Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\mathrm{H}\mathrm{e}$ and the resonant states of the nuclei ${}^2$He and ${}^3$He in the s-wave, and those of ${}^5\mathrm{H}\mathrm{e}$ and ${}^5\mathrm{L}\mathrm{i}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.