Atom-diatom scattering

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

Schinke, R. and Bowman, J.M. (1983). Rotational rainbows in atom-diatom scattering, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin). 

Smith, N. (1986). On the use of action-angle variables for direct solution of classical nonreactive 3D (Di) atom-diatom scattering problems, J. Chem. Phys. 85, 1987-1995. 

The coordinate system used in the close-coupling method is the space-fixed frame. For simplicity we consider the atom-diatom scattering. The wave function iM(.R,r,R) for an atom-rigid rotor system corresponding to the total energy E, total angular momentum J, and its projection M on the space-fixed z axis can be written as an expansion,... 

The particular sets of channel functions needed are different for each type of scattering problem, and it would be quite impossible to enumerate all the possibilities, so just two relatively simple examples will be given here atom-diatom scattering and collisions of metastable helium atoms. 

Forrey, R.C., Balakrishnan, N., Kharchenko, V., and Dalgarno, A., Feshbach resonances in ultracold atom-diatom scattering, Phys. Rev. A, 58, R2645, 1998. 

Magill, P.D., Stewart, B., Smith, N., and Pritchard, D.E., Dynamics of quasiresonant vibration-rotation transfer in atom-diatom scattering, Pliys. Rev. Lett, 60,1943,1988. 

Nielsen, E., Suno, H., and Esry, B.D., Efimov resonances in atom-diatom scattering,... 

In an lOS approach the application of both the energy sudden and the centrifugal sudden" decoupling scheme reduces the exact Schroedinger equation for the atom-diatom scattering into a set of fixed angle of approach (7) two mathematical dimension ones. In the Body Fixed formulation these equations read as... 

Contents J.M.Bowman Introduction. - D.Secrest Inelastic Vibrational and Rotational Quantum Collisions. -G. C.Schatz Quasiclassical Trajectory Studies of State to State Collisional Energy Transfer in Polyatomic Molecules. - R. Schinke, J. M. Bowman Rotational Rainbows in Atom-Diatom Scattering. - M.Baer Quantum Mechanical Treatment of Electronic Transitions in Atom-Molecule Collisions. - Subject Index. 

Note that I and K are diagonal matrices, and we interpret the Im indices of U lmlomo r) as final state indices and Zq o as initial state indices. In addition to the regularity condition at r = 0 (which for typical potentials in atom-diatom scattering becomes the condition that U lmlomo 0) = 0), we want to impose the asymptotic condition... 

As is usually done in atom-diatom scattering theory [263-266], we expand the final-state wavefunction in terms of diatomic basis functions. We choose these functions to be harmonic oscillator rigid rotor functions... 

Equation 7.94 are identical to that that arises in the atom-diatomic scattering problem. They are a set of coupled differential equations. Each equation, or channel, is labeled by the set of quantum numbers (nl). The solution of these equations with the appropriate boundary conditions... 

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