Resonances that originate from shadow poles of the scattering matrix in multiphoton processes

We have calculated solutions of the Floquet equations for the photodetachment of an electron bound in a one-dimensional Gaussian potential, by using a discrete basis set that includes continuum waves satisfying appropriate boundary conditions. These different solutions correspond to dominant poles or to shadow poles of the scattering matrix; they originate from bound-state solutions in the zero-field limit. We show that one of the ``extra'' resonances found in a previous complex-coordinate calculation [J. N. Bardsley, A. Sz\"oke, and M. J. Comella, J. Phys. B 21, 3899 (1988)] can be traced to a shadow pole of one of the bound states of the zero-field system. This example provides further evidence that shadow poles may play an unforeseen and possibly important role in multiphoton processes.