PHYSICAL REVIEW A DECEMBER 1998VOLUME 58, NUMBER 6

Variation of photofragment angular distributions near the isolated Lorentzian resonances:Influence of the continuum-continuum interaction

Sungyul LeeDepartment of Chemistry, Kyunghee University, Kyungki-do 449-701, Korea

~Received 14 January 1998!

The variation of the product angular distributions near isolated Lorentzian resonances is theoretically ana-lyzed. We show that interactions between the asymptotically degenerate dissociative states can give a mono-tonic variation of the anisotropy parameters of O(3Pj , j 50,1,2) with different slopes near isolated Lorentzianresonance in the predissociation of the OH molecule. The anisotropy parameters are shown to change near theresonance even in the simplest situation where the predissociation occurs through only one dissociative state,noninteracting to the first order with other asymptotically degenerate states. This finding is attributed tosecond- and higher-order interactions.@S1050-2947~98!09509-2#

PACS number~s!: 33.80.Gj

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I. INTRODUCTION

The dynamics of predissociation is very different from tdirect ~off-resonance! dissociation processes in many rspects. In direct dissociations dynamic observables sucthe product branching ratios or angular distributions rapiapproach diabatic limit values@1# at energies well above thdissociation threshold. An interesting dynamics is expecto be observed only at near-threshold energies as a coquence of the influence of nonadiabatic interactions amthe asymptotically degenerate states at large internucleartances called the recoupling region. The measurement ofnamic properties at intermediate energies easily providesformation on the symmetry of the excitation process anddissociation mechanism@1#. On the other hand, very interesting dynamics exist both at near-threshold energies anintermediate energies in predissociation processes. Themiliar occurrence of resonance is a typical dynamic conquence of predissociation at intermediate energies, whiccaused by the interactions between bound~gateway! statesand the dissociation continuua.

Dynamics in the vicinity of isolated Lorentzian resonanmay look intuitively simple. Indeed, we have shown@2# thatthe product branching ratios do not change as functionthe energy across the symmetric~Lorentzian! resonancesThis observation simply stems from the fact that for Lorezian resonances the partial cross sections to photoprodexhibit resonances whose linewidths and positions are idtical to those of the total cross section. However, recentperimental and theoretical studies indicate that the dynamnear the simplest~isolated and Lorentzian! type of reso-nances may not be simple at all, as a consequence ointeractions among dissociative states. For example, thinteractions were predicted@3# to affect the line shape oasymmetric resonances. The very interesting observationLiyanageet al. @4# on the very diverse~adiabatic, diabatic,and intermediate! patterns~depending on the nature of thgateway state! of the branching ratios of the Cl-atom finestructure states produced in HCl predissociation were pposed@5# to arise from the interactions among dissociatstates carrying the quantum flux in the photodissociation p

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cesses. These type of interactions were also shown to athe magnitude of the molecular phase@6# in (v1 ,v3) coher-ent control.

While interactions between discrete and continuum staare well known to be the origin of the phenomena of predsociation and autoionization@7#, the effects of the couplingbetween dissociative states~when there exists more than ondissociative states carrying the quantum flux! have rarelybeen treated in indirect dissociation processes. In Fano’s@8#classic treatment, for example, continuum states weresumed to be ‘‘prediagonalized’’ before interacting with dicrete states. When more than one kind of photofragmentbe produced from the predissociation process, several BOppenheimer states may correspond to these products,the nonadiabatic coupling between the dissociative electrostates may significantly affect the dynamics@1#. Consideringthat the vector properties of photodissociation are more ssitive indicators@1# of the dynamics than the scalar propeties, it will be very interesting to examine how they would baffected by the interaction among the asymptotically degerate dissociative states in the vicinity of resonance. Tmost fundamental question would be whether the vecproperties would remain constant near isolated Lorentzresonances like the scalar properties~product branching ra-tios! treated earlier@2,3#.

We address this important question in the present woWe show that the anisotropy parameters may exhibit anificant variation near isolated Lorentzian resonances evethe absence of quantum interference between direct anddirect dissociation pathways. This finding is attributed toteractions among the asymptotically degenerate dissociastates. Eliminating these asymptotic couplings gives an idtical variation of anisotropy parameters across the renances. However, we show that very gradual changespersist even in this simplest situation, where only a sinnoninteracting dissociative state is mostly responsible fordissociation.

II. THEORY AND COMPUTATIONAL METHODS

In this work we treat vector properties@1,9–15# of photo-fragments for predissociation processes of OH. The poten

4981 © 1998 The American Physical Society

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4982 PRA 58BRIEF REPORTS

curves of the electronic states included in the present calations are depicted in Fig. 1. Two oxygen terms, O(3P) andO(1D), are involved in the dynamic process consideredthis work. The ground stateX 2P and the repulsive state4S2, 2S2, and 4P correlate with the triplet oxygen O(3P),while the A 2S1, 2D, and 22P states correlate with thesinglet oxygen O(1D) term. TheA 2S1 state, correlatingwith O(1D), crosses with the repulsive states4S2, 2S2,and 4P that dissociate to O(3P). Predissociation of theA 2S1 state results from spin-orbit couplings betweenbound stateA 2S1 and the three repulsive states4S2, 2S2,and 4P. The optical transition considered in the presework is from the vibrationally ground level of theX 2P stateto the n859 level of the A 2S1 state, and the transitionenergy is about 6.3 eV.

The frame transformation matrices@1#, which connect theadiabatic Born-Oppenheimer~ABO! states to the corresponding atomic term limits, are the most important elemof the theory. Since the spin-orbit interactions betweenA 2S1 state and the4S2, 2S2, and 4P states do not vanishat infinite internuclear distances in the OH molecule,twotransformation matrices must be constructed, each of whdescribes the correlation between ABO states and the cosponding atomic term limits@O(3P) and O(1D)#, as shownin Ref. @2~a!#. It must be noted that the theory can includevariety of interactions~except the hyperfine couplings!, andthat it studies their effects on the photodissociation dynaics.

A continuum wave function~14314 matrix! of good par-ity is propagated using the renormalized Numerov meth@16#, and appropriate boundary conditions are imposed atend of the propagation. The transition amplitudes for disciation to a specific fine-structure component of the oxygatom is calculated by applying the golden rule. The pottials and the spin-orbit interactions employed in the presstudy were described in Ref.@2~a!#.

FIG. 1. Potential-energy curves of OH. The zero of energydefined as the baricenter of the energies of the triplet oxygen-afine-structure states.

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III. RESULTS

In the photodissociation of the OH molecule, quantuinterference between the direct dissociation pathway~via2S2! and the indirect pathway~via A 2S1! would giveasymmetric resonances@2,3# for then8>7 vibrational levelsof the A 2S1 state, since both the dissociative2S2 and theboundA 2S1 states are optically coupled with the grounX 2P state. In order to examine the product angular disbutions near isolated Lorentzian resonance, however,eliminate the effects of quantum interference by employvanishing transition dipole moments for transitions from tinitial X 2P state to the repulsive2S2 state. The resultingdynamics is the ‘‘pure’’ predissociation of theA 2S1 stateby coupling with the three repulsive4S2, 2S2, and 4Pstates. It should be noted that the latter three repulsive stcan interact with each other by spin-orbit and Coriolis intactions. The behavior of the scalar properties@2,3# ~totalcross section and product branching ratios! are simple in thissituation: The resonances are Lorentzian, and the probranching ratios are independent of energy near the rnance as depicted in Fig. 2. Figure 3 depicts the prodangular distributions for this purely indirect dissociation prcesses. It can be seen that the anisotropy parameters exsignificant variation, and that the slopes of the variationsdifferent from each other. The changes in the anisotropyrameters near isolated Lorentzian resonances are monotin contrast to the more drastic~exhibiting maxima! changesof the vector properties across the asymmetric resonashown in earlier works@9#.

In order to elucidate the underlying mechanism for thvery intriguing variation of the product angular distributioshown in Fig. 3, we investigate the situation where predisciation occurs by a single channel (4S2 state!. This isachieved by employing vanishing spin-orbit couplings btween A 2S1 and the other two repulsive2S2 and 4Pstates. The4S2 state, however, is still allowed to interacwith the other two repulsive2S2 and 4P states inasymptotic region in thissingle-channeldissociation. Theresulting anisotropy parameters are depicted in Fig. 4.

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FIG. 2. Partial cross sections~solid and dotted lines! and theproduct branching ratios~dashed lines! O(3Pj , j 50,1,2) neariso-lated Lorentzianresonance corresponding to theN52 andn859levels of theA 2S1 state. The initial ground state is theX 2P3/2

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angular distributions exhibit monotonic parallel variationear the resonance, with small differences in the valuethe anisotropy parameters in this situation. Thus, even insingle-channel dissociation, it seems that the nonadiab~spin-orbit and Coriolis! interactions between the4S2 state,which carries the quantum flux, and the2S2 and 4P states,can yield small differences in the anisotropy parametersO(3Pj , j 50,1,2).

Finally, we isolate the residual effects of the nonadiaba~spin-orbit and Coriolis! interactions by eliminating thedi-rect ~that is, first order! interactions among the dissociativstates (4S2, 2S2, and 4P), and obtain the anisotropy parameters depicted in Fig. 5. Now, all the differences in aisotropy parameters of O(3Pj , j 50,1,2) vanish, and they

FIG. 3. Angular distributions of O(3Pj , j 50,1,2) near theiso-lated Lorentzianresonance corresponding to theN52 andn859levels of theA 2S1 state. Direct dissociation via the2S2 state iseliminated. Predissociation occurs by the spin-orbit couplingtween theA 2S1 state and the three dissociative (4S2, 2S2, and4P! states. The initial ground state is theX 2P3/2

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FIG. 4. Angular distributions of O(3Pj , j 50,1,2) nearisolatedLorentzianresonance corresponding to theN52 andn859 levelsof the A 2S1 state. Direct dissociation via the2S2 state is elimi-nated. Predissociation is allowed to occur only by the spin-ocoupling between theA 2S1 and 4S2 states. Asymptotic couplingsbetween the three dissociative (4S2, 2S2, and 4P! states arere-tained. The initial ground state is theX 2P3/2

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show identical, very slow and monotonic variation near tresonance. Thus it clearly shows that the differences betwthe values of the anisotropy parameters of O(3Pj , j50,1,2) shown in Fig. 4 can be attributed to the directteractions among the asymptotically degenerate dissociastates. It is very intriguing that the anisotropy parametersexhibit a small degree of variation near the resonance evethis simplest situation. We emphasize that the predissotion occurs only by a single channel (4S2 state!, and that the4S2 state does not directly interact with other repulsistates in this hypothetical scheme. Thus it may seem thaother dissociation channels are ‘‘spectators’’ that wouldaffect the dynamics at all. However, it should be noted tthe 4S2 state can still interact with other repulsive statesan indirect ~second- and higher-order! way through theboundA 2S1 state near the crossing points. This latter tyof interaction between continuum states has rarely beencussed although, it was shown that the second- or higorder interactions between resonances~via continuum states!may affect the shape of asymmetric resonances in the presociation of Cs2 @17#. Although this effect is weak in thepresent case, it may yield a more rapid variation of phofragment angular distributions for systems with large copling between the gateway and the dissociative states,consequently with larger coupling among the dissociatstates.

IV. CONCLUSIONS

The calculations presented in this paper demonstratethe anisotropy parameters of the photofragments may exhsignificant variation acrossisolated Lorentzianresonancesdue to several different kinds of interactions betweendissociative states. The present findings clearly indicatethe interactions between the dissociative states in prediciation can significantly affect the vector properties of phtodissociation. It is shown that the interactions between dsociation channels can give different variation of tanisotropy parameters of O(3Pj , j 50,1,2). First-order in-teractions among the asymptotically degenerate statesalso shown to result in parallel variation of the anisotroparameters. Only eliminating these effects gave identicalisotropy parameters of O(3Pj , j 50,1,2) near the reso

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FIG. 5. Identical to Fig. 4, but with the asymptotic couplingbetween the three dissociative (4S2, 2S2, and4P! statesremoved.

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nance. Even in this simplest case, second- and higher-ointeractions among the repulsive states are shown to yievery gradual variation. Thus, as a limiting case of this veintriguing trend, it can be concluded that the product angudistributions are independent of energy near isolated Lorzian resonances, only when the predissociation occthrough a single, noninteracting~to any order! dissociativestate. It must also be pointed out that this limiting case w

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ACKNOWLEDGMENTS

This work was supported by the Korea Science and Enneering Foundation~Grant Nos. 971-0305-032-2 and 950501-13-3! and by Kyunghee University.

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