Low-energy differential elastic scattering of Ar* by HBr: Comparison with the scattering of K by HBr

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HOW-ENERGYDIFFERENT'IALELAST~CSCA~ERINGoFAA3Y HBr: COMPARISdNWITHTHESCATTERINGOFKBYHBr~ D.H. WINICUR, J.L. FRAITES and F.A. STACKHOUSE* Chemistry

Department

und the Radiariort Indiana

Laboratory,

46556,

Chiversiry

of Norre Dame,,

USA

Received 30 July 1973

Differential elastic cross section measurements of electronically excited, mctastable argon atoms Are by IlBr molecules show a shallow rainbow. Parameters are deduced assuming an L-J (12,6) potenlial and arc compared to those which

hove been reported

identical

but the potential

for the scattering

of

K by HBr. The location

well depth for Ari + tIBr is lo-20

percent

.l. Introduction

electrons

minima

energy elastic scattering. The only previous work comparing the elastic scattering ofa metastnble rare gas atom with its alkali ana-

system.

log was reported

2. Experimental details

by Rothe et al. [4]. They compared

f Work supported, in part, by Research Corporation Grant No. A:FY73-7-19. l Present address: Chemistry Department, California Institute of Technology, Rgdenn, California, USA.

is

potential paranleters are extracted and compared with those derived from the eleastic scattering of the K-HBr

such as low-

integral elastic scattering cross sections of metastablyexcited helium by rare gases to that of lithium by rare gases and found that the absence of an inner Is electron increased the strength of the interaction by about 20 percent. The advantage of using differential elastic scattering cross section measurements to derive the intermolecular potential have been discussed extensively [S] . We have chosen to compare the differential scattering of Ar* by

for the two systems

HBr with that of K by HBr because the differential scattering of K by HBr has been measured over a range of energies, is characterized by a well.developed rainbow (which becomes increasingly shallow at low energies) from which potential parameters have been obtained, and has a relatively large total reactive cross section of about 30 ,%? [6,7]. We report here measurements of the differential elastic scattering of Ar* by HBr at 1.3 kcal/mole, from 4 to 46’ (cm.), from which

The e!ectronicallyexcited, metastable state of argon Ar *< 3 P) and the ground electronic state of potassium K(IS,,,) both have a single electron in the 4s shell and have similar ioniu;ition potentials, masses, and polarizabilities [l--3] _The essential difference between this excited state of argon and its alkali annlog lies in the absence of the inner 3p electron which suggests that their behavior should be similar in experiments which are sensitive mainly to outer-shell

of lhe potential

lower than for K + IIBr.

An aerodynamically-intensified (nozzle) beam of argon atoms is excited to the 3P2,~ metastzble state by impact with 1 10 eV electrons [H] _The Ar beam is mod-’ ulated nt 80 Hz and collimated to 0.12” full-width-athalf-maximum (fwhm) before it enters the collision region. Charged particles are removed by a deflecting tield. The Ar* beam Mach number of approximately 21 corresponds to a veloc’ty resolution of 8.7% fwhm. The HBr crossed beam, formed from a room-temperature. capillary channel array source, has an angular spread of ” 18’ fwhm producing a scattering volume of 0.005 cn$. Taking the most probable velocity of the capillary array source (capillary length 0.305 cm, presstire 0.4 mm ,Hg; l.LJ

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temperature 296°K) as I.06 times that of an effusive source operating at the same conditions [9] , the most probable relative energy E = I .3 kcal/mole. Scattered Ar” atoms are detected by emission of secondary electrons from a Be-& electron multiplier. The multiplier is housed in a differentially-pumped, liq uid-nitrogen-cooled chamber which is rotated about the scottcring center in the plane of the two beams. The entrance slit, located 6.2 cm from the scattering center, is 0.74” wide _Ground-state argon (or HBr) does not produce secondary eiectrons and is not detected. The electron multiplier current is amplified by an operational amplifier (Kiethley 301), with a 107R feedback resistor located in the scattering chamber. The ;mplitier output passes through an 80 Hz narrowband filter followed by a lock-in amplifier (PAR 120). The PAR signal is fed into a voltage-to-frequency converter

(Dymec) followed by a digital counter (Hewlett-Packard) which intregrates over 100 set intervais[lO]. The flight time of the metastable atoms from the excitation region to the detector is 7 X IO4 set whereas photons coming from this region reach the detector in less than 10eg set and are not seen in the lock-in amplifier signal. The natural radiative lifetime of the argon metastables is between I and 8 set [I I] so the fraction of Ar* atoms which decay should be negligible. Photons produced by tftis decay are emitted nearly isotropically and would be expected to broaden t!re primary beam profile [ 121 . No such broadening is observed. The lockin amplifier output signal is therefore proportional to the intensity of the elastically-scattered Ar’ atoms, Scattered intensity measurements are made by comparing the 80 HZ Ar* signal with any residual 80 Hz background when the crossed beam is pivoted out of the path of the primary beam. After every second measurement, a reference cross section is measured at a reference angle of3.6” (5.5” c.m.).

3. Experimental

data

Fig. 1 shows the experimental cross section, transformed to c.m. coordinates, using the approximation of monoenergetic beams [13] , multiplied by the sine

of the cm. angle 0. Two different experiments are shown, repeated after a period of two months. Both experiments are normalized at the same reference angle (5 5” cm.). 124

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: The rainbow is very shallow, reduced to a broad pla‘teau between 26” and 36%:m. The rainbow angle Or = ‘. 44 + 3’ using the,relation suggested’by Mason et al. [14], i.e., 8, = B,,, + 0.772(0,, - Brati) where 0,, is the angle of the rainbow peak and 8,, that of the pre-

ceding minimum.

4. Comparison

with K + HBr

The broad rainbow and the location of 0, are consistent with the pattern seen in the scattering of K by HBr [6]. Or is about 10 percent smaller than would be expected for K + HBr at the same energy. For an assumed potential function of the form L-J (12,6) the observed rainbow angle corresponds [ 141 to K E E//E= 2.84 + 0.18 yielding a value for the potential well depth e = (3.2 f 0.2) X 1O-l4 erg. The experimental results are compared with cross sections calculated by the quantum mechanical method of partial waves a has been previously described [IS]

The calculated cross sections are averaged over the experimental relative energy spread AE/E = 1 .OS and over a cm. detector width Ax = 1.14O.AL? is the fwhm of an assumed triangular distribution in which the effect of angular divergence of both beams has been included. &is equal to the detector entrance slit width (0.74”) multiplied by the average value of the c.m./lab angle. The solid curve in fig. I is calculated using an L-J (12,6) potential. The effect of the averaging is shown in fig.2. The multiple rainbow strUctures are reduced to a single broad rainbow. The value of Or, computed from the

Mason et al. [14] relation, is unchanged. The rapid oscillations are considerably reduced in magnitude but are unchanged

in position.

Their amplitudes

increase

in

the regions corresponding to the rainbow structures. The potential parameters obtained from this comparison, for an L-J (12,6) potential, are: r,= 4.4 f O.SA, l = (3.5 2 0.3) X 1O-l4 erg where );n is the position of the potential minimum. The limits reflect the sensitivity of the location and shape of the rainbow to the choke of potential parameters. The value of E is larger than that determined directly from 8, but the range of values obtained from this comparison overlaps the range obtained directly from 0, from 3.2 to 3.4 X IO-t4 erg:, Greene et al. [6] suggest the following exe-6 (a.= 12) potential parameters for the scattering of K

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Fig. 1. Differential elastic suItering cross sections for AI * scattered by HL4r, in cm. coordinates, scattering angle. The rainbow angle 0, = 44’. The solid curve represcn~ cross sections calculated

x IO- I4 erg, averaged

rm=4.4Aande=3.5

multiplied by the sine of the cm. loran L-J (12.6) potential with over the relative energy spread AL//E= I.08 and c.m. detector width Ax = I .14’.

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multiplied ,t4y the sine of the cm. ScattcIiflr anFig. 2. Caiculated differential e!astic scattering cros sections in c.m. coordinates, erg. The heavy CUTVO. averaged.bver gle. Both curves zue calculated for an L-J (12, 6) potential with rm =.4.4r9 and E = 3.5 X. lothe relativeenergy spread AE/E = 1.08 and c.m. detector width Ax = 1.14”) is the same as shown in fig. 1.

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Fig. 3. Differential elastic scattering cross sections for Ar* scattered by HBr, in cm. coordinstcs, multiplied by the sine af the c.m. scaltering angle. The solid carve represenls cross seclions cslculated for an L-J (12.6) potential with parameters derived from the scattering of K by Wr: r,.,, = 4.JA e = 3.82 X IO-” erg. The calculated CIOSSsections are avenged over the relative energy spread d and c.m. detector xvidth of rhe Ar + HBr experiment: ti/E = 1.08, Ax = 1.14”.

by HBr based on their analysis of differential elastic cross sections at five energies from 1.49 to 4.49 kcal/ mole: rm =4.4 *0.4A, Ez(3.95 f 0.07)X IO-l4 erg. Eu [7] derives the following L-J (13,6) parameters from the same data: rm = 4.4A E = 3.82 X lo-l4 erg. The positions of the pitential mimima for Ar* + HBr and K + HBr are the same but the potenrial well depth of Ar* + HBr is about IO-20 percent lower than its alkali analog. Fig. 3 compares the Ar* + HBr data with cross sections calculated using Eu’s K + HBr potential averaged over the Ar* f HBr experimental energy spread and dpt.ccror width. The cross sections calculated from the K f HBr potential show a broader rainbow which yields a.larger ialue of 0,, consistent with the deeper well depth and larger value of 0, expected at 1.3 kcal/ mole for K + HBr [6] _ The presence of an inner 3p electron strengthens the intermolecular potential whereas the presence OF ah inner Is electron appears to weaken it. Similar experiments comparing neon and krypton with their alkali analogs are planned to determine whether the difference is due to the shell level or.the’difference in‘orbi-

tals. Further experiments with Ar” + HBr at higher energies are in progress to provide information on the effect of the 3p electron on chemical reactivity.

Acknowledgement The authors appreciate the valuable help of Mr. Donald Schifferl and Mr. Harold Zielinski in the construction of the apparatus. Thanks are also due to Mr. James Donovan for his help in measuring the cross sections. One of u (D.H.W.) would like to acknowledge the support and encouragement of professor Aron Kuppermann during the early stages of the design of the apparatus.

References ‘[l] C.E. Moore, NBS CircuIar467. Vol. 1 (1949). [2] E.E. hIuschlitz Jr., Science 159 (1968) 599. (31 B:Bederson

10 (196611. .’

and E.J. Robins&,

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.’ i41 ,E.W. Rothe. R.i-I..Neynab& and S. hf. Trujiuo, J. Cherrt. Phys. 42 (196-C) 3310. -’ Chem. #ITS. 10 (1966) 75; [Sl R.B. Bernstein:Advan. H. Payly and J.P. Toenriies. Advan. At. hIol. Phys: 1 (1965) 195; Meth. Esp. Phys. 7 (1968) 227; J.R. Luoma and CR. hlueller. J. Chem. Phys:46’(1967) 680. 161 E.F. Greene, A.L. hfoursund and J. Ross, Advan. Chem. Phys. 10 (1966) 135. and references therein. [71 B.C. Eu, J. Chem. phys. 52 (1970) 3021. 181 D.H. Winicur and E. L. Knuth, Chem. Phys. Letters 12 (1971) 261. 191 D.R. Olander, R.H. Jones and W.J. Siekhaus, J. Appl. Phys. 41 (1970)

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110) R.W. Bickes Jr. and R.B. Elcrnstein, Chem. Phys. Lelters 4 (1969) 1 I I. Ill] D.H. Stedman and D.W. Setsef, Progr. Reaction Kindtics 6 (1971) 193; R-S, van Dyck’Jr., C.E. Johnso? and H.A. Shugart, Phys. Rev. A5 (1972) 991. [12] D.H. Winicur, W.E.Rodgersand E.L. Kn;th, Rev. Sci. Instr. 40 (1969) 1192. [I31 F-A. Morse and R.B. BeFnslein, J. Chem. Phys. 37 (1962) 2019. [ 141 E.A. hlasnn, R.J. Mu&and F.J. Smith, J. Chem. Phys. 44 (1966) 1967. [ 151 D.H. Winicur, A.L. hloursund, W.R: Devereau, L.R. Martin and A. Kuppermann, J. Chem. Phys. 52 (1970) ‘. 3300.

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