Allowing for Coulomb effects in the effective range expansion for two coupled channels

A Coulomb-modified matrix of scattering amplitudes (an (F)\tilde]\tilde F matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital angular momenta (l ₁ and l ₂ = l ₁ + 2). Matrix elements of the (F)\tilde]\tilde F matrix are expressed in terms of the matrix elements of a (K)\tilde] ^{- 1}\tilde K^{ - 1} matrix inverse to a modified reaction K matrix. The elements of the (K)\tilde] ^{- 1}\tilde K^{ - 1} matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic normalization coefficients are expressed.