OVERLAPPING RESONANCES AND S-MATRIX UNITARITY

If two overlapping resonances of the same spin and parity, both coupled to C open channels, are superimposed on an energy-independent background, unitarity imposes 2(C + 1) constraints on their S-matrix residues (i.e., partial widths and phases). These constraints are worked out explicitly for the general case of a nondiagonal background matrix (direct reactions present), and compared with the simpler Breit-Wigner constraints which obtain when the resonances are non-overlapping and the background is elastic. The phase angles of the two resonances are found to be related in an especially simple manner when the background is elastic. The case of T-violating interactions is considered briefly in Section VI. © 1969.