Shape of the 4.438 MeV $\gamma$-ray line of $^{12}$C from proton and $\alpha$-particle induced reactions on $^{12}$C and $^{16}$O

We calculated in detail the angular distribution of gamma-rays and the resulting shape of the gamma-ray line produced by the nuclear deexcitation of the 4.439 MeV state of ^12C following proton and alpha-particle interactions with ^12C and ^16O in the energy range from threshold to 100 MeV per nucleon, making use of available experimental data. In the proton energy range from 8.6 to 20 MeV, the extensive data set of a recent accelerator experiment on gamma-ray line shapes and angular distributions was used to deduce parameterizations for the gamma-ray emission of the 2^+, 4.439 MeV state of ^12C following inelastic proton scattering off ^12C and proton induced spallation of ^16O. At higher proton energies and for alpha-particle induced reactions, optical model calculations were the main source to obtain the needed reaction parameters for the calculation of gamma-ray line shapes and angular distributions. Line shapes are predicted for various interaction scenarios of accelerated protons and alpha-particles in solar flares