Hyperspherical coordinate three-atom case

In the three-atom case we introduce the hyperspherical coordinates the hyperradius p and the two hyperangles 0 and Euler angles a, (3, and 7 giving the orientation of the triangle in space. The connection to ordinary Jacobi coordinates is obtained through the equations... 

Hyperspherical coordinates have the properties that q motion is always bound since q = 0 and q = P correspond to cases where two of the three atoms are on top of one another, yielding a very repulsive potential. Also, p —> 0 is a repulsive part of the potential, while large p takes us to the reagent and product valleys. 

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