A test of factorization methods in coupled channel reaction theory

Factorization methods used in shell-model approaches to nuclear reactions provide a good starting point for perturbative treatments of direct coupling. General algebraic equations are given for zero and higher orders. Problems of convergence of the Born series are tested with a soluble model. It is shown that the zero-order approximation is quite good. First- and second-order corrections are calculated and exhibit a rapid convergence. The influence of parameters entering in factorization formulae is discussed.