The quantum dynamics of three-dimensional reactive triatomic systems

2 The quantum dynamics of three-dimensional reactive triatomic systems 

Reactive-scattering formalism. We start out by choosing a system of coordinates that spans the 6-MD configuration space in which the motion of the triatomic system, after removal of the motion of the center of mass, takes place. Let Oxyz be a system of coordinates whose origin 0 is the center of mass of the system and whose axes are parallel to a system of laboratory-fixed axes (the laboratory frame ). The space-fixed (SF) coordinate system Oxyz is also called laboratory-fixed (LAB) system. The spherical polar coordinates of the scaled Ra in this system are Let us also define a 

In this presentation BF coordinates are chosen because they lead to simpler final expressions for the cross sections and to a simpler solution to the bifurcation problem. However, SF coordinates can also be used [121]. In terms of these BF coordinates, we wish to find the solutions of the Schrbdinger equation  

The sum in the right-hand side of (5.48) includes the closed-channel terms, for which E c jx E, for the reasons given following (5.3). 

In the present formulation the and A atoms have been considered 

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