Use of theKMatrix in Nuclear Reaction Theories

Abstract

In the original article the formal solution to the integral equation for the reactance operator $K$ was found and shown to differ from the generally accepted form. The incorrect expression for $K$ has been used in projection-operator formalisms for nuclear reactions by Bloch and Gillet (BG) and by MacDonald and Mekjian (MM). We applied these scattering formalisms to a simple soluble model. The discrepancy arising from the use of the incorrect $K$ was found to have no observable consequences for the MM treatment. We did not succeed in finding an explicit expression for the discrepancy between the BG prediction and the exact result for the simple scattering model. In this addendum the discrepancy of the BG formalism for the simple scattering model is found. This discrepancy is found to be nonzero at all energies. In the neighborhood of certain energies for zero-range potential scattering, the BG discrepancy can become very large. In addition, by examining the explicit expression for the $K$ matrix for zero-range potential scattering, we are able to provide a simple interpretation of the difference between the correct form of the reactance operator and the generally accepted incorrect form.