Inversion of experimental data to calculate the potential function RKR

Inversion of experimental data to calculate the potential function (RKR) 

The required form of the potential function Vj(R) for a diatomic molecule has already been given in equation (6.358). It can be seen that it is a function of both R and J. Let us consider the integral 

a knowledge of the derivatives of X with respect to E and J will allow us to determine the turning points at energy E. 

The experimental input into the RKR calculation comes from the vibrational energy levels G(v) and the rotational constants for each level B(v). If it is possible to define the integral X(E,J) in terms of G(v) and B(v), we can use equations (6.390) and (6.392) to determine Toffs ). The link is provided by the semi-classical quantisation condition, which has a form very similar to that of equation (6.389)  

The Abelian transformation is carried out at this point. After a certain amount of work (see, for example, Zare [92] or Miller [93]), the variable R in the integral (6.383) can be replaced by v, which we recall is continuous in the semi-classical world  

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