On the non-invariance of distributions of reaction matrix parameters under changes in boundary conditions

Abstract

Contrary to current opinion, the statistical distributions of level spacings and reduced widths when applied to the reaction matrix, are not invariant under changes in the boundary condition matrix or the matching radius. General arguments are given, together with specific examples which violate the invariance requirements. We conclude that it is the parameters of the collision matrix which should be analysed and considered as the invariant parameters.