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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 may be the parameters of the collision matrix which should be analysed and considered as the invariant parameters. It is shown that if, for a specific set of boundary conditions, the distributions of level spacings and reduced widths are uncorrelated, then correlations between the level spacings and widths must exist when different boundary conditions are used.

On the Non-invariance of Distributions of Reaction Matrix Parameters Under Changes in Boundary Conditions