series we used two different sources. For both ovens the principle of construction was the same there are two separately heated chambers, a bigger reservoir and a smaller unit containing the nozzle. In the first variant the oven conststed all over of stainless steel, Inconel 600, which limited the nozzle temperature to a maximum value of 1370 K In the second variant we made the nozzle chamber of tantalum. In this case the temperature was hnuted to 1720 K by our nozzle heating system The nozzle diameters. were 0.3 mm and 0.2 mm for the first and the second oven, respectively. To produce CaCl we used two reactions. during the first series of experiments. Ca + M&l,
+ CaCl + Mg + Cl,
(I)
during the second 1331. Ca + NaCI --, CaCl + Na.
(II)
Reaction (I) has the disadvantage that it leads to d rapid corrosion of the stainless steel probably due to the formation of atomic Cl. Reaction (II) produces an intense Na beam even at low oven temperatures. Almost all of the Na had to be removed before we could observe the fnst CaCl signal. Under these condttions the intensity of the CaCl beam was 1.5 x 10” particles/sr s, when seeded in
Ch.w.msnsuc
Garner gas
hwm
Pressure (mbar)
d.un -I’
Speedmu0
T(K) cdrrier
CKI
c.w-w _gas
72
15
66
145
40 30
-
90
-
103
-
.?F
Hrt Kr
750 600 500
CKI
=’ Rcacnon (I) source temprratur+137-O h nozzle dwnrrsr 03mm
500 mbar He. and 2 x lOI particles/sr s. Lxhen seeded in 300 mbar Kr. These Lalues haxe been obtained from the mass spectrometer signals calibrated by an effusive He beam. The recorded CaCl intensity decreased \\ith increasing mass of the carrier gas and. aside from He. \~iithmcreasmg carrier-gas pressure_ Both effects seem to reduce the reaction yield. Only He leads to an enhancement of the CaCl signal with increasing stagnation pressure up to a temperature-dependent mallmum. Raismg the pressure above this point decreases the CaCl signal rapidly. The ma\irnum p. D values for a detectable CaCl signal \xere found to be = 22 Torr cm \\iithhehum. 14 Torr cm with argon and 7 Torr cm with krypton. u herep, is the stagnation pressure and D the nozzle diameter. The CaCl mtenstty could be increased b> d factor of t\\o by raismg the nozzle temperature from 1570 to 1720 K. Unfortunately. the need of re.isortable hfctime for our nozzle heating s?stsm limited the attainable nozzle temperature to 1520 K for permanent operation The resenoir temperature was kept at 1050 K since raising the remperature above this value did not increase the beam intensity_ Typical beam data for different carrier gases are given in table 1. xxhhsreths translational temperature T and the speed ratio charactertze the expanston [2].
3. spectroscopy In order to investigate the rotAtiona rsla\atton m the beam WC hd\e to deal \\ith the CaCl spectrum in the \isible. Wtth a rhodamin 6G d,e laser
U Buck et al / Relax-arron and spectroscopy of CaCI m seeded superronrc
204
can conventently induce a transitton from the X ‘X+ state to the ftrst excited A21f or the second B’Z+ state. We have chosen transrtrons to the B ‘Z-I state because the spectrum IS less complex than in the A”TI case. Nevertheless the spectrum of the X ‘XC-B ‘Z+ transttton 1s very dense due to the stmilar potentials in the ground and excited states In addloon, the existence of the Ca7’C1 Isotope with a natural abundance of = 25% complicates the analysis. Since both states are ‘Z states four rotattonal branches, R,, R,, P,. P2 and wtth lower mtensittes the R, and Pa satellite branches can be observed Our denommatlon follows Herzberg [34] so that the R branch denotes a AJ = + 1 transmon, the P branch a AJ = - 1 and the indices 1 and 2 denote J = Iv -I- l/2 and J = N - l/2, respectively. From 592.98 to 593.32 nm we measured the absolute frequencies of = 230 rovtbronic CaCl B ‘2+-X ‘Z+ transittons. For the Isotope Ca”CI we have obtamed the R, and Rz branches of the Au = 0 sequence wtthm 0 < N” < 50 and Y” = 0. 1. 2 and 3 (see also table 2). A portion of this htgh-resolution spectrum is shown in fig. 2. The full wtdth at half maximum of the lutes caused by Doppler broadening due to the angular divergence of the beam was = 150 MHz with He as carrier
one
593 14
593 15
593 16
Laser
wavelength
hems
gas. and ‘t: 90 MHz wrth Ar as carrier gas. The dtfference is due to the different velocities of CaCl when seeded m different carrter gases. For a pure CaCl beam the linewidth would reduce to = 40 MHz which is the hmit caused by the hyperfme structure [21]. A high-resolutton spectrum recorded whtle seeding with Ar permitted the resolution of the very weak R, satellite branch. Our frequency calibration was given by the stmultaneously recorded I?-absorption spectrum. The wavenumbers of the todine lines were taken from Gerstenkorn and Luc [35] They give a stattstrcal error of *O-O005 cm- ’ and a possible systematic error due to their calibration with uranium lines of f 0 002 cm-‘. Our error in determmmg the absolute transition frequencies of CaCl was +O 005 cm-’ wtth respect to the iodine hnes. This error contains both the statistical and a possible systematic component. In order to identify our observed CaCI transitions we computed the CaCl transition frequencies usmg several sets of spectroscopic constants There are essentially three complete sets of constants available for the X “Z and the B’Z state. The set of Domatlle et al [ 171 IS dertved from a combined fit of the laser excitation spectrum of the X-B system. the microwave spectrum of the ground
593 17
593 18
lnm
Fag 2 Obsened fluorescence excnatlon spectrum of a CaCl beam seeded m 500 mbar He m the B’Z-X
‘2
bdnd system
state
and the optlcal-optical double resonance spectrum of the E-B system Since only the lowest vibrational states are involved in thts analysis (v” = 0. 1, 2). Telle [ 131 derrved a new set of constants
essentially based on the results of ref. [17] but also fttted to higher vtbrational states (up to u” = 12) of new measurements. Fmally there is a very detailed laser spectroscopic investrgation of the X-B system by Berg et al. 115). who used 1124 lures of the AL’= 0. + 1 sequences for A!” < 120 and Y” < 11 together with information from other transrttons. e g the X-A system 1141. for the ground state. Two very recent high-resolutton mvestigattons of the ground state complete the avarlable data. Moller et al. [22] measured the mtcrowa\e spectrum and obtained very precise rotational constants. Childs et al. [21] performed a molecular beam laser-rf double resonance expertment and determined the hyperfme-structure and spin-rotation constants to an extreme precision_ In both cases the vibrational and rotational dependence of
the spin-rotational data
constant is extracted
from the
The compartson of the observed lme positions of our measurements with calculations revealed that the constants of Domaille et al. [ 171 could not reproduce the measured frequencies within the derrved accuracy. Only the constants given by Telle [ 131 and Berg et al. [ 151 could be used to Identify the lines. Smce the line-to-line compartson did not show any anormal behavtor we used the normalized root-mean-square deviations (RMS) of every rotational branch as a measure of the devration from the predicted line positions
The results are hsted m table 2 A value smdller than 1 0 means that the predictions is consistent wrth the data within the stated error hmrts. Table 2 clearly shows that the improvement of the Telle set is remarkable compared to the Domaille set. Still, there are some larger discrepancies of the Telle constants for the R,(2.2) and R,(3.3) branches. The constants of Berg et al. [ 151 give. on the average, the best agreement with the data. with the largest deviations for the R,(2,2) and RJ2.2)
T&k
2
A’
L\“_c’
Ref [IS]
Rd [IS] + ref
Rcf
Ref
I131
1171
1X] RI
o-24
00
0 s5
100
0 75
27
R,
00 1.1
0 97
2’1
R, R, Rz R,
6-28 19-41 16-36 30-50
R2
2s-44
11 22 22 33 3.3
1 26 1 57 2 IS 0 93 075
I 10 1.77 1 75
065
RI
l-20 8-33
2 75 3 30 I 9’ 1 Y3
3 77 135 6 91 1 ss
1.1s
OYS 0 7,
69 39 14 s b5 ‘7 1 135
branch. In order to improve this result. \\e combined the precise rotatronal constants of the ground state of Moller et al [22] 111th the constants of Berg et al. for the vtbratron and the excited state. Unfortunately. this data set leads to an mcreased difference bet\\een measured and calculated transttton frequencies. very probably due to a correlation of the excited- and the ground-state constants of Berg rt al. [15]. The use of different carrier gases permits us to identify sixt>-four lmes of the C&Cl Isotope belonging to the R, and R, branches of the 1~ = 0 sequence for 2 Q N” G 23 and L”’ = 0. 1. Because of the much more enhanced rotational relaxation for Ar as carrier gas. small umdentifted lures of higher vibronic transitions vanished \\hrle loller vrbronic transitions of Ca”C1 increased in intensity proportronal to the mtensmes of the correlated C$‘Cl trdnsnions. The root-mean-square devrations for the measured and calculated transition frequencies for Ca”Cl are given in table 3. The calculated Lalues \\ere obtdmed b> multlply-
ing the Ca”Cl constants of Berg et al. 1151. and Telle 1131 by an appropriate poaer of the ratio p = ( p”‘/p37)l/2.
where p IS the reduced mass of the molecule [19]. Smce only a fm Ca’7Cl lines were rdenttfred we could not decide I\hether the relative strong deviation between calculated and measured frequencies is due to slightly incorrect Ca-“Cl constants or a breakdown of the mass-scalmg procedure. To demonstrate the accuracy of the measurement He determine the spin-rotation constants by
U Bud
206 Table 3 Root-mean-square
RI R2
R, R,
et al / Relaxarron and spectroscop)
0”
2-19 2-18 8-23 6-20
0.0 0.0 1.1 1.1
. I)’
Ref 1151
Ref [13]
19 23 30 30
17 19 22 IS
means of a least-squares fit from sixty-five lines for Ca-“Cl and twenty-eight hnes for Ca37C1 out of the data fields given above The vlbratlon-rotatlon-dependent value of the spin-rotation mteractlon strength is given by Y=Yoo+Y,o(U+~)+Yo,N(N+
1).
(1)
Using the ground-state values of ref. [22] we derive the values for the B’Z’ state The results are listed m table 4, together with values of Berg et al 1151. Our data are not sensitive to yo, because only lines with N” d 50 were measured. The magnitude of yoo compared to the ground-state value clearly indicates that the B’Z state 1s perturbed by the close-lying A’II state. Following the treatment of Zare et al. 1361 the spin-rotation constant of the B state is equal to the negative A-doubling constant p of the A state and is given m the unique perturber approximation by y = - 2AB(njL+la’)‘/ AE, where A is the spin-orblt interaction, B the rotational constant, L, the raising operator for the orbital angular momentum and AE the energy difference between the electronic states n, n’_ In a further approximation, van Vleck’s case of pure precession [37], it is assumed that the valence electrons have a well-defined angular momentum and the matrix element gives f(f + 1). Using the constants of ref. [14] for the A’IT state and I = 1
sphttmg
constantsof the CaCl B’X’
stale in cm-’
CzPCl
Yoo YIO
YOl
get y = -0 060 cm-’ which IS not too far away from the experimental value, but clearly outsrde the experlmental error. However. the experrmental value of p = 0.0642 (2) cm- ’ of the A state [ 141 is close to our experimental result for y. We conclude that the umque perturber model is a good descriptlon for rhe interaction of the states but they are not :n pure precession. The reason is a contribution of d wavefunctlons to the p character which IS slightly different for the two states [ 14,16.17]. rhe present results for Ca’SCl are in good agreement with the yoo and ylo reported by Berg et al. [15]. The yoo value agrees also well with yoo = - 0.0652 (2) obtained by Domallle et al [ 171 The spm-relation constants for Ca37C1 determmed in the same way are also hsted in table 4. The results are compared with predlctions based on the appropriate powers of the reduced mass ratio times the Ca3%1 constants of this work. The values agree within the error limits. The validity of the mass-scaling relation for the spin-rotation constant has also been found for the ground-state data [21,22]. None of the available sets of molecular constants fits all our measured line positions within the given experimental error. The constants of Berg et al. [15] are a good representation for the Ca3’Cl spectra except for the R, (2.2) and R2(2,2) branches. To decide whether these deviations are we
devmtrons Ca3’Cl
N
Table 4 Spm-roratlon
OJ CaCI IO weded srrperronrc heanls
due to erroneous constants or local perturbations we have to extend the measurements to larger N values. The rgreement wth Ca3’C1 IS worse. TO
improve the accuracy of the molecuIar constants for CaCl our measurements (possibly extended to a larger wavelength range) have to be evaluated m a simultaneous fit together with the precise microwave data of the ground state [22].
Numbers in parentheses refer to 20 unceriamtles m last dlglls Ca37Cl
thus work
ref 1151
this HOA
calculated a)
-0.06513(9) -3 9(3)X10_’ -
-006531(14) -40 (12)x10-4 1.36(12)x IO-’
- 0 0630(2) --44(17)X 10-4 -
- 0 6325(9) -3.7(3)x1o-J
*) Calcuiated from the Ca3%l constants of tis
uork and the appropriate power of the reduced mass ratios
4. Rotational
relaxation
Lure-intensities from high-resolution scans with the laser yield direct information about the relative number of molecules in a specrfrc vibrational and rotational state of the electronic ground state once the spectroscopic constants are known [ 11. in frg 3 the number of CaCl molecules m specific rotational levels is plotted against the rotational term value F. In thus measurement He was used as carrier gas at a stagnation pressure of 500 mbar. In fig. 3 the R, and R, branches of different vrbrational bands are marked by different symbols. All values are normalized to the strongest populated state m each branch. The different behaviour of the curves IS essentially due to the rotattonal states N measured in the different branches. The semilogarithmic plot illustrates directly the devratron from the Boltzmann distnbutron which should give a straight hne The deviations are largest for the small N values. A temperature determined by the slope of the number density versus the term energy curve 1s only meaningful in an infinitesimal sense as the derivative in one point and we like to call this quantity the local temperature d ln[n( F’)/(ZJ
T;‘(F)=k
+ I)]
dF
I-F
(2)
From fig 3 ue computed the local temperatures and plotted them against their term values. as shown in fig. 4. In ftg. 4 there is no normalization Despite a relatively large deviation of single points the general behaviour of all points could be represented by the formula
T,= T,[l
-eeup(-M-)1_
(3)
where F IS the rotational energq ‘_ From a leastsquares fit we obtamed the parameters T, and b_ As can be seen in ftg. 4 T, has the meaning of a “final rotational temperature”. which is reached at large F, whereas the “dynamic parameter” h determines the curvature or. m other words. ho\\ fast the final temperature TAis approached_ From fig. 4 it is also immedrately clear that there is no large difference in the rotational populattons of various spin states (R, and R,) and Larious \ibrattonal levels. because this aould produce different curvatures or at least different final temperatures for each vibratronal-rotattonal branch. With the assumptton that eq. (3) is Ldhd for all vibrational levels the number of molecules in specific rotdtional states is obtamed by integrating the Boltzmann distribution
-p( - F/X ?, )
~~=C(2J+1)~l_e\P(_bF)]I,1T,b-
(4)
with T, and b the same as before and the normahzation constant C_ For large bF values the expresston
approaches
a
Boltzmann
dlstnbution
with
T,.The solid lines in ftg 3 dre calculated using this expression ~11th the parameters derhed from the frt displaced In frg. 4 The various cumes for various branches differ only b! an additional constant which is used to shift them parallel to the-1 a& until they coincide with the points. It can be seen that within the experimental error the above expression represents the measured data Fig. 4. also shox\s that the local temperature T=
L 0
.
J 100
200 F(J I km-‘)
300
&OO
Fig 3 Measured rotatlonal-state populations of CaCl seeded m 500 mbar He as a function of the rotattonal energ F for a source temperature of r, = 1320 K and a nozz.Ie dumetsr of D = 0 3 mm The dlfferent branches are marked as follous- 0 R,(O.O).oR, (0.0). + R2(1.1).&R, (1.1) 0 Rl(OO). x R, (2.2). 0 Rz (3.3). v R, (3 3) The sohd hnes are calsulatcd dccordmg to eq (4) \hllh T_ = 243 K and b = 0 011 cm The pomts are normahzed to the largest values of each branch
+ In :he formula T, apprcuchcr zero as F approarhcs zero Thus bchaviour can be rsmoksd b> addmg a constant X&IS Ea IO F. But m our mxcbtlgauonz Ihc de\aatmn 13 30 small 1ha.r we could not deternuns the \.duc E, b> uhlch Ihc tune haz IO be shlfted to _e~\eA reahcrlc behaviour of T, near F= 0 as ought bc nccssssq m orher mxesclgarions of low-.X’ reialauon\
U Bud
208
er al / Relaxarron and specrroscop~ of CaCl IR seeded supersonrc beam
varies over more than one order of magnitude being smallest for low-N states and largest for large-N states. This result is also found in other hrgh-resolutton studies on I, [7], CO [28], Nz [29.30] and NO [38] and shows that low-N states relaxe much faster than high-N states because of the dtfferent energy gaps. However, It dtsagrees with several other investigations on I, [8,9] and Br, [lo], mostly performed with hmtted resolution and limited N-range. where the data could be described by a single temperature. In order to test the assumption of equal rotational population in different vibrational states, we have to compare dtfferent vibrational branches which have been measured for the same rotational levels. An example for such a comparison for the R,(2,2) and the R1(3,3) branches is shown in fig. 5. The N range investigated lies in a region of term values
greater
than
100 cm-’
where
the local
rotational temperature varies only slightly and can be approximated by one temperature. It is easily derived from the slope of the Boltzmann-type plot [In n/(2J + 1) versus F(J)] As can be seen from hg. 5 there is a small difference between the two branches of T, = 160 f 30 K and T, = 226 f 30 K Just outside the error bars. This seems to indicate a slightly different rotational population in different vibrational levels. However, in view of the errors involved. in the further course of the work. we will make the assumption of a nearly equal rotational population in various vibrational levels. Several high-resolution spectra were recorded wrth different carrier gases and stagnation pressures. Table 5 shows the final ftt parameters T, and b for the local-temperature expression at various source conditrons. For these measurements the nozzle temperature was kept at 1520 K with the nozzle diameter of 0.2 mm. With increasing stagnation pressure the “final temperature” T, decreases and the parameter b, the “dynamic parameter”, increases. This holds for both carrier species He and Ar although the relaxation is strongly enhanced by use of Ar. This result is a reflection of the larger cross sectrons for rotational relaxation of CaCl-Ar collisions. Sirmlar results have been found in several investigations [8-lo]. However, our detailed information on the rotattonal relaxation with a range of local rotational temperatures, makes it impossible to evaluate the data by means of a simple relaxation model [39], since this model a priori assumes the existence of one temperature to describe the relaxation process. Under the present experimental conditions where more
Table 5 Dara for rotatIona Camer
pdmbar)
POD (Torr cm)
T,(K)
b(cm)
500 750 1000 1250 300 500 750
7.6 114 15.2 19.0 46 76 11.4
243 217 127 111
0011 0015 0.02 1 0031 0031 0 037 0 042
gas He
I
I
200
100 F /J) km-’
I
I
300
)
fig 4 Measured local rotauonal temperatures derived from the data of fig. 3. For the ongn of the dtfferent pomls see also fig 3
Ar
relaxauon of CaCI a)
a) For the meanrng of the parameters D=OZmm
68 44 34
T. and b see eq (3)
c
-
=-a\
lo’-
R,
(3.3)
R2
(2.21
\
0
100
200
300
FIJJ Icti’l FIN 5 Measured rocat~onal populations of the Rz (3.3) and Rz (2.2) branch of CaCI as a function of the rotatIona The
straight lmes correspond
to rotational
energy F
temperatures
be fitted. would deviate from the value estimated from the pure rotational drstribution fits. In all cases the deviation was less than 10%. In fig. 6 two measured lo\\-resolution spectra are displayed_ The points represent the digitized measured spectrum whereas the solid line is the best-fit computer simulation of the spectrum. The resulting vibrational population is sho\vn in the inserts as a functton of the vtbrational quantum number. The difference of the spectra is due to the completely different rotational dtstributions. This leads, in the case of the Ar carrier gas \\ith a IOU T,_ to a nearly structureless spectrum. xxhereas for He the P-band heads are clearly seen. In all cases. the vibrational population could be represented by
of
226 -t 30 K and 160 + 30 K. respecwel,
than 100 rotational states are involved, the application of methods that assume a thermodynamic modellmg of the expansion with a kinetic description of the relaxation by use of state-to-state rates and the master equation [40,41] requires a prohibitively large amount of calculations.
03
02
5. Vibrational
01
relaxation
The small portions of the CaCl spectrum recorded with high resolution could not dehver information about the vibrational relaxation in the seeded beam. Therefore we changed to low resolution. that means to multi-mode laser operation. The spectra obtained in this way have been fitted by a least-squares fit in order to get the vibrational distribution This fit program mcluded the deviation of the rotational populatton from the Boltzmann distribution_ This population was held fixed during the ftt procedure with the parameters T, and b from the investigation of the rotational relaxation at the same stagnation pressure_ The dependence of the vibrational population on the dynamic parameter b is only small This is not surprismg because the deviation from an equilibrium rotational distribution is only noticeable for low N. In some test calculations we proved whether or not the fmal temperature. if allowed to
0 09 09 07
2
06
-ii
5 -
05 0‘
Wave
length I nm
Fig 6 Lou-resolunon spectra of a CaCl beam seeded m (a) 750 mbar He and (b) 500 mbar Ar al a source lcmpcrarurc of To = 1520 K and a nozzle dlamcrer of D = 0 2 mm The pnmrs represent the measured specu-um The sohd hnes are computer slmulaiions of the spectrum Hith !iired rorauonal dlsrnbuuons from rhs h&resolutlon
scans. The results for Ihe ubranonal-
state dxsrnbuuon are shoun in rhc mssrls The IUO spectra ..xe charactsnzed b! (a) TV,,. =965 K. T,=217 K 6=0015 cm and (b) T_,,, = 1170 K. TS = 4-I K h = 0.037 cm
210
U Buch ex al / Relaxanon
and specrroscopb
of CaCl m seeded supersonrc heamr
Table 6 Data for vtbrattonal relaxatton of CaCl T0=1320K.D=03mm
T0=1520K.D=02mm
Garner pas
He
Ar
&bar)
D r+orr cm)
TV,h (K)
PO (mbar)
POD (Torr cm)
T “,h (K)
500 750 1000 1250 1500 300 500 750
76 11.4 15 2 190 228 46 76 II 4
1130 965 890 sso 920 1400 1170 860
160 500 1000
3 65 114 22s
1132 811 791
46
1000
55 IO0 300 600 70 150 300 500
1.25 228 6 84 13 6S 1 60 3.42 6 S4 1140
1286 1279 1150 963 984 819 654 589
300
Kr
a Boltzmann-hke dtstributron function characterized by a single Mbrational temperature T,,*_ The results for two different sets of data, one obtained wrth To = 1520 K and D = 0 2 mm and one with T, = 1320 K and D = 0.3 mm are given in table 6. In order to compare the two results, frg 7 shows the reduced vibrational temperatures T,,JTe as a function of rr,D, where no is the source density and D the nozzle diameter. These results are characterized as follows- (1) The two data sets with different nozzle diameters coincide within then expenmental errors for He, Kr and low-pressure data for Ar. The points for Ar at rr,D = 5 X 2Ol6cmz doffer for the two data sets. (2) Besides this deviation the general order for the coohng efficiency of the vibrational degree of freedom is Ar < He < Kr. In order to denve quantrtattve relaxation cross secttons we have applied the method of Quah [39]. Given the classical relaxation equation and the isentropic Mach-number relations, the variation of the vibrational temperature Tvlb, with reduced distance from the nozzle X = L/D, is given by
d(T,,,/T,) = dX
B
1-
(T,lb/T,)Cl- i(K - w21
K’/zM[l
++(h._
1)@]‘(4
’
(5)
,
1
0
5
10
15
Dno 11016cm-*1 Fig 7. Measured reduced vibrational temperatures of a CaCl beam seeded in He (0. l), Ar (A. A). and Kr (a I) as a function of the product of the nozzle diameter D times the source density n, The open symbols refer to expanstons from D = 0 3 mm nozzle dtameters while the full symbols refer to expanston from D = 0 2 mm nozzle diameter The sohd hnes are calculated usmg the relaxation model of Quah [39]
where T, 1s the source temperature, K the specific heat ratio and M the Mach number. The parameter B is given by B = 4n,DQ,,,(
m/2np)“‘,
(6)
where PIo is the atomic number density, Q, ,b is the relaxation cross sectron, err the mass of the carrier gas and p the reduced mass of the atom-molecule system. Eq. (5) is numerically integrated using the known dependence of M on X for free-jet expansion until T\,,., is constant. The result is a curve which relates T,,,/T, to the dimensionless parameter B from which Qblh 1s obtained by a frt to the measured data. The solid lines in ftg 7 are calculated by this method based on the relaxation cross sections Q, ,b = 0.27 2 for He, 0.12 2 for Ar and 0.62 AZ for Kr. The fact that He is more effective than Ar in promoting vibrational relaxation is to be expected from any pure collisional relaxation model. The transition probability for the impulsive Landau-Teller model [42] gives p a exp( -afIE/ott).
(7)
where AE is the transferred energy, a the rangeparameter of the interaction potential and u the relative velocrty. Smce u is largest for He it should give the largest probability. This relation is confirmed by theoretical considerations on the complete coupled-channel equations [43] and also by solving these equations by exact methods 1441 Always the hghtest scattering partner is most efftcrent m producmg vrbrational transitions. Therefore the result for Kr cannot be explained by purely Impulsive collisional relaxatron. It might be possrble that complex formation due to orbiting collision or formatron of van der Waals complexes is responsible for the enhanced vibrational relauation. Similar conclusions have been derived in seeded beam studies of I, in the excited 126.451 and m the ground state [8] The process itself proceeds via the vibrational predissociation of the complex to the ground state and has been extensively discussed in the literature [25,46.47]. For Kr we expect, because of its deeper well with respect to CaCl, a higher probability for forming complexes than for He. The behaviour of Ar confirms thus conclusion. At low p10D values and for those data with the larger nozzle diameter Ar behaves
normal, the relaxatron 1s due to drrect collisions and less effectrve than for He. However. for the two values at hrgher noD obtamed with smaller nozzle diameters the relaxation vra complex formation starts and becomes more effectrxe than for He. Holding no D constant a smaller nozzle diameter D means that CaCl undergoes more termolecular (or even higher-order) collisions which favours the formation of van der Waals complexes. We conclude that in the case of He and most of the Ar points \ve have colhsional rela\atron nhereas for Kr the relaxation 1s enhanced by the vibrational predrssocration of van der Waals molecules or another process \vhich is more effective than a purely impulsive collision_ To investigate this quostion further a better relaxation model has to be applied which allo\vs the direct extraction of the state-to-state rates [41] The reversed order of heavier rare gases in quenching vibrationally e\cited molecules has also been found in ref. [32]_ Although the authors claim that the Landau-Teller transition probabilities explain their result. a careful inspection of therr fitted parameters sho\\s that then range parameters are unph>sically small and an addrtronal scaling parameter was mtroduced to reverse the order according to eq. (7) [S].
Acbno\\ledgement We are grateful to Dr. H Tells and Dr. H-L!. Schutze-Pnhlmann for pro\ idmg their results prior to publication The computations were performed at the GWD. Gottmgen.
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212
U Buck ef al / Reluxarron and spec:roscop_s of CaCI m seeded supersonrc beams
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