Faraday Discuss. Chem. SOC., 1991, 91, 79-90 Product Rotational Alignment for the Reaction o(3~) + cs(x lz+) + co(x I,+) + s(3~) Finn Green, Graham Hancock” and Andrew J. Orr-Ewing Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OXI3QZ, UK Rotational alignment of the CO(X ‘C+, u ’ = 14) product of the O(3P)+ CS(X ‘E+) reaction has been measured relative to the velocity vector k of the reagents. O(3P) atoms were produced with k aligned in the laboratory frame by pulsed laser photolysis of NOz, and the CO product was detected by polarised laser-induced fluorescence. Transformation of the measured laboratory-frame rotational alignments to the required values of the align- ment parameter (P,(J‘ * k)) were carried out using previously determined values of the translational anisotropy for the photodissociation of NO2, making allowances for both the thermal distribution of CS radicals and the spread of recoil energies of the 0-atom fragment.Values of (P2(J’ - k)) were measured for J ’ between 12 and 35, and found to be close to zero to within the range 0 f 0.25, with the mean value being slightly positive. Measurements of the Doppler profiles of the transitions are in qualitative agreement with those predicted for an isotropic distribution of product velocities about the k direction. These preliminary results illustrate the scope of laser based methods of extracting quantum-state-resolved data on scattering dynamics under experimental conditions which do not involve the use of molecular beam methods. Since the first crossed molecular beam experiments were carried out in the mid-l95Os,’ reaction dynamicists have been interested in the vector properties of the outcome of a chemical reaction, as well as the scalar attributes of the distribution of energy in the degrees of freedom of the products.The first vector correlations to be measured were between k and k’, the relative velocity vectors of reagents and products, and gave rise, for example, to the now commonplace terms of forward and backward scattering. As more vector correlations have become amenable to experimental study, the field has matured, been the subject of two recent symposia,233 and has been comprehensively r e ~ i e w e d . ~ - ~ This report describes laser-based measurements of the correlation between the relative velocity vector k of reagents in an atom-exchange reaction, and the rotational angular momentum J’ of the diatomic product.Correlations of this kind are normally observed in systems which possess cylindrical symmetry about a laboratory axis (which might be, for example, the axis of the velocity vector k ) , and are described in terms of expectation values of Legendre polynomials (P,,(J’ k ) ) , with odd and even values of n relating to ‘oriented’ and ‘aligned’ populations, re~pectively.~” Experimental condi- tions normally result in the production of aligned products only, and yield measurements of (P,(J’ k ) ) , reflecting the quadrupole moment of the J‘ vectors about k. Alignments of this kind in reaction products have been measured by molecular beam deflection methods,8-10 by observation of the polarisation of fluorescence from electronically excited products,831 ‘-19 and by laser-induced fluorescence (LIF) probing of the ground-state species.20 The last method has found wide use in photodissociation processes, where correlations between J’ and k’, the fragment velocity vector, have been measured, and 7980 Product Rotational Alignment for O(3P) + CS(X 'E+) the mutual correlations of these vectors to p, the transition dipole in the parent molecule, have been exp10red.~-~ For collisional processes the LIF technique also has the potential, via Doppler profile measurements of the products' recoil velocity distribution, of providing insight into the ways in which k, k' and J' are mutually related.Such 'multiple vector correlations' are still in their infancy, but examples are emerging from both collisional reactions' ' and energy-transfer2' processes.Laboratory-frame measurement of product rotational alignment by LIF is now a straightforward task under the condition of axially symmetric reagent preparation, thanks to the 'experimentally friendly' description of the procedures in the literat~re.~ In previous studies of J',k correlations in reactive processes, the alignment has been referenced to the laboratory-frame velocity vector of the reactants when the latter is defined by crossed molecular beam9-" or by beam-gas12-20 collisions. An alternative method of reagent velocity selection has been used in the present study, namely laser photolysis of a suitable precursor molecule whose product velocity distribution relative to the polarisation vector of the photolysis laser is known.Time-resolved LIF detection of the reaction products is then used to measure the J', k correlation and, via Doppler profile measurements, to explore if k' is related to k. The technique is simply the vector extension of the method used in many previous studies of the scalar properties of reaction dynamics,22 has been used previously, in studies of the 0 + HC123" and H + 0,236 reactions, and is under investigation in the O( ID) + N20 The technique is not without its difficulties, as the photodissociation process will inherently yield a velocity distribution which, although well defined, will be less anisotropic, and possibly less monochromatic, than those produced by molecular beam methods.The effect of the velocity distribution is to place a reduction on the limits expected for the alignment, but these limits, as will be shown below, are still within experimental observation. The reaction studied is the atom-exchange process, o ( ~ P ) + CS(X IZ+) -, CO(X lz+) + q3p) ( 1 ) Previous work has shown that a high degree of the reaction exothermicity is channelled into product vibration through attractive energy release before the nascent CO bond reaches its equilibrium ~ a l u e . ~ ~ - ~ ' These highly energetic products (the vibrational population peaks at v' = 13) can be detected by LIF of the CO A 'n-X 'Z+ transition, using excitation wavelengths [for example the (6, 14) band at 220 nm], which can be straightforwardly generated by standard dye laser systems.The fluorescence is anti- Stokes shifted [e.g. the ( 6 , l ) band lies at 140.9 nm] into the vacuum UV region, and can thus be observed by a solar-blind photomultiplier in a highly sensitive and noise-free fashion.32 An added advantage for alignment measurements in CO is that the 'X+ state possesses only rotational angular momentum, and degradation of the alignment by coupling to electronic and nuclear momenta (as occurs for example in ground-state OH and NO) is avoided.33 Velocity alignment of the O(3P) reagent is achieved by laser photolysis of NO2 at 355 nm. The alignment in the laboratory frame is described by the translational anisotropy parameter p, defined by the expression for the intensity distribution o( 8) of fragments scattered at angle 8 between the electric vector &ph of the photolysis beam, and k, the fragment's relative velocity vector where cos 8 is the scalar product k 'Eph, and N is a normalisation factor.For NO2, p has been measured as between 0.9 and 0.46 for this wavelength r e g i o r ~ , ~ ~ - ~ ~ some way from its limiting values of 2 and -1 (the limits which would occur for prompt dissociation of a linear molecule). The 0-atom distribution of kinetic energies is also not ideal (i.e. not 'monochromatic'), the photolysis at 347 nm showing two peaks corresponding toF. Green, G. Hancock and A. J. Orr-Ewing Nd:YAG laser 81 I 1 I L r Fig. 1 Schematic diagram of the experimental arrangement. NOz was photolysed at 355 nm using horizontally polarised radiation (E,,, in the plane of the diagram). CO was probed using both horizontally and vertically probed radiation, and LIF was detected by a solar-blind photomultiplier viewing fluorescence emitted in the direction perpendicular to the plane of the diagram the formation of NO( v = 0) and ( v = 1 ) with mean 0-atom kinetic energies of 25 and 12.5 kJ mol-’, respectively.These values still largely define k, as the velocities of the CS reagent (formed thermalised by a microwave discharge in CS2) are an order of magnitude smaller. All these smearing effects, however, can be accounted for and used to predict the range of alignment parameters expected from the reaction dynamics. Many previous studies of J‘, k, correlations have observed the effects of kinematic constraints in reactions in which a light atom is formed in an A+BC In such cases, angular momenta in reagents and products are dominated by orbital ( L ) and rotational ( J ’ ) values respectively, and thus in this limit k (which is perpendicular to L ) is perpendicular to J’.Reaction ( 1 ) is not such a limiting case, and although under such conditions alignment affects are expected to be less pronounced, they should be far more sensitive to the details of the potential-energy surface.6 No ab initio calculations for such a surface exist for reaction ( l ) , but classical trajectories on a surface derived from MNDO/CI calculations have reproduced the vibrational energy distribu- tion, and predicted the rotational energy partitioning and some degree of angular scattering for thermalized (300 K) reagents.” We present below our first measurements of the alignment of CO formed by reaction (1) in one vibrational level, u’= 14, together with preliminary data on the Doppler linewidths. These results suggest that the distributions both of J’ and k’ relative to k are close to isotropic.Nascent rotational distributions in CO have also been determined for u’ = 12 and 14. The results show that for thermal reagents the fraction of the available energy appearing in rotation, f r , is considerably lower than that for translation, f t . However, the ratio fr/ft increases markedly for the translationally hot 0 atoms produced by photodissociation of NO2, indicating an efficient conversion of this energy into rotation of the CO product.Details of these results, and of their comparisons with trajectory calculations on a LEPS surface, will be published e l ~ e w h e r e . ~ ~ Experimental Fig. 1 shows the experimental arrangement. CS radicals were formed by a low-power microwave discharge in a flow of CS, at a pressure of ca. 1 Torr, and admitted to the reaction vessel through a pinhole. The distribution of the internal states of CS was82 Product Rotational Alignment for O(3P) + CS( X ‘Z+) measured as Boltzmann at 300 K by LIF observations of the A ‘II-X ‘X+ transition. An approximately equal flow of NO2 was added to make the total pressure (as measured at the centre of the reaction vessel by a Penning gauge) between 5 x Torr, maintained by a partially throttled 700 dm3 s-’ diffusion pump. NO2 was photolysed at 355 nm by the frequency-tripled output from an Nd3+ YAG laser (JK System 2000).The output was horizontally polarized and apertured to give a beam of 2 mm diameter at a fluence of CQ. 0.1 J cm-2 at the centre of the cell. CO was detected by LIF of the (6,14) band near 220 nm, the radiation being generated by a frequency-doubled excimer pumped dye laser (Lambda Physik DL 3000). The dye laser output was reduced to ca. 100 p J per pulse, and expanded to a diameter of 6 mm before passing into the reaction vessel collinearly with the 355 nm beam at a time delay of 1 ps from the firing of the latter. The dye laser polarisation was controlled by a KD*P Pockels cell, and was switched between horizontal and vertical polarizations for a preset number of laser shots before the dye laser was stepped to a new wavelength position.The dye laser bandwidth was 0.4cm-’ for the alignment scans, and reduced to 0.04cm-’ by means of an etalon for the Doppler profile measurements. Fluorescence was detected by a solar-blind photomultiplier (EM1 Gemcon G-26E3 14LF) perpendicular to the laser beams’ axis, and the collection of the data, firing of the lasers, and the stepping of the dye laser wavelength were controlled by a microcomputer (IBM PC XT). Laser energies were stored for each shot and used for data normalisation. and At the combination of total pressures and delay times between the two lasers, a nascent CO molecule formed immediately following firing of the photolysis laser has a probability of between 10 and 20% of undergoing a gas-kinetic collision, with these probabilities reduced for molecules formed at later times.Population ratios, alignments and Doppler profiles were invariant with pressure in this narrow range: lower pressures and delay times produced inadequate signal-to-noise ratios. The most compelling evidence that the data collected under the collisions are not substantially affected by collisional processes, comes from the observation of Doppler lineshapes, in which (as discussed below) velocity distributions were observed corresponding to the full release of kinetic energy from the reaction. The combination of pressure and delay time is similar to that used in previous studies of pump and probe dynamics.22 Care was taken to ensure that both the photolysis and probe lasers did not saturate the NO, and CO transitions, respectively, and LIF signals were measured to be linear with laser power in both cases over the range of energies used.The probe laser beam was deliberately expanded to be larger in diameter than the photolysis beam to ensure that nascent reactants were not able to fly out of the detection volume during the 1 ps delay betwen photolysis and probe lasers. Fig. 2 shows part of the LIF excitation spectrum of the nascent CO near 220nm, with the wavelength positions marked for P, Q and R branches in the (6, 14) band of the A ‘ll-X ‘Z+ transition. Rotational populations peak around J’ = 25, in marked contrast to the far lower rotational excitation found in the reaction of thermal (300 K) reagents.” The raw data for the determination of CO alignment were obtained by scanning the dye laser (0.4 cm-’ bandwidth) over a non-overlapped line and measuring at each dye laser wavelength the LIF signal for both horizontal and vertical polarisations of the probe laser (corresponding to the electric vector of the probe laser E~~ parallel and perpendicular to that of the photolysis laser, &ph, respectively).In principle the ratio of these intensities, integrated over the complete lineshape, can be related to (P,(J’ Eph)), where the reference direction is taken as the (horizontal) electric vector &,h of the photolysis laser.’ In practice it was found that the ratios of the signals for the probe laser horizontal ( E ~ ~ 1) &ph) and vertical (&pr I Eph) were greater than unity forE Green, G.Hancock and A. J. Orr-Ewing Pc 30 3 32 33 36 35 36 27 28 (2,. 22 23 24 25 26 . 16 I 220.2 17 ii 1.3 19 1 2 20 n 2 .4 22 ?11 220.6 83 A/nm Fig. 2 Part of the LIF excitation spectrum of CO(X ‘X+, u’ = 14) formed in the 0 + CS reaction. The positions of P- Q- and R-branch lines in the A ‘n-X ‘X+(6,14) band are marked. 0 atoms formed from NOz photolysis at 355 nm, CS radicals produced by microwave discharge of CS2 both Q branch and P or R branch measurements, although the values of the ratios were different in the two cases. It appears that our excitation and detection system was more sensitive for horizontal than vertically polarised probe light. Careful checks were made to ensure that the laser beam energy measurements were not polarisation sensitive, that the shape of the probe beam did not change position markedly with polarisation, that the Pockels cell switching resulted in full polarisation rotation of the beam, and that the response to the solar-blind photomultiplier was not polarisation sensitive. Small changes in the intensity distribution over the beam profile may have been responsible for these effects, and they were allowed for in the following way.A ratio of signals for horizontally and vertically polarized probe light was measured for Q-branch excitation, QH/ Qv. The dye laser wavelength was then moved to the corresponding P- or R-branch line, and the ratio, P, RH/P, R,, measured. The ratios of these two measurements S = ( QH/ Qv)/( P, RH/ P, R,) were then taken as the raw data.The same procedure was carried out for an isotropic distribution of thermal NO excited in the A 211-X 2C+ (0,O) band near 226nm, and the ratios S measured agreed within experimental error to the (non-unity) values predicted theoretically’ for the present excitation geometry. Table 1 lists the raw data for CO as a function of J’, with the values indicating the extent of the reproducibility of measurements carried out over a period of several weeks. With the dye laser narrowed to a bandwidth of 0.04 cm-’, line profiles were measured for J’=4,17 and 28 in the (6, 14) band. The experimental geometry has so far only allowed these profiles to be measured in one configuration, namely with the probe laser propagation axis perpendicular to Eph (see Fig.1). Fig. 3 shows the profiles of the Q(4) and Q( 17) lines taken with E~~ parallel to Eph (the data for epr perpendicular to &ph were almost identical, but showed ca. 10% narrower linewidths), and the expected trend of increasing linewidth with decreasing J’ was observed. Measurements of the profiles for the reaction between thermal 0 atoms and CS at low pressures showed considerably84 Product Rotational Alignment for O(3P) + CS(X '2+) I 1 I -0.4 -0.2 0 0.2 0.4 displacement from line centre/cm-' Fig. 3 Measured Doppler profiles of the Q(4) and Q( 17) lines in the CO A'II-X 'V (6,14) band. The experimental arrangement was such that the propagation vector of the probe laser was perpendicular to the electric vector of the NOz photolysis laser &ph, and thus perpendicular to the most probable value of k, the 0-atom velocity vector. The solid lines show calculated Doppler profiles for an isotropic distribution of the CO product velocities k' about k as explained in the text lower translational excitation, and for measurements taken at high pressure (200 mTorr Ar added to the system) and long delays (100 ps), the expected room-temperature Doppler profiles were recorded.Discussion We first note the magnitudes of the ratios of polarisations S ( J ' ) listed in Table 1. An isotropic distribution of CO molecules will produces values of S ( J ' ) which are not unity, and these are shown in Table 1 to be close to those experimentally observed. ToF. Green, G. Hancock and A. J. Orr-Ewing 85 Table 1. Values of the parameter S for different values of J ‘ for excitation of CO(u’= 14) pro- duced in reaction (1) 12 1.44 17 1.29, 1.24, 1.27, 1.45 18 1.18 23 1.40, 1.50 24 1.22, 1.36 26 1.40, 1.01, 1.42, 1.13 29 1.24, 1.24 32 1.57 35 1.34, 1.51 1.24 1.25 1.25 1.25 1.25 1.26 1.25 1.26 1.26 S is defined as the ratio (QH/QV)/ (P, RH/ P, Rv), where the QH and Qv are signals for Q-line excitation with the probe beam horizontally and vertically polarised respec- tively, and P, RH and P, Rv are the correspond- ing signals for the P- or R-branch line.Also listed are the values of Siso expected for an isotropic distribution of CO. v c - 0 V 8 0 0 0 B 0 0 - 0.54 0 I I I 0 10 20 30 c J ’ Fig. 4 Values of the alignment parameter (P2(J‘ k)) as a function of J’ for CO(X ‘X+, u’ = 14) formed in the 0 + CS reaction.k was defined by polarised laser dissociation of NO2 at 355 nm, and the values of (P2(J‘ . k)) were calculated from the measured alignments in the laboratory frame by the formulae given in the text and in the Appendix. The limits of alignment + 1 (J’ 1) k and -0.5 (J’ I k) are shown. The data points at each J’ have not been averaged and their scatter gives an indication of the limits of precision of the measurements. To within these limits (ca. *0.25) the alignment is seen to be zero86 Product Rotational Alignment for O(3P) + CS(X ‘X+) see if this implies that k and J’ are not correlated we first need to make estimates of the range of alignment parameters that might be expected experimentally. In the following analysis we assume that the measured polarisation is sensitive only to the even multipole moments of the alignments of J’ along the chosen symmetry axis (the horizontal axis in the laboratory which coincides with &ph),7 we neglect the contribu- tion of the hexadecapole moment in comparison with the quadrupole moment of J’ relative to &ph,7’20’40 and we assume that the angular distributions of products are sampled with equal probability’ (in these measurements the laser bandwidth exceeded the experimental linewidth).With these restrictions we first convert the measured polarisa- tions to the quadrupole alignment (P,(J’ &ph)) using the formalism given by Greene and Z a ~ e . ~ To relate these values to the alignment of J’ with k we use the azimuthally averaged addition t h e ~ r e m ~ ” ~ (P2(J’ .Eph)) = (P2(J’ k))(P2(k &ph)) (2) We thus need to calculate the value of( P,(k Eph)), which applies to the photodissociation of NO, in our experiment. For a single-photon process, the probability w ( k , E p h ) of finding vectors k and &ph related by their scalar product is o ( k , &ph) = “1 + PP2(k &ph)l (3 1 where p is the translational anisotropy factor. A comparison of the expansion of o(k, &ph) in terms of Legendre polynomials with eqn. (3) yields the identity i.e. (P,(J‘ & p h ) ) = $ ( P , ( J ’ k ) ) . (4) The term & represents the smearing of the alignment of J’ with k when reagents are produced by photodissociation with an angular distribution described by the parameter p (-1 d /3 2) and with a single value of the recoil speed.A further smearing occurs due to ( a ) the 0 atoms interacting with a set of thermally distributed CS radicals and (b) the 0 atoms produced from the 355 nm photolysis of NO, not being mononergetic. Appendix 1 outlines the way in which this changes p in eqn. (4) to an effective value PeFf. The smearing due to ( a ) is calculated to be 3-4% when 0 atoms are given the mean velocity of those produced by photolysis at 348 nm,34 confirming the intuitive view that thermal motion in the heavier CS reagent has little effect on the dynamics of reaction with ‘hot’ 0 atoms. The effect of the distribution of energies for 0 atoms was treated similarly: the combined effects yielded a value of Peff that was ca. 0.9p. Three sets of measurements appear in the literature of the translational anisotropy of fragments in the photolysis of NO, at wavelengths between 347 and 349 nm.34-37 The values of p range from 0.7 to 0.9 for the NO co-product formed in v = 0, and from 0.46 to 0.6 for NO ( v = 1).Photolysis at 355 nm has been studied only for the v = 1 fragment, where the p value was unchanged from that at 34811m.~~ At 347nm approximately equal amounts of NO in the two vibrational levels are formed,34 and if we assume this will be true also at 355 nm then an average value of p over v = 0 and 1 from all these studies can be taken to be 0.65. If we now take the value of Peff = 0.9 p, this results in the values of (P2(J’ k ) ) from eqn. (4) being ca. nine times larger than the (P,(J‘ &ph)) values derived from the experimental measurements.( P2(J’ k)) lie within the limits +1 (J’ 11 k) and -0.5 (J’ I k), and thus the (P2(J’ &ph)) values are constrained by this factor of p/5, so that experimental errors in the determination of the laboratory-frame alignment will be amplified when this is transformed to the alignment about k. Fig. 4 shows the values of ( P2(J k)) calculated from the data of Table 1 and using Peff = 0.58, with the limits of +1 and -0.5 shown. The figure shows that the precision of the derived values of (P2(J’ k)) indicated by the scatter of the data for different experiments at theF. Green, G. Hancock and A. J. Orr-Ewing 87 same J’ is quite low (ca. * 0.25), but that there is no marked trend with J‘, and that the majority (>70%) of the values lie within k0.25 of zero (all the values with two exceptions lie in the range 0.4 to -0.2).The average value of (P2(J’ k ) ) is > O , but care should be taken not to overinterpret this fact in the light of the experimental uncertainties in the data. We conclude that the alignment parameters are far from their limiting values, and our experiment is unable to distinguish their mean value from that expected for an isotropic distribution, i.e. there is no clear J’, k correlation. Before we discuss possible reasons for this, we note the limits of uncertainty in the data imposed by the photolytic method of 0-atom production. The value of 0 = 0.65 is a factor of three lower than that expected for prompt dissociation of a linear molecule in a parallel transition. Had such a convenient source of O(’P) been available to us the precision of the derived values of (P2(J’ k ) ) would have increased by a factor of three.Although this would still not have produced as aligned a source of 0 atoms as in an atomic beam, it illustrates that useful data can be extracted from photolytic preparation of reagents, and that the present 0-atom source is regrettably not the most suitable for high-precision studies. Previous studies of vector correlations in reaction dynamics have shown that for cases in which there is no obvious kinematic constraint ( i e . where a light atom is not a reactant or product) values of (P2(J’ k ) ) lie in the range -(0.1-0.3),9~10~15916~20 less aligned than the kinematically constrained limit of -0.5. In the present reaction both the reagent orbital angular momentum L and the CS rotational angular momentum J are of the same order of magnitude (from the measured rate constant26 ILI can be estimated as 10 h, and the most probable value of (JI for CS at 300 K is 1 1 h ) and thus the initial total angular momentum is less well defined than in the constrained systems.We have carried out trajectory calculations on a LEPS surface which reproduces the product vibrational d i ~ t r i b u t i o n . ~ ~ Values of (P2(J’ k ) ) were found to be markedly negative (ca. -0.35) in contrast to the experimental results, and this may well reflect the colinear lowest-energy path that this surface favours. A bent transition state has been invoked to explain the results of the O+ HCl where a lack of correlation was observed between J’ and both k and the alignment of the reactant molecular axis.Although a linear geometry has been calculated for the transition state for reaction on the lowest OCS38 triplet surface, the influence of bent geometries may be of increasing importance at high reagent kinetic energies where we find a larger proportion of the available energy appearing in product rotation than for thermal 0 + CS reagents. Trajectories on the OCS triplet surface have shown that there is no pronounced purely forward or backward scattering or products at the present values of the reagents’ kinetic energies.38 Information from the Doppler profiles can in principle be used to provide some indication of the correlation between reactant and product velocity vectors, i.e.the differential cro~s-section,~~ and methods of extraction of data from such systems have been described in the l i t e r a t ~ r e . ~ ~ Fig. 3 shows preliminary data on the profiles of two lines in the (6, 14) band, each taken with the single experimental configuration of the probe laser’s propagation vector perpendicular to &ph (and hence perpendicular to the most probable velocity vector k ) . The data need to be improved in S I N ratio before quantitative information can be extracted from the profiles, and here we consider only what the predicted lineshape would be if CO was formed in the limiting case of its velocity k’ being isotropically distributed about k. Along a given direction (for example the probe beam’s propagation axis z ) the CO velocity component takes the simple form P( v , ) = 2 n j up( u ) du where p ( v ) is the (isotropic) speed distribution of the CO molecules.For a monoenergetic distribution at a speed vo this predicts a ‘top-hat’ profile centred at frequency vo with width 2 ~ ~ 2 1 ~ / c . In Fig. 3 the profiles are calculated using a p ( u ) function which reflects m I U I I88 Product Rotational Alignment for O(3P) + CS(X ‘Z+) the energy available for partitioning into translation due to the exothermicity of the process o(~P,) + cs( ‘z+) -+ co(x ‘z+, U’ = 14, J ’ ) + s(~P,) calculated from the AH: value43 together with the kinetic energy distribution in 0 atoms as measured by Busch and Wilson.34 The latter contribution to p ( v ) does not change the Doppler profile markedly from the ‘top-hat’ shape and when this is convoluted with the dye laser profile, this simple prediction is seen to fit the data tolerably well.The observed shapes certainly indicate that there is no strong preference for the velocity vector of CO to lie parallel (forward or backward scattering) or perpendicular (sideways scattering) to k. Conclusions For the O+CS reaction, no alignment of the rotational angular momentum J’ in CO( v’ = 14) relative to the velocity vector k of the reagents could be discerned within the experimental precision offered by the photolysis method of production of 0 atoms. Values of (P2( J’ - k)) lay between -0.2 and 0.4 with the majority in the region *0.25, the limit of the experimental precision. Analysis of the Doppler lineshapes shows that a simple model of isotropic scattering gives at least qualitative agreement with the results.For this particular range of reagent and product energies there appears to be little correlation between k and either J‘ or k‘. The results and analysis presented in this paper are clearly preliminary, but illustrate the potential of the purely laser based methods of studying alignment relative to the initial velocity vector of the reagents in a chemical reaction. Future experiments with improved data collection times, with varying laser polarisations and with different 0-atom sources are planned in order to put the present conclusions on a more quantitative basis. Appendix To calculate the effect of a thermal distribution of CS radical velocities on the transla- tional anisotropy p we first assume a singZe recoil speed uo for the 0 atom produced by NO2 photolysis, ie.the velocity distribution takes the form p ( U ) du = N [ 1 + pP2( u Eph)]6( u - UO) du where 6( u - u,) is a Dirac S function. The distribution of relative velocities u thus takes the form of a modified Maxwell-Boltzmann distribution 1 p ( q u ) do = {exp -( u - ~ ) ~ / 2 u * ] du u3(2 p2 where u2 = k,T/m. To obtain the full distribution of relative velocities, p ( u , u ) must be integrated over all values of the velocity u (remembering that this integration is now only over the angular part of u, as we assume lul= uo is a constant): This integral takes the form1 .o 0.8 0.6 0.4 0.2 0.0 Q. 3 6 NO(v=I) NO(V-0) E Green, G. Hancock and A. J. Orr-Ewing 89 D Fig.5 Values of the ratio of the effective anisotropy factor, Peff, to the measured value, P, for the 0 + CS system as a function of the relative velocity of the reactants. Marked on the x axis are the values of the 0-atom velocities for the photolysis of NOz at 347 nm forming NO( o = 0) and NO( o = 1) fragments. The value of Peff varies by only 3-4% over the range of relative velocities expected from 0 atoms produced with NO( u = 0) and NO( u = 1) cofragments. Peff = 0.9 /3 rep- resents the smearing of the translational anisotropy over all reasonable 0-atom velocities. P was taken as 0.65 (see text) resulting in Peff = 0.58 where 8, is the angle between o and &ph, and the I , / 2 , 5 / 2 are modified spherical Bessel functions. Allowance is made for a spread in the oxygen-atom speeds, caused by the internal excitation of the NO cofragment, by numerical integration over a distribution of speeds estimated from the time-of-flight data of Busch and Wil~on,’~ using Monte Carlo techniques.It was necessary to resort to numerical integration because the analytical form of the integral for a Gaussian distribution of speeds proved intractable. A fit of the resulting data points to a general Legendre expansion yielded an expression contain- ing only zeroth- and second-order terms, from which Peff, corrected for the oxygen atom speed distribution, can be deduced. From the functional form of Peff it is apparent that the separation of the distribution of relative velocities into angular and speed terms is not complete.Calculations of the variation of Peff with v are shown in Fig. 5 and demonstrate that for all but low values of v, Peff is close to its limiting value, and essentially constant. Marked in the figure are the average relative velocities for oxygen atoms formed with NO( v = 0) and NO( v = l ) , showing that for the purposes of our experiment, we can assume a constant value of Peff. The calculation illustrates the limitations of this experimental method as the speed of the photofragment approaches the mean speed of the thermal gas (i.e. as v approaches zero). We are grateful to Dr. N. J. B. Green for help with the calculation of the Peff values and to Prof. J. P. Simons and Dr. M. Brouard for valuable discussions. 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