Measuring the Fusion Cross-Section of $^{\mathrm{18}}$O $+$ $^{\mathrm{12}}$C with Low-Intensity Beams near and below the Coulomb barrier

Fusion between neutron-rich light nuclei in the crust of an accreting neutron star has been proposed as a heat source that triggers an X-ray superburst. To explore the probability of such fusion events and examine their decay characteristics an experimental program using beams of neutron-rich light nuclei has been initiated. The evaporation residues (ERs) that result from the fusion of $^{\mathrm{18}}$O and $^{\mathrm{12}}$C nuclei, are directly measured and distinguished from unreacted beam particles on the basis of their energy and TOF. Using an experimental setup developed for the measurement with low-intensity (\textless 10$^{\mathrm{5}}$ ions/s) radioactive beams the fusion excitation function for $^{\mathrm{18}}$O$+^{\mathrm{12}}$C has been measured in the sub-barrier domain down to the 820 $\mu $b level. The measured fusion excitation function is compared to the prediction of a density constrained TDHF model. In addition to the measured cross-section, the measured ER angular distributions provide insight into the relative importance of the different de-excitation channels. These ER angular distributions are compared to the predictions of a statistical model code, EVAPOR revealing an under-prediction of the de-excitation channels associated with $\alpha $ emission. The de-excitation channels associated with proton emission following fusion will also be investigated.