  We report on a study of electric resistivity and magnetic susceptibility
measurements in electron irradiated SrTi$_{0.987}$Nb$_{0.013}$O$_3$ single
crystals. Point-like defects, induced by electron irradiation, lead to an
almost threefold enhancement of the residual resistivity, but barely affect the
superconducting critical temperature ($T_c$). The pertinence of Anderson's
theorem provides strong evidence for a s-wave superconducting order parameter.
Stronger scattering leads to a reduction of the effective coherence length
($\xi$) and the deduced coherence length in the clean limit ($\xi_0$) is around
the BCS coherence length ($\xi_{BCS}$). Combined with thermal conductivity data
pointing to multiple nodeless gaps, the current results identify optimally
doped SrTi$_{1-x}$Nb$_x$O$_3$ as a multi-band s-wave superconductor.
