Plane-Wave Matrix Approach to Direct Reactions

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Abstract
A new method based on plane-wave representations is developed and applied to the theory of direct reactions. The coefficients of the plane-wave expansions of propagators are determined either by the requirement that they fit the scattering matrix for an auxiliary potential both on and off the momentum shell or by the use of an effective unit operator. Such expansions lead to the reduction of typical direct reaction problems to simple matrix algebra, the basic matrices being either plane-wave matrices or auxiliary potential matrices. Particular attention is given here to finite-range distorted-wave matrix elements and coupled-channels theory, where the possible advantages of the present approach can be understood even at a formal level.