Abstract In an earlier source theory investigation it was shown that the vacuum polarization of a massive gauge field is finite, provided that the conservation of current is imposed everywhere, including the interior of the sources. It is shown in the present paper that radiative corrections to a vertex function (two-particle production by an external source) are also finite if the same requirement about current conservation is imposed. In other words one-loop corrections turn out to be finite in both calculations. The cancellations leading to convergence may be understood in terms of Ward identities. The three form factors that appear are not only shown to be finite but are also explicity found.