STUDYING COLLISION AND REACTION DYNAMICS USING LIGHT SCATTERING

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STUDYING COLLISION AND REACTION DYNAMICS USING LIGHT SCATTERING

K. Burnett

To cite this version:

K. Burnett. STUDYING COLLISION AND REACTION DYNAMICS USING LIGHT SCATTER- ING. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-279-C1-286. �10.1051/jphyscol:1985128�.

�jpa-00224504�

JOURNAL _DE PHYSIQUE

Colloque CI, supplkment au nO1, Tome 46, janvier 1985 page Cl-279

STUDYING COLLISION AND REACTION DYNAMICS USING LIGHT SCATTERING

K. Burnett

Spectroscopy Group, BZackett Laboratory, InrperiaZ College, London SW7 2B2,U.K.

Resum6 - Les aspects spectroscopiques de la dynamique collisionnelle et rhactive sont presentgs. On pr6cise sur des exemples simples le type d'information que l'on peut extraire d'une 6tude par spectros- copie, photoabsorption et diffusion de photons.

Abstract - Collision and reaction dynamics are discussed from a spectroscopic point of view. The nature of the information one can obtain using spectroscopy, light absorption and

scattering, are discussed for simple examples.

Introduction

I want to d's u s some elementary spectroscopy of

collisions. What I mean by the term spectroscopy will become apparent from the subsequent discussion: A few hints at my meaning are in order here. We all know how to do spectroscpy of bound systems based on the traditional methods:

Born-Oppenheimer approximation, Franck-Condon Principle. I want to discuss the direct extension of these traditional techniques to systems where one or both of the levels participating in the transition are not bound. (Collision

induced absorption and photo-dissociation).

The classification of the free (unbound state) can proceed if the nature of the wave function does not vary rapidly

everywhere. In other words, we need there to be regions of adiabaticity where the quantum labels do not vary rapidly. For atom-atom collisions it is usually valid to consider coupling between adiabatic Born-Opp nheimer states occuring at well defined avoided crossings.' This means that the Franck-Condon Principle can be applied in many regions within a collision.

The spectroscopy one obtains thus produces R-dependent approximate labels.

Rigorous descriptions of this proc dure for a om atom collisi9;g have been given by Mies 5 , Julienne and de Vries and

k

George. This discussion will rely more on pictures than maths and I apologise for their naivety.

For atom-molecular scattering the problem is much more complex and the ideas I will discuss more speculative. In all of the examples we discuss the common theme is transition between adiabatic states followed by evolution to the asymptotic fragments that one observes.

The second part of the spectroscopic description is, therefore, the connection between the interacting adiabatic states and the asymptotic products. This can be c st into the Jost-Matrix description as Fano has emphasized.' The above ideas will be Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985128

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discussed using simple examples. I shall use elementary, well known, and perhaps naive, arguments. The examples have helped me to understand what one might learn from the new experiments one can perform using tunable lasers. Perhaps they will help others.

2. Atom-Atom Collisions: non-degenerate states (a) Free-Free transitions

In fig.1 we see the process of absorption from a ground molecular state to an excited molecular state, during a collision. Let us suppose that we have determined the ground state potential. The 'normal ' method^^^^^^ can be used.

Let us suppose we now do the 'ideal' spectroscopic experiment.

We send in atom-atom pairs with a given energy in the c. of m.

frame. The probability of absorption is, of course, proportional to the Franck-Condon factor

<E+ilO excited state - I E ground state+> = Oe

Here, I + > is the incoming state on the ground surface and I ->

is the outgoing state on the excited surface.

Let us suppose we measure the excitation as a function of incoming laser frequency. We know that the maximum

cross-section will occur when the point of excitation occurs to a turning point on the excited surface (fig.1). This is the Franck-Condon Principle (FCP) at work. We can, in this way, construct the excited state potential by finding this peak for all incoming E.

We could be more formal since we know V ( R ) we know the ground state wavefunction as a function of E. we could measure 0,

Fig. 1

Absorption During a Collision.

we can produce, in effect, a decomposition of the upper state wavefunction in terms of known ground state wavefunctions and

hence obtain the potential.

We also need to measure the angular distribution of the excitation produced. This is analogous to measuring the rotational spectrum sicnce g L / d P r ~ in the effective potential determines both these properties.

The above experiment is rather idealised and the usual

collision induced experiments use thermal distributions. The combination of the temperature dependence and the FCP can be combined to get the ground excited state potentials. Some ground state scattering data is still needed as input.

If the initial state is bound then the determination of the ground state potential proceeds via the usual ro-vibrational spectroscopy. We then proceed with the ideal

photo-dissociational experiment. Starting from a specific ro-vibrational state we measure the dissociation cross-section as a function of frequency. If we start with the ground state then the FCP implies that the maximum ill occur when the transition occurs to a turning point. 1J

Again, knowing V (R) we know the wavefunction of the bound state and hence ean predict Ve(R) Vg(R) + *aL

Fig. 2

Photodissociation of Diatomic Molecules.

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The analogous procedure to varying the incoming energy in the free bound case is varying the ground state excitation. We can view this again as building up the excited state from

successive overlaps with different bound states. The same information is also obtained from observing re-emission before dissociation. So for bound-free and free-free the FCP tells all.

3. Atom-Atom Collisions: Degenerate states

So what happens when there are several excited states e.g.

corresponding to different projections of the electronic angular momentum along the internucler axis. In the region where excitation occurs we shall suppose we have a ground

state and and excited states (fig.3). The first part of the method is the same we find Vg(R). In the second part of the experiment we shall find two peaks: one for - ;C and one for

z-

n

polarizations. We can still do it here as long as we know what atomic MJ states will be produced by an excited C ^{or a} /1

state.

Fig. 3

potentids

Absorption During a Collision:

x - x

The transition from molecular and atomic states can be viewed in this as as being due to adiabati rotation of the molecule until decoupling occurs at large R. 56

Now in this case it is easy to see that adiabatic tation depolarizes a z - s t a t e far more than a r) state. " ^{So when}

appreciable rotation occurs before decoupling states give far higher polarizations. This means the C a n d n s t a t e s are :easily distinquished.

In the case of photo-dissociati y9,ygry little rotation may occur be£ ore decoupling occurs. If that is so then we can discern from n simply from the angular distribution of excited atoms. It will be peaked along thel&ight polarization axis* for states ( -Lr for

n

Again in practical experiments we will not have such ease of inversion but the power of the technique eve for thermal distributions has already been demonstrated." In order for the method to work the transformation from molecular to atomic states should not be rapidly varying with energy. Actually we need discrimination not accuracy. Once we have labelled C or n we can measure the transformation from moleculr to atomic. Similarly, we need any rapid variations of coupling scheme with R to be localised. (Asymptotically it does not matter so much since we do not get localised absorption anyway). So a description of the transformation between different R's enables us to label continuum states.

4. Atom-Molecule collisions

(a). Photo-dissociation of Poly-atomics

We now consider the photo-dissociation of a linear tri-atomic.

The particle moving on the excited state now does not have a simple one-dimensional tur ng point and there is not a single absorption maximum. Pack

''

multidimensional F.C.P. Let's suppose the ground and excited states are as shown in Fig.4. There is a set of unstable periodic states tht stradle the ridge. For states with the correct energies of the periodic states their velocity

perpendicular ( L r in fig.4) to the ridge is very small. The motion is, therefore, adiabatic with respect to vibration along the ridge (11 in fig.4). So, close to the ridge we can

construct potential energy surfaces which are adiabatic to vibration along the ridge.

We should expect, therefore that the periodic trajectories will correspond, in the semi-classical sense, to wavefunctions with m a ~ i m 3 ~ o n the ridge with a quantization condition along the

ridge States with different amounts of vibrational

excitation will then have different tuning points. We should then expect a set of absorption peaks corresponding to

different amounts of vibrational excitation along the ridge.

Extra vibrational structure should be present if the adiabatic potentials have wells.** This extra structure in the

photo-dissociation may also be viewed as arising from

*1n thermal experiments where this cannot be used

depolarization by molecular rotation could be enh3bced by intense field trapping of the dissociating atoms.

** Such structure may also be2gf~fent in photoionization of atoms in intense magnetic fields.

JOURNAL DE _PHYSIQUE

Fig. 4

resonances in scattering on the excited surface. A method for constructing co-ordinates in which adiabati5ity arises

naturally has been given by Pollak & Child. Similar

features in dissociation cross-section~6can be discussed using the time-dependent approach of Heller. Structure in that approach arises from recurrences in wave packet propagation.

One can construct the absorption spectrum using any sensible set of conditions. Hyperspherical co-ordinates may be better2' since they have been shown to need fewer channels to describe the strongly interacting wavefunction in treatments of reactive scattering. This co-ordinate system is also advantageous for other reasons e.g. it can handle 3-body break-up efficiently. ^{2 8}

It has also been shown that non-9giabaticity is strongly localised on the potential ridge.

So given the existence of a region of adiabaticity we can obtain potentials. The position of the photo-dissociation peaks gives us the potential ridge. We can do more and find the shape i.e. the spatial distribution of the resonance states by using the F.C.P. We need to overlap excited ground states with the resonances. The final step will be to measure the

cross-section for producing different vibrational states of the dissociated molecules. This then gives us the transformation from the molecular complex to atomic states the half reaction.

We can in this way build up a complete picture of a reaction on the excited surface.

(b) Free-Free Transitions in Reactions

If we know the ground state of a reactive complex (what a big IF!) we could play the same games as above. But the problem of finding the ground state is an enormous task in itself. The infra-red absorption spectrum may offer some help in this regard but I certainly do not want to expose my very limited knowledge of how this could be done.

5. Discussion and Conclusion

I hope I have shown how some rather elementary ideas can be juxtaposed to give a useful approach to the "half-collision"

business. The touchstone as I see it is one type of adiabaticity or another along with the F.C.P.

Acknowledgements

I have benefited from many discussions with my colleagues: J.

Cooper, W.J. Alford, N. Andersen, U. Fano, P.S. Julienne, V.

Aquilanti and F.H. Mies.

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