Use of the Projection-Operator Method in Nuclear Reaction Theory
Open Access
- 20 February 1968
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 166 (4), 1036-1044
- https://doi.org/10.1103/physrev.166.1036
Abstract
Feshbach has shown how the introduction of the projection operator onto the bound states of a system of nucleons can facilitate the calculation of the transition amplitude for a nuclear scattering reaction. Feshbach's method is based on the relationship of the transition amplitude to the matrix. In this paper we show how the projection-operator method can be applied to the generalized -matrix expression for the transition amplitude. In order to test the validity of the approximations customarily employed in applications of the projection-operator formalism, we have applied the method to a simple soluble model. We find that the method works quite well provided that all second-order terms are retained. The generalized -matrix method is found to work better than the -matrix method, but the -matrix method depends sensitively on the choice of the value of the boundary radius.
Keywords
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