Shape of the 4.438 MeVγ-ray line of12Cfrom proton andα-particle induced reactions on12Cand16O

We calculated in detail the angular distribution of γ rays and the resulting shape of the γ-ray line produced by the nuclear deexcitation of the 4.439 MeV state of ${}^{12}\mathrm{C}$ following proton and α-particle interactions with ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ 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 γ-ray line shapes and angular distributions was used to deduce parametrizations for the γ-ray emission of the $2^{+},$ 4.439 MeV state of ${}^{12}\mathrm{C}$ following inelastic proton scattering off ${}^{12}\mathrm{C}$ and proton induced spallation of ${}^{16}\mathrm{O}.$ At higher proton energies and for α-particle induced reactions, optical model calculations were the main source to obtain the needed reaction parameters for the calculation of γ-ray line shapes and angular distributions. Line shapes are predicted for various interaction scenarios of accelerated protons and α particles in solar flares.