Formulae for calculating CAM pole positions and corresponding S-matrix residues are derived within the framework of the phase-integral method of Froman and Froman (1965, 1974). The formulae allow for the use of higher-order approximations with rigorous error estimates. The contributions from two and three isolated tuning points are considered, which allows applications in the study of rainbow and diffraction features as well as orbiting phenomena in elastic scattering processes.
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