Sensitivity study for the $^{12}$C($\alpha,\gamma$)$^{16}$O astrophysical reaction rate

The $^{12}$C($\alpha,\gamma$)$^{16}$O reaction has a key role in nuclear astrophysics. A multilevel R-matrix analysis was used to make extrapolations of the astrophysical S factor for this reaction to the stellar energy of 300 keV. The statistical precision of the S-factor extrapolation was determined by performing multiple fits to existing randomized E1 and E2 ground state data, according to experimental errors. The impact of a future proposed experiment at Jefferson Laboratory (JLab) was assessed within this framework. The proposed JLab experiment will make use of a high-intensity low-energy bremsstrahlung beam that impinges on an oxygen-rich single-fluid bubble chamber in order to measure the total cross section for the inverse $^{16}$O($\gamma,\alpha$)$^{12}$C reaction. The importance of low energy data as well as high precision data was investigated.