Two-Channel Effective Range Expansion and Bound-State Properties

The S matrix and the f matrix amplitudes are considered for the case of two coupled elastic scattering channels, which differ in values of orbital angular momenta. Matrix elements of S and f matrices are parametrized in terms of scattering phases ?? _i (i?=?1, 2) and a mixing parameter ${\epsilon}$ and are expressed in terms of matrix elements c _ij = (K ^?1) _ij where K is the reaction K matrix. Quantities ${g_{ij}(k)=k^{l_i+l_j+1}c_{ij}(k)}$ are expanded in powers of k ², k being the relative momentum of colliding particles B and C. Then functions g _ij (k) and c _ij (k) are continued analytically to the pole of amplitudes f _ij corresponding to the bound state A of colliding particles. This procedure allows to get the position of the pole as well as the residues of amplitudes f _ij at that pole which are related directly to vertex constants and asymptotic normalization coefficients corresponding to the vertex A ?? B?+?C.