Use of theKMatrix in Nuclear Reaction Theories

Two recent formulations of nuclear reaction theory have been based on the reactance operator $K$. Expressions given in these formulations for the reactance operator are identical in form with those that hold for the transition operator $T$, except that the scattering Green's function is replaced by the standing-wave Green's function. We have used formal scattering theory to find the formal solutions to the Lippmann-Schwinger equations for $K$ and $T$. We find that the solution for $K$ differs from that used in these two formulations. The discrepancy appears to be significant for one of the formulations but not for the other.