Abstract
The cross sections for meson-exchange reactions induced by pions are calculated with a method which assumes that, for high angular momentum or high impact parameter b, the Born approximation is valid and that for small impact parameter b the reaction amplitude vanishes. For treating intermediate values b we introduce a step-function η( b) which goes from zero to one at b∼ R within an interval d. Both R and d are slowly varying functions of s, which are assumed to be the same for all pion-induced reactions. The expressions for the Born approximation are completely determined by the coupling constants of the exchange particles with the reaction partners. For reactions in which the coupling constants are given, the only unknown input are the values of R and d. The latter ones are determined by fitting the pion charge-exchange reaction at several energies. The main features of many other pion-exchange reactions are then well reproduced by this method.
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