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

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