To date, the possible effects of coupling to nucleon transfer reactions on the elastic scattering and fusion of weakly bound exotic nuclei have been largely neglected. The $^{15}\mathrm{C}$ nucleus presents a virtually unique opportunity to test these effects for an almost pure s${}_{1/2}$ single neutron halo nucleus. We present a series of coupled reaction channel calculations of the sub-barrier elastic scattering and single neutron transfer reactions, plus near-barrier excitation functions of the total fusion cross section for the $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, and $^{15}\mathrm{C}+^{208}\mathrm{Pb}$ systems. The method is validated against data for $^{12}\mathrm{C}$ and $^{13}\mathrm{C}+^{208}\mathrm{Pb}$. A large effect on the sub-barrier elastic scattering due to coupling to the ($^{15}\mathrm{C}$,$^{14}\mathrm{C}$) single neutron stripping reaction is found, ascribed to the 2s${}_{1/2}$ halo nature of the $^{15}\mathrm{C}$ ground state, in contrast to the two stable carbon isotopes. We also find a significant diminution of the above barrier total fusion cross section for $^{15}\mathrm{C}$ due to this coupling, again in contrast to the stable isotopes.
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