Taming the Yukawa potential singularity: Improved evaluation of bound states and resonance energies

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using the Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and construct a video showing how bound states cross over into resonance states by varying the potential parameters.