Differential cross sections for the competing charge-transfer reactions K ~ ' ( ~ P , / ~ ) + Kr('~0) -+ Kr('so) + K ~ + ( ~ P , / ~ ) and

K ~ + ( ~ P , / ~ ) + Kr('so) -+ Kr('so) + K ~ + ( ~ P ~ ~ ~ )

STEPHEN L. HOWARD, ALAN L. ROCKWOOD, WALTER TRAFTON, BRETISLAV FRIEDRICH, STEPHEN G. ANDERSON, AND JEAN H. FUTRELL

Departmerlt of Chemistry, University of Delaware, Newark, DE 19716, U. S . A .

Received September 18, 1987

The crossed-bcam method was used to invcstigatc thc chargc-transfer reaction of K~'( 'P. , /~) with Kr at collision energies of 9.2 and 19.9 eV. A weak plasma ion source was uscd to gencratc a ncarly pure Kr'( '~,/r) beam. The purity of the beam was tested+ by using CH, as a probe reaction; because K~'( 'P, /~) gencratcs CH: and K ~ ' ( ' P , / ~ ) generates CH:, thc ratio, CHJ :CH, , could be used to evaluate the spin-state composition of the reactant ion bcam.

The resonant reaction occurs via a process well described by a rcctilinear-trajectory impact-parameter model proceeding via a Kr; intermediate in which the elcctron "holc" is shared equally by both partners. Also evident is thc endoergie fine-strueture reaction with A J = - 1. At 9.2 eV, the endothcrniic-channel product is scattered at a definite angle. suggesting a short-range interaction that selects a particular impact parameter. At the higher energy investigated, the fine-structure splitting is also evident once the data are deconvoluted. However, the scattering angle is rcduccd to near zero, corresponding to nearly rectilinear tragectories for both channels at this energy. The population of both channels is in general accord with accepted theories for ion-atom charge exchange, but the energy range at which i t is observed is far removed from that predicted (we observe nearly equal cross sections for both channels at energics three orders of magnitude lower than those predicted by theory).

La mCthode de faisceaux croisCs a CtC utilisCc pour Ctudier la rCaction de transfert de charge de Krf ('P,/?) avec Kr, h des Cnergies de collision de 9,2 et 19,9 eV. Une faiblc source plasma d'ions a CtC utilisCes pour produire un faisceau presque pur de K~'( 'P, /~) . La purett du faisceau a CtC testCe en utilisant CH, comme rCaction sonde; Ctant donnC quc Krf ( ' P , ~ ~ ) produit C H ~ et K ~ ; ( ~ P , , ~ ) produit CH:, le rapport CHi:CH: peut servir h determiner le rapport des Ctats de spin dans le faisceau utilist pour produire la rkaction de transfert de charge.

La rkaction de rCsonanee se produit selon un proeessus bien dCcrit par un mod&le de parametre d'impaet avec trajectoire rectiligne que, avee un Kr+ intermtdiaire dans lequel le cctrou ,, Clectronique est partage Cgalement entre les deux partenaires. I1 est aussi tvident qu'il se produit une rCaction endo-CnergCtique de structure fine avec A J = - 1 . A 9,2eV, le produit de la voie endothermique,est diffust h un angle bien defini, ce qui suggkre unc interaction A courte portCe choisissant un parametre d'impact particulier. A la plus haute des Cnergies utiliskes, la siparation de structure finie est aussi manifeste, aprts dCcon- volution des donnCes. L'angle de diffusion est ccpendant rdduit h unc valcur presquc nulle correspondant h des trajectoires presque reetilignes pour les deux voies, A cettc Cnergie. La population des deux voies est en accord gCnCral avec les thCories acceptCes pour 1'Cchange ion-atomc, mais les valeurs de I'Cnergic pour lcsquclles elle est observCe sont bien CloignCes des prkdictions (nous observons des sections efficaccs presque Cgales h dcs Cnergics infkricures par trois ordres de grandeurs h eelles qui sont prCdites par la thCorie).

Can. J. Phys. 65, 1077 (1987) [Traduit par la revue]

1. Introduction Charge-transfer reactions for simple ion-atom systems such

as the title reactions are well suited for investigating details of energy-conversion processes in single-collision chemical re- actions. The precision with which translational-energy changes are readily measured permits such changes to be interpreted as changes in specific internal quantum states as the reactants evolve into products. Several studies have used state-selected reactant ions to probe these processes in considerable detail (1-3). These studies have investigated total cross sections for these processes as a function of ion internal state and trans- lational energy. Fine-structure transitions in the analogous charge-transfer system Ar+(Ar, Ar)Ar+ have been investigated using crossed beams by McAfee et al., who utilized a mixed internal-state preparation of reactant ions Ar+(2P312) and Ar+('PII2) generated by electron impact (4). In the present paper, we report the study of differential cross sections for an ion-atom system using state-selected KI-+(~P,~,) ions.

The state-to-state analysis of charge transfer is based on simple expressions derived from the conservation of energy. The total energy, E,,,, is the sum of the relative translational energy of the reactants, T, and the internal energy, U.

[ l ] E,,, = T + U = TI + U1

The unprimed quantities refer to reactants; the primes, to prod- ucts. It therefore follows that

[2a] T' - T = -(U1 - U)

Measurement of translational-energy changes can, therefore, be used to investigate internal-energy changes in charge- transfer reactions ( 5 , 6). For low-energy collisions in the atomic ion - atom case considered here, AT is precisely correlated with the endothermic nature of the fine-structure reaction,

[31 Krt('P3,) + &('So) + &('SO) + Kr'('P112)

In addition to the intrinsic interest in the dynamics of elementary chemical reactions, we anticipate that the new in- formation presented here will be useful for understanding the dynamics of rare-gas dimers, which are present in rare-gas type lasers (7-9). Information on transition moments and potential-energy curves are important in the optimization of these lasers and in designing other rare~gas systems. Modifi- cation of present quantum-mechanical descriptions of simple

Printed in Canada 1 Imprim6 au Canada

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1078 CAN. J. PHYS. VOL. 65. 1987

> charge-transfer reactions is also necessary if correct models and predictions are to be made.

2. Experimental The Utah crossed-beam apparatus used in the present

study has been described elsewhere (10, 11). A high-pressure electron-impact plasma source was used to generate an ion beam of nearly pure ground-state Kr+(2P3/2). An ion-source pressure in the order of 1 Torr (1 Torr = 133 Pa) in com- bination with a trapping electron current in the order of

A resulted in a large number of energy-relaxing collisions before ion extraction. Many more ion-neutral collisions were required to relax the Kr+(2Pl12) initially formed by electron impact than actually occurred under these conditions in our ion source (12). We therefore think that the energy-relaxing mech- anism is primarily superelastic ion-electron collisions. The extracted ion current was typically in the order of lo-' A.

The mass-selected ion beam was then decelerated to the desired energy and crossed at 90" with a He-seeded supersonic neutral beam: The energy spread of the ion beam was 0.3 eV with an angular spread of less than lo, and the molecular-beam angular width was about 2". Laboratory angle and energy dis- tributions were taken at about 90" for the ~roduct ion. The data were then transformed into scattering contour diagrams using Cartesian probability functions (13, 14). Such probability functions were used to analyze relative cross sections for energy-exchange processes in the following relation:

where 0 is the center-of-mass scattering angle; Pc(u,, u2, u3) is the probability density of finding the product with a velocity defined by the Cartesian coordinates infinitesimally close to u u2, and u3; and P(Tr) is the probability density of the products being formed with relative translational energy Tr.

3. Results and discussion Because state-selected reactant ions are required to allow a

good definition of the internal-energy changes as measured by the translational-energy changes, the quantum-state purity of the ion beam is important in this study. This parameter is readily evaluated for krypton, because the krypton ion reacts rapidly with methane with J-specific reactions as shown by [5]-[7] (15, 16):

Most other studies of Kr+ symmetric charge transfers have not differentiated between the two ground states of Kr+ and treat the two ions as one (17, 18) or assume the statistical value of 2 : 1 for the ratio h+(2P3/2) : Kr+(2P,12) (19, 20).

The above reactions [5] - [7] are diagnostic for the reactant ion-beam composition, provided we assume the endothermic channel (7) is not reached in our experiments. By setting the bandpass of the energy analyzer and the observation angle to accept only those ions formed with negligible momentum ex- change, we can insure that we are observing products origi- nating only from reactions [5] and [6]. Figure 1 shows the resulting mass spectrum when Kr+ is extracted from the high- pressure source, as operated under the conditions cited in the Experimental section. As shown, the amount of CH: formed

FIG. 1. Mass spectrum of product ions from Kr+(*P,) + CH, showing that the major product is CH: resulting from reaction 5.

FIG. 2. Scattering contour diagram for the charge-transfer reaction Kr+(Kr,Kr)Kr+ at 19.9 eV collision energy. The crosses mark the center-of-mass (cm) velocity and the cm velocity of Kr prior to col- lision. The break in the line indicates that the velocity-vector dif- ference between the Kr neutral and the center of mass is not to scale. Contours define the probability densities of product velocities (in Cartesian coordinates) and demonstrate that a direct mechanism populates a resonant charge-transfer channel. The slight wing shows that more than the resonant channel is present but that it is masked by the resonant contribution.

from reaction [6] is less than 2% of the total ion product. We therefore estimate that the amount of the upper state, Kr+(2P112), in our reactant ion beam is about 2% of the total primary-ion intensity. Accordingly, the contribution of the upper state is neglected in subsequent discussion.

At the two collision energies investigated, scattering contour diagrams presented in Figs. 2 and 3 show that the resonant charge-transfer reaction

imparts very little momentum to the product. The product ions are moving with nearly the same velocity vectors as those of the neutral Kr beam prior to the collision. We therefore infer that a direct mechanism involving relatively large impact parameters is the appropriate model to describe this system.

The two-state model of Rapp and Francis (21) gives the probability of charge transfer in a:collision at a particular rela- tive velocity, u, and impact parameter, b, as

[9] P(b, u) = sin2(Jn(E, - E,) dxlhu)

where E, and E, are, respectively, the energies of the symmetric and antisymmetric states that describe the nonstationary+state (the state at collision) of the collision-intermediate Kr, (for Kr:, the spin-orbit interaction results in six potential-energy curves rather than two; this point is discussed later). Here E, - E, is the resultant component along the collision orbit, x, and depends only on the internuclear separation of Kr+ and Kr

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> ET AL. 1079

FIG. 3. Scattering contour diagram for the charge-transfer reaction Kr'(Kr,Kr)Kr' at 9.2 eV collision energy. The crosses mark the center-of-mass velocity and the cm velocity of Kr prior to collision. The break in the line indicates that the velocity-vector difference between the Kr neutral and the center of mass is not to scale. Contours define the probability densities of product velocities (in Cartesian coordinates) and demonstrate that a direct mechanism populates a resonant charge-transfer channel and that the slightly endoergic reaction 3 is active.

(which is equal to (x2 + b2)'I2). This model predicts a critical impact parameter of about 4 A for Kr' : Kr at 20 eV collision energy. At these impact parameters, the motion of the two particles is well approximated by linear trajectories. The model begins to break down at lower energies as curved trajectories become more important than rectilinear trajectories.

At such large impact parameters, minimal momentum is transferred between the collision partners, and their initial velocity vectors are not disturbed. Also in the resonant charge- transfer process, the electron involved in charge transfer cannot distinguish between the two ionic cores. The rapidly oscillating function, which describes the electron's motion, therefore results in two possible outcomes of the collision event, de- pending on the number of electron exchanges: a direct mech- anism (the initial ion departs as the ion) and charge transfer (the initial ion departs as the neutral). Our crossed-beam study only allows the detection of the charge-transfer product.

The collision energy available in the experiment illustrated in Fig. 2 is large enough to access excited states of Kr (such as Kr 5s[3/2]?), which then radiatively decay (22). Our study emphasized the dynamics of resonant and near-resonant charge- transfer reactions of Kr+ (Kr, Kr)Kr+, and these highly endo- thermic channels (AH is about 10 eV) leading to radiative states (with a threshold barrier of about 12.5 eV above the ground state) were not investigated. They would form products located much closer to the center of mass (cm) and were not detected in an angular scan near the cm; it was inferred that the cross section to generate these channels is much lower (in the order of 1% or less) than the cross section for resonant charge transfer.

Figure 3 shows clearly that an endoergic channel is open at the lower collision of 9.2 eV in addition to the resonant charge- transfer channel (reaction [8]). The concentric circles in the figure show the loci of velocity vectors corresponding to the resonant charge-transfer reaction [8] and the endothermic reaction [3].

Figure 4 analyzes the relative translational energy dis- tribution of the products resulting from the integration of the scattering diagram shown in Fig. 3 over the angle and energy

FIG. 4. Relative translational-energy distribution of products ex- pressed in terms of the translational exoergic energy observed for the reaction Kr'(Kr,Kr)Kr' at 9.2 eV collision energy. The correlation with U is shown with a superimposed scale for the J = 112 and 312 states of Kr'.

using [4]. As can be seen, reaction [3] has almost the same contribution to the total ion product as does the resonant channel, reaction [8], at this energy. When the relative cross section, ul12/u312, is computed by integrating each peak in Fig. 4, the ratio 1.05 is obtained. Within experimental error, this value implies equal contributions by both reactions to the overall cross section for Kr'(2P312) charge transfer.

As we have already noted in discussing the resonant case, charge transfer is mediated by the properties of the Kri inter- mediate in which the electron is exchanged between the fast and slow particles (lab frame). Our analysis has examined only the charge-transfer products with velocity vectors near the ini- tial neutral velocity space (the backscattered hemisphere in cm coordinates). A similar peak for the endothermic channel (3) is probably located in the forward-scattered hemisphere but is difficult to detect in the wings of the primary beam (which is lo5 times larger in intensity). No careful search has been made for this product channel.

Figure 2 also shows a wing of intensity corresponding to the fine-structure transition reaction [3]. However, the data require deconvolution to remove the dominant resonant charge-transfer product to identify this channel clearly. Because the resonance charge-transfer product involves no net energy or momentum change, the spatial and energy location of the product can easily be located by characterizing the neutral-beam velocity vectors. Accordingly, energy profiles of the neutral beam (ion- ized by an off-axis electron gun at the collision region) have been taken at various laboratory angles corresponding to the region about the neutral velocity vector on the scattering diagram. These profiles have then been normalized to the ob- served intensity maximum in Fig. 2 and subtracted from the observed reaction-product profiles at corresponding angles. The resultant profiles have been used to construct a probability contour diagram in the same manner as the original profiles were used to construct Fig. 2. Figure 5 shows the result of this deconvolution in which the resonant charge-transfer product, as represented by the neutral-beam profiles, has been removed by subtraction.

Translational-energy analysis of the resulting diagram shows that the endoergic product present in the wings of the dominant resonant process in Fig. 2 is the fine-structure transition re- action [3]. In contrast to Fig. 3, the angular separation from the resonant charge-transfer product is greatly reduced at higher collision energies (19.9 eV vs. 9.2 eV). The relative contri- bution to the overall charge-transfer reaction is also reduced.

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1080 CAN. J . PHYS. VOL. 65. 1087

FIG. 5. Scattering contour diagram for the fine-structure reaction channel present in the charge-transfer reaction Kr'(Kr,Kr)Kr' at 19.9 eV collision energy. The crosses mark the center-of-mass velocity and the cm velocity of Kr prior to collision. The break in the line indicates that the velocity-vector difference between the KI neutral and the center of mass is not to scale. Contours define the probability densities of product velocities (in Cartesian coordinates) and demonstrate that after removing the exactly resonant reaction 8 from Fig. 2, the fine-structure channel contributes to the overall cross section.

FIG. 6. Relative translational-energy distributions of the products expressed in terms of the translational exoergicity observed for two channels in the reaction Kr'(Kr,Kr)Kr+ at 19.9 eV collision energy. The solid curve shows the contribution of the resonant reaction 8 and the dashed line shows the contribution of the fine-structure reaction 3. The correlation with U is shown with a superposed scale for the J = 112 and 312 states of Kr+.

Figure 6 shows the analogous relative translational-energy distributions, P(T1), of the resonant and spin-change channels at 19.9 eV. The relative cross section, as defined previously, is estimated to be 0.4. From this we infer that at least one maximum in the relative cross section,

is located at an energy below 20 eV. The reduction in angular deflection shows that less angular momentum is transferred in the reaction at this energy, implying that the critical impact parameter is larger at 19.9 eV even though the probability for charge transfer at this impact parameter is reduced.

This result contrasts with the conclusions of both Campbell et dl. (22) and Johnson for this system (23). Campbell's experi- mental results do not show any effects of the fine-structure reaction at energies up to 2000 eV (lab). However, no angular information can be obtained with his instrument. and the ener-

getic information contained in the center-of-mass frame is "scrambled" in the laboratory frame, so extensive decon- volution would be required to see fine-structure transition events.

Johnson has calculated the cross sections for both the endo- thermic and exothermic fine-structure collisions and resonant charge-transfer collisions using the general time-dependent quantum-mechanics formulation of Nikitin (24), which uses atomic eigenfunction expansions and neglects momentum transfer. Six coupled equations for the C. and Il states, includ- ing spin-orbit effects as an energy defect, were solved both with and without rotational coupling, and resulting transition probabilities were integrated approximately. His calculations predicted that reaction [3] should have an observable threshold at about 800 eV collision energy and the maximum should not occur until almost 10 000 eV collision energy is reached (23). He further predicted that the excitation functions for resonant and fine-structure collisions should scale with the spin-orbit splitting energy. For Xe, the threshold and maximum cross sections should, therefore, occur at about 10 times the collision energies quoted for Kr; while for Ar, the collision energies should be much less.

There are experimental data for Ar supporting Johnson's theoretical predictions (3, 4). McAfee has observed angular fine structure in Ar scattering at collision energies between 100 to 200 eV in a crossed-beam experiment (4). For this system, Johnson predicts a threshold at about 3 eV and a maximum at about 20 eV with a slow falloff above 20eV (24). In McAfee's energy range, the predicted relative cross section for the fine- structure reaction is about 11% of the total cross section, while McAfee's results suggest about 16% (4).

Competition between resonant and fine-structure charge- transfer collisions have been carefully investigated in the elegant, crossed ion-neutral photoionization total cross sec- tion study by Liao et al. (3) in the energy range 1-4000 eV (lab). Their measured profiles for the kinetic-energy depen- dence of the cross section for the 'P3/, + 2P112 transition, analogous to reaction 3, fall between the two calculated curves of Johnson for the Ar+/Ar system computed with (higher absolute values) and without (lower absolute values) rotational coupling. All three curves (Johnson's two calculations plus Liao et al.'s experimental curves) have qualitatively the same shapes and exhibit the same threshold and maxima as a function of collision energy.

It appears from our work that the nice general correspon- dence between theory and experiment found for Ar+/Ar is not found for Kr+/Kr. It is, therefore, interesting to speculate that the low-energy channel observed in our work proceeds by a different mechanism than that considered in Johnson's theory (25). It would also be interesting to investigate Xe+/Xe col- lisions, because this system exhibits much larger spin-orbit splitting than the other rare gases.

The theoretical papers referenced above do not calculate the differential cross sections for the two reactions considered (re- actions [3] and [8]). The crossed-beam experiments of McAfee et al. (4) show that the two channels occur at different lab- oratory angles for Ar. Unlike the present study, however, their analysis does not resolve the product as a function of center- of-mass angles. Such an analysis shows that because the 2P112

product is scattered at a preferred angle of 8" at 9.2 eV, a shorter range interaction than that proposed for the resonant channel may be inferred. It has been suggested by Jones that a repulsive curve crossing coula allow reaction [3] to proceed

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HOWARD ET AL. 1081

(26). The lowest energy crossing would involve the II(1/2), curve of the Krg system for J equal to 112 and the I(1/2), curve for J equal to 312. Such a crossing occurs at about 6 eV collision energy (26, 27), which should correspond to the threshold for the J-transition fine structure. This is a possible explanation for the mechanism observed in the present study.

4. Conclusions In summary, the distribution of ions produced by the high-

pressure plasma ion source in the Utah crossed-beam machine has been tested using diagnostic reactions [5] and [6]. The reac- tant ion beam has been shown to contain at least 98% Kr+ (2~312). With this knowledge, state-resolved reactions using ground- state ions have been studied. The resonant charge-transfer reaction of Kr+(2~312) with Kr is well described by the rec- tilinear-orbit impact-parameter model of Rapp and Francis. Electronically endoergic reaction [3] is also present and con- tributes significantly to the overall reaction-especially at low energies. Such an opening of a J-transition channel is predicted theoretically to occur only at much higher collision energies. Curve crossing on the repulsive part of the spin-orbit coupled curves for Krg is suggested as a possible mechanism to ration- alize our results.

Acknowledgements This work was supported by the National Science Founda-

tion, Grant CHE 80-17794, and carried out at the University of Utah, Salt Lake City, UT 841 12.

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