Measurements of the $^{16}$C + $^{12}$C and $^{16}$C + $^{13}$C Total Fusion Cross Sections with Implications for Astrophysics*

X-ray superbursts are powered by runaway thermonuclear burning deep inside of a neutron star, where the pycnonuclear fusion of neutron-rich isotopes may be an important heat source. We measured the total fusion cross sections of $^{16}$C + $^{12}$C and $^{16}$C + $^{13}$C for E$_{C.M.}$ = 8 - 22 MeV. The experiment was conducted using the active-target MUlti-Sampling Ionization Chamber (MUSIC) detector at the Argonne Tandem LINAC Accelerator System (ATLAS) facility at Argonne National Lab using a radioactive $^{16}$C beam. The measured cross sections show good agreement with theoretical models. While studies indicate that $^{16}$C has a larger mean radius than $^{15}$C, the $^{16}$C + $^{12, 13}$C cross sections are measured to be smaller than the $^{15}$C + $^{12}$C cross section. This indicates that an enhanced s-wave tail of the $^{15}$C wave function might be increasing the $^{15}$C fusion cross section or that neutron pairing effects in $^{16}$C may reduce the $^{16}$C cross sections.