The excitation of atomic gases by short high-intensity optical pulses leads to significant electron ionization. In dilute systems, the generated distribution of ionized electrons is highly anisotropic, reflecting the quantum mechanical properties of the atomic states involved in the many photon transitions. For higher atomic densities, the Coulomb interaction in the electron-ion system leads to the development of an isotropic electron plasma. To study the ionization process in the presence of the many-body interaction, a fully microscopic model is developed that combines a generalized version of the optical Bloch equations describing the optical excitation with a microscopic description of the many-body interactions. The numerical evaluation shows that the Coulomb interaction significantly modifies the distribution anisotropy already during the excitation process. Whereas a reduced anisotropy is still present after the pulse for low ionization degrees and pressures, it is completely absent for elevated gas densities. An ionization degree is predicted that is significantly enhanced by the many-body interactions.