For some potentials, such as the Hulthen and Yukawa potentials, the number
of possible bound states depend on an internal potential parameter. Even if
the parameters are chosen Such that no bound state exists, resonances occu
r after coupling these systems to the continuum, e.g., by an additional ext
ernal electric field. We will discuss those resonances which have no bound
predecessor. The computations are based on complex coordinate rotations and
finite elements.