  We implement a full nonlinear optimization method to fit continuum states
with complex Gaussians. The application to a set of regular scattering Coulomb
functions allows us to validate the numerical feasibility, to explore the range
of convergence of the approach, and to demonstrate the relative superiority of
complex over real Gaussian expansions. We then consider the photoionization of
atomic hydrogen, and ionization by electron impact in the first Born
approximation, for which the closed form cross sections serve as a solid
benchmark. Using the proposed complex Gaussian representation of the continuum
combined with a real Gaussian expansion for the initial bound state, all
necessary matrix elements within a partial wave approach become analytical. The
successful numerical comparison illustrates that the proposed all-Gaussian
approach works efficiently for ionization processes of one-center targets.
