Impact of ${}^{16}\mathrm{O}(\gamma ,\alpha ){}^{12}\mathrm{C}$ 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, plays a key role in nuclear astrophysics. It has direct impact on the evolution and final state of massive stars, while also influencing 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 major goal for the field. In this work, we study the role of potential new measurements of the inverse reaction, ${}^{16}\mathrm{O}(\gamma ,\alpha ){}^{12}\mathrm{C}$, 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 ${}^{16}\mathrm{O}(\gamma ,\alpha ){}^{12}\mathrm{C}$ reaction. In particular, we consider a proposed Jefferson Laboratory (JLab) experiment that 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 reaction. The importance of low-energy data as well as high-precision data is investigated.

Figure 1

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 solid curves represent the best fits and are based on the parameters in Table 1, while the data are taken from Refs. [24, 25, 26, 27, 28, 29, 30, 31, 32, 33].

Figure 2

Projections of the astrophysical $S$ factor to 300 keV for simultaneous fits of existing $E1$ and $E2$ data (top panel) and for $E1$, $E2,$ and proposed JLab data (bottom) 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 data 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

Energy dependence of $S_{E1}+S_{E2}$ from a fit to “all” data indicating the $\pm$ 1, 2, and 3 standard-deviation bands shown as the dash-dotted, short-dashed, and long-dashed curves, respectively. The curves are based on the parameters in Table 1. The open triangles represent a sum of $E1$ and $E2,$ where both $E1$ and $E2$ data exist. The standard deviation at 300 keV is given by the first line and fourth column of Table 2. The projected JLab data are represented by the red triangles.

Figure 4

Standard deviation from 1000 fits with a channel radius of 5.43 fm to “all” data with no JLab data (open square), with projected JLab data (solid squares) as a function of the cumulative number of JLab data points beginning with the highest energy JLab point, the same with JLab projected statistical errors divided by a factor of 2 (solid circles), and the projected JLab statistical errors divided by a factor of 10 (solid triangles). The error limits shown in the figure are just the standard errors for the fits.

Figure 5

Histograms of the subthreshold $E1$ reduced width amplitudes the 6.5-fm fits for the “all” data case, solid curve, and the “$E>1.6$ MeV” data case, dashed curve. The red dashed and blue dash-dotted vertical lines indicate the projections for the fit to the original data for the “all” and “$E>1.6$” MeV data, respectively.