We present a fully relativistic analytical model for calculating synthetic spectra from beam-target fusion reactions. When the target particle is assumed at rest, Monte Carlo sampling of reactant velocities can be avoided, and spectrum computations are considerably faster. A fully analytical treatment additionally gives more insight into the spectrum formation. The fully relativistic formulation now makes it possible to handle massless particles in the model, for example from one-step gamma-ray reactions, and the results are corroborated by simulations from established codes.
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