Measuring ^24,26Mg + ²⁰Ne Fusion Cross Sections at Low Energies for Applications in Pycnonuclear Burning in Acccreting Neutron Stars

Pycnonuclear burning is a density driven fusion reaction that is predicted to be an important source of crustal heating in accreting neutron stars. The isotopes predicted to be significant contributors to pycnonuclear burning rates are in the A = 30 mass region that includes, but is not limited to the fusion between Mg and Ne isotopes. However, there is a lack of experimental data in both the neutron-rich and the stable mass regions at low energies for these isotopes, and as a result cross-sections and astrophysical S-factors are unconstrained across different models spanning orders of magnitude at the relevant energies for pycnonuclear burning, near 0 MeV. To better understand neutron rich cross-sections for these isotopes, preliminary experiments focusing on the stable mass region between ^{24, 26}Mg + ²⁰Ne have been conducted at the Nuclear Science Lab of the University of Notre Dame, using the FN Tandem Accelerator and the ND-Cube, an active-target detector. Different analysis techniques using Monte Carlo simulations and total least-squares fitting in combination with the Hough transform performed on these preliminary experiments will be presented in this work along with the development of a gas recirculation system for the use of recycling isotopically enriched ²⁰Ne gas. The measurement of fusion cross sections for ^{24, 26}Mg + ²⁰Ne, will be a first step in constraining the S factors for the neutron rich mass regions relevant for pycnonuclear reactions.