Saddle points and critical trajectories associated with Coulomb plus short-range interactions with complex coupling
We consider the Schroedinger problem for a Coulomb plus short-range interaction with complex coupling parameter lambda, and we study the poles of the T operator for such a potential as functions of lambda. The trajectories of these poles in the complex plane are to a great extent determined by saddle points. Assuming that the short-range interaction is separable, we derive accurate asymptotic formulas for the infinite number of saddle points and for the associated critical values of lambda. In the particular case of the Coulomb plus Yamaguchi potential we obtain excellent agreement with previously published purely numerical results.