Sfactor and scatteringparameter extractions from {}(3}\mathrm{He}+{}({4}\mathrm{He)) { > }(7}\mathrm{Be) +\gamma
Abstract
Previous studies of the reaction ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ 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 ${}^{3}\mathrm{He}$  ${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$ 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 angleintegrated capture data alone. We use the nexttoleadingorder (NLO) amplitude in an effective field theory (EFT) for ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ to perform the extrapolation. At this order the EFT describes the capture process using an swave scattering length and effective range, the asymptotic properties of ${}^{7}\mathrm{Be}$ and its excited state, and shortdistance contributions to the E1 capture amplitude. We extract the multidimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total S factor $S(0)\,={0.577}_{0.016}^{+0.015}$ keV b, while the branching ratio for excited to groundstate capture at zero energy, ${Br}(0)={0.406}_{0.011}^{+0.013}$ , both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value $S(0)=0.56\pm 0.03\,\,\mathrm{keV}$ b, but has a smaller error bar. We also find significant constraints on ${}^{3}\mathrm{He}$  ${}^{4}\mathrm{He}$ 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 ${}^{7}$ Be bound states' wave functions. Data on these could further reduce the uncertainty on S(0).
 Publication:

Journal of Physics G Nuclear Physics
 Pub Date:
 May 2020
 DOI:
 10.1088/13616471/ab6a71
 arXiv:
 arXiv:1909.07287
 Bibcode:
 2020JPhG...47e4002Z
 Keywords:

 effective field theory;
 nuclear reaction;
 solar neutrino physics;
 nucleosynthesis;
 nuclear astrophysics;
 Bayesian analysis and uncertainty estimation;
 Nuclear Theory;
 Astrophysics  Solar and Stellar Astrophysics;
 Nuclear Experiment
 EPrint:
 19 pages and 10 figures (including the supplemental materials)