The spectral broadening of characteristic gamma-ray emission peaks from the reaction C-12(He-3, p gamma)N-14 was measured in D(He-3) plasmas of the JET tokamak with ion cyclotron resonance heating tuned to the fundamental harmonic of He-3. Intensities and detailed spectral shapes of gamma-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 N-14 excitation levels yielding the observed gamma-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.