S-factor and scattering-parameter extractions from 3He + 4He → 7Be + γ

Xilin Zhang, Kenneth M. Nollett, D. R. Phillips.


Previous studies of the reaction 3He+4He→7Be+γ have mainly focused on providing the best central value and error bar for the S factor at solar energies. Experimental measurements of this capture reaction at higher energies, the 3He – 4He scattering phase shifts, as well as properties of 7Be and its excited state, have been used to constrain the theoretical models employed for this purpose. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for 3He+4He→7Be+γ to perform the extrapolation. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic properties of 7Be and its excited state, and short-distance contributions to the E1 capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the 7Be ground and excited states are well constrained. The total S factor S(0)=0.577\frac{+0.015}{−0.016} keV b, while the branching ratio for excited- to ground-state capture at zero energy, Br(0)=0.406\frac{+0.013}{−0.011}, both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value S(0)=0.56±0.03keV b, but has a smaller error bar. We also find significant constraints on 3He – 4He scattering parameters, and we obtain constraints on the angular distribution of capture gamma rays, which is important for interpreting experiments. The path forward for this reaction seems to lie with better measurements of the scattering phase shifts and S(E)’s angular dependence away from zero energy, together with better understanding of the asymptotic normalization coefficients of the 7Be bound states’ wave functions. Data on these could further reduce the uncertainty on S(0).