Background phase shift in R-matrix theory

It has been shown recently by Cugnon in his generalized version of the R-matrix theory that the hard sphere phase shift used in the standard R-matrix theory is arbitrary and can be replaced, in general, by any other phase shift. In the present paper similar results have been derived in a straightforward manner, within the framework of the standard R-matrix theory, from the usual division of R matrix into a background matrix R0 plus a matrix R' containing pole terms and further constraining R0 to be a diagonal matrix. Thus Cugnon's theory and the standard R-matrix theory lead to algebraically equivalent results. An expression for the renormalization factor for the reduced width has also been given in terms of the new phase shift and the hard sphere phase shift