Three-body resonant radiative capture reactions in astrophysics

Abstract

We develop the formalism based on the S-matrix for $3\to 3$ scattering to derive the direct three-body resonant radiative capture reaction rate. Within this formalism the states, which decay only/predominantly directly into three-body continuum, should also be included in the capture rate calculations. %The results obtained indicate that some theoretical calculations are %incomplete. Basing on the derivation, as well as on the modern experimental data and theoretical calculations concerning ${}^{17}$Ne nucleus, we significantly update the reaction rate for ${}^{15}$O($2p$,$\gamma$)${}^{17}$Ne process in explosive environment. We also discuss possible implementations for the ${}^{18}$Ne($2p$,$\gamma$)${}^{20}$Mg, ${}^{38}$Ca($2p$,$\gamma$)${}^{40}$Ti, and ${}^4$He($n\alpha$,$\gamma$)${}^9$Be reactions.

Comments: 9 pages, 3 figures