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This dissertation work is a study of positronium formation for positron-hydrogen and positron-helium collisions in the Ore gap (the energy region between the threshold for ground-state positronium formation and the first excitation level of the target atom) using variational K-matrices. We have fitted the K-matrices using multichannel effective range theories and using polynomials. Using the variational K-matrices and their fits, we have located zeros in the positronium-formation scattering amplitude and corresponding deep minima in the positronium-formation differential cross section. The zeros are related to the vortices in the extended velocity field associated with the positronium-formation scattering amplitude. For positron-hydrogen collisions, we have found two zeros in the positronium-formation scattering amplitude, and corresponding deep minima in the positronium-formation differential cross section, while we have obtained a zero in the positronium-formation scattering amplitude for positron-helium collisions. We have connected the zeros in the positronium-formation scattering amplitude to vortices in the extended velocity fields. Our work shows that vortices can occur for charge exchange in atomic collisions.