Radiative 3He-alpha reaction in Halo Effective Field Theory

Abstract

In this work we study the radiative capture of ${}^3\mathrm{He}$ on ${}^4\mathrm{He}$ within the halo effective field theory (EFT) framework. At leading order the capture amplitude comprises the initial state $s$-wave strong and Coulomb interactions summed to all orders. At the same order in the expansion, leading two-body currents contribute as well. We find delicate cancelations between the various contributions, and the two-body current contributions can be replaced by appropriately enhancing the asymptotic normalizations of the ${}^7$Be ground and first excited state wave functions. The next-to-leading order corrections come from the $s$-wave shape parameter and the pure Coulomb $d$-wave initial state interactions. We fit the EFT parameters to available scattering data and most recent capture data. Our zero-energy astrophysical $S$-factor estimate, $S_{34}\sim 0.55$ keV b, is consistent within error bars with the average in the literature.

Comments: 27 pages, 9 figures. Misprints and one wrong equation corrected. To be published at The European Physical Journal A