Complex scaling in the description of nuclear resonances

A powerful approximation method based on the separable expansion of the potential has been used to solve the Schr\"odinger equation for a complex rotated Hamiltonian with nuclear short-ranged and nuclear short-ranged plus Coulomb potentials. It is shown that for potentials analytic in a proper domain of the complex r plane (e.g., the Woods-Saxon potential up to its first pole) solving the rotated Schr\"odinger equation on the real harmonic oscillator wave function basis is equivalent to solving the original equation on the complex harmonic oscillator wave function basis. For nonanalytic potentials (e.g., the nuclear charged-sphere Coulomb potential which is discontinuous in the complex r plane) the equivalence does not hold and it is the latter version that gives the correct solution. It is demonstrated that the method leads to an accurate determination of the resonance energy and (for not very broad resonances) of the wave function as well.