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

The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction, an important component of stellar helium burning, has a key role in nuclear astrophysics. It has direct impact on the evolution and final state of massive stars and also influences the elemental abundances resulting from nucleosynthesis in such stars. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a longstanding and important goal. In this work, we study the role of potential new measurements of the ${}^{16}\mathrm{O}(e,e^{\prime }\alpha ){}^{12}\mathrm{C}$ reaction in reducing the overall uncertainty. A multilevel $R$-matrix analysis is used to make extrapolations of the astrophysical $S$ factor for the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ 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 ${}^{16}\mathrm{O}(e,e^{\prime }\alpha ){}^{12}\mathrm{C}$ reaction. In particular, we consider a proposed MIT experiment that would make use of a high-intensity low-energy electron beam that impinges on a windowless oxygen gas target as a means to determine the total $E1$ and $E2$ cross sections for this reaction.

Figure 1

Projections of the astrophysical $S_{E1}$ factor to 300 keV for fits of existing $E1$ data (a) and for existing $E1$ plus proposed OSEEA data (b) for a channel radius of 5.43 fm. The blue dashed vertical lines indicate the projections for the fit to the original data, while the histograms represent the results of 1000 fits to randomized pseudodata that would lie along the fit to original data. The red dotted curves are Gaussians based on the means and standard deviations found from the fits.

Figure 2

Projections of the astrophysical $S_{E2}$ factor to 300 keV for fits of existing $E2$ data (a) and for existing $E2$ plus proposed MIT data (b) for a channel radius of 5.43 fm. The blue dashed vertical lines indicate the projections for the fit to the original data, while the histograms represent the results of 1000 fits to randomized pseudodata that would lie along the fit to original data. The red dotted curves are Gaussians based on the means and standard deviations found from the fits.

Figure 3

The astrophysical S factor for the $E1$ ($E2$) cross section as a function of center-of-mass energy is shown in the top (bottom) panel. The dash-dot black lines represent the $\pm \mathrm{\Delta }S$ best fit curves and are based on the parameters in Table 1; the long dashed outer green lines represent the $\pm 3\mathrm{\Delta }S$ best fit curves; and the short dashed inner blue curves represent the $\pm \mathrm{\Delta }S$ best fit including the projected MIT data [7, 17] shown as the solid black circles, which represent the projected data for a 114 MeV incident electron beam, an electron scattering angle of ${15}^{\circ }$, and case A in Ref. [7]. The existing data are taken from the Refs. [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

Figure 4

Comparison of fit results for existing data (solid squares), including projected JLab data [4, 8] (solid circles), and including projected MIT data (small crosses) for total $S$(300 keV), $S_{E1}$ (300 keV), and $S_{E2}$(300 keV).