New approach to determining radiative capture reaction rates at astrophysical energies

Abstract

Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty ($\ensuremath{\approx}100%$) in the measured rate of the $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\gamma})^{16}\mathrm{O}$ reaction is the largest source of uncertainty in any stellar evolution model. With development of high-current energy-recovery linear accelerators (ERLs) and high-density gas targets, measurement of the $^{16}\mathrm{O}(e,{e}^{\ensuremath{'}}\ensuremath{\alpha})^{12}\mathrm{C}$ reaction close to threshold using detailed balance allows a new approach to determine the $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\gamma})^{16}\mathrm{O}$ reaction rate with significantly increased precision ($<20%$). We present the formalism to relate photo- and electrodisintegration reactions and consider the design of an optimal experiment to deliver increased precision. Once the new ERLs come online, an experiment to validate the approach we propose should be carried out. This approach has broad applicability to radiative capture reactions in astrophysics.