$S$-factor and scattering parameters from ${}^3$He + ${}^4$He $\to {}^7$Be + $\gamma$ data

Abstract

We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^3$He + ${}^4$He $\to {}^7$Be + $\gamma$ to perform the extrapolation of higher-energy data to solar energies. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic behavior of ${}^7$Be and its excited state, and short-distance contributions to the E1 capture amplitude. We use a Bayesian analysis to infer the multi-dimensional posterior of these parameters from capture data below 2 MeV. The total $S$-factor $S(0)=0.578_{-0.016}^{+0.015}$ keV b at 68% degree of belief. We also find significant constraints on ${}^3$He-${}^4$He scattering parameters.

Comments: 4 pages, 2 figures. Submitted to the proceedings of the 22nd International Conference on Few-body Problems in Physics, Caen, France, July 9-13, 2018. Uses svproc.cls