Investigation of the one-neutron transfer in ${}^{13}$C + ${}^{28}$Si at E${}_{lab}$ = 30 and 34 MeV

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: $\mathit{\text{psdmod}}$ for the two-neutron transfer, and $\mathit{\text{psdmwkpn}}$ 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 $\mathit{\text{psdmod}}$ and $\mathit{\text{psdmwkpn}}$ shell model interactions. Results: The spectroscopic amplitudes from the $\mathit{\text{psdmod}}$ 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 $\mathit{\text{psdmod}}$.