Transition Operator for Matrix Potentials: An Application to the Pion-Nucleon Interaction

Abstract

The transition operator corresponding to a separable nonlocal and of a matrix-type potential is studied theoretically. It is shown that the transition operator possesses the same $\overrightarrow{\mathrm{r}}$ (or $\overrightarrow{\mathrm{k}}$) dependence and properties of separability and nonlocality as the potential and that it is also of a matrix type. This transition operator is then explicitly calculated. A numerical application is made to the simple but physically important case of the low-energy pion-nucleon interaction. The behavior of the transition operator coefficients versus the incident energy are discussed in detail for $S$, $P$, and $D$ waves.