  Background: Neutron transfer measurements for the $^{18}$O + $^{28}$Si system
have shown that the experimental one-neutron and two-neutron transfer cross
sections are well reproduced with spectroscopic amplitudes from two different
shell model interactions for the Si isotopes: \textit{psdmod} for the
two-neutron transfer, and \textit{psdmwkpn} for the one-neutron transfer.
  Purpose: The origin of this ambiguity can be related to a more complex
mechanism in the one-neutron transfer that requires the unpairing of neutrons
prior to its transfer in the ($^{18}$O,$^{17}$O) reaction. Studying a nucleus
where this characteristic is absent ($^{13}$C) should help to elucidate this
question.
  Method: One-neutron transfer cross sections were measured for the $^{13}$C +
$^{28}$Si at E$_{lab}$ = 30, and 34 MeV, and compared with coupled reaction
channel calculations using spectroscopic amplitudes derived from the
\textit{psdmod} and \textit{psdmwkpn} shell model interactions.
  Results: The spectroscopic amplitudes from the \textit{psdmod} interaction
for the relevant states in $^{29}$Si provide a good description of the
experimental data and the corresponding values agree with previous estimates
obtained from the (d,p) reaction.
  Conclusions: The experimental data for the one-neutron transfer to $^{28}$Si
induced by ($^{13}$C,$^{12}$C) reaction is well reproduced using spectroscopic
amplitudes from the \textit{psdmod}.
