An analytical model for two-step reaction gamma-ray spectroscopy in magnetized plasmas

We present a method to analytically compute gamma-ray spectra generated via two-step fusion reactions, where a gamma-ray is emitted from the excited nucleus generated in the first step of the reaction. If one reactant is energetic and the other is at rest, the first step of the reaction can be treated analytically. The second step, which is the gamma-ray emission from the excited nucleus, can always be treated analytically. The model we derive is tested against the established forward-model code GENESIS, obtaining very satisfactory results. Our fully analytic treatment is a far less expensive technique than standard Monte Carlo methods, achieving several times faster computations. Fast calculations of spectra are especially beneficial when working with finely-resolved 3D-4D phase spaces. Furthermore, tractable analytical expressions give insight that is not provided by Monte Carlo methods. The formalism used for the first step of the reaction additionally allows the computation of birth distributions of fusion products from any beam-target reaction with one reactant at rest, e.g. fusion-born alpha distributions.