The spectral broadening of characteristic γ-ray emission peaks from the reaction (12)C((3)He,pγ)(14)N was measured in D((3)He) plasmas of the JET tokamak with ion cyclotron resonance heating tuned to the fundamental harmonic of (3)He. Intensities and detailed spectral shapes of γ-ray emission peaks were successfully reproduced using a physics model combining the kinetics of the reacting ions with a detailed description of the nuclear reaction differential cross sections for populating the L1-L8 (14)N excitation levels yielding the observed γ-ray emission. The results provide a paradigm, which leverages knowledge from areas of physics outside traditional plasma physics, for the development of nuclear radiation based methods for understanding and controlling fusion burning plasmas.