The random phase approximation formulation of the many-body Green function formalism is applied to inelastic transitions, in e+-atom scattering. Explicit numerical calculations are performed for excitation to the n=2 and n=3 manifolds of an He target. Theoretical results for excitation to the 21P state are found to be in very good agreement with available experimental values of the literature, generally attributed to excitation of the 21S level of He. It is further pointed out that the cross section for excitation of the 31P level is, generally, bigger than that leading to the 21S state and, possibly, within reach of present experimental sensitivity.