Impact of $^{16}$O($e,e'\alpha$)$^{12}$C and $^{16}$O($\gamma,\alpha$)$^{12}$C measurements on the $^{12}$C($\alpha,\gamma$)$^{16}$O astrophysical reaction rate*

The $^{12}$C($\alpha,\gamma$)$^{16}$O reaction, an important component of stellar helium burning, plays a key role in nuclear astrophysics. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a major goal for the field. In this work, we study the role of potential new measurements of the inverse reactions, $^{16}$O($e,e'\alpha$)$^{12}$C and $^{16}$O($\gamma,\alpha$)$^{12}$C, in reducing the overall uncertainty. A multilevel $R$-matrix analysis is 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 is determined by performing multiple fits to existing $E1$ and $E2$ ground state capture data, including the impact of possible future measurements of the $^{16}$O($e,e'\alpha$)$^{12}$C and $^{16}$O($\gamma,\alpha$)$^{12}$C reactions. In particular, we consider a proposed MIT experiment that will make use of a high-intensity low-energy electron beam that impinges on a windowless oxygen gas target and a proposed Jefferson Lab experiment that will make use of bremsstrahlung and a bubble chamber in order to measure the total cross section for the inverse reaction.