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The effective-range theory taking into account the Coulomb interaction has been developed and applied to computing the nuclear vertex constants for a decay (fuse) A<->B + C and for relating the asymptotic normalization coefficients of the radial wave functions for a nucleus A. We study the 3He s-wave bound state and the resonant s-wave states of 2He, 3He, 8Be,the p-wave states of 5He and 5Li, and the d-wave state of 8Be. Experimental phase shifts and pole positions are used as input data.