The calculation of reactions of the type (a,ab) using the plane-wave expansion method. I

A formalism for the evaluation of the transition matrix element for reactions of the type (a, ab) in the direct distorted-wave approximation is presented. The plane-wave expansion method is used to represent the optical model wave function for the entrance and exit channels. Because of the use of the plane-wave expansion method the completely off-the-energy-shell behaviour is easily demonstrated when distorted waves are used. The use of this expansion method also shows how difficult it is to extract the momentum dependence of the bound particle. The plane-wave expansion method is also applied to evaluate the transition matrix element for the effective t-operator DWTA approach. An approximation to the complete transition matrix element which seems equivalent to the DWTA but yet makes use of completely off-the-energy-shell matrix elements is also discussed. (Auth.)