The double-differential cross sections of outgoing neutrons and alpha particles of the 12C(n,xn) and 12C(n,x) reactions are measured. A new nuclear reaction model for light nuclei is proposed to analyze the measured data. Because of a strong recoil effect in light nucleus reactions, the energy balance is strictly taken into account. Based on this new method, the LUNF code is developed to calculate all kinds of reaction cross sections and energy-angular distributions for the n + 12C reaction in the 4.8- to 20-MeV energy region. The reaction channel of (n,n'3) may proceed via a number of different reaction channels, as sequential particle emissions and two-body separation. The comparisons of the calculated results with the measured experimental data indicate that the model calculations are successful for outgoing neutrons. Also, kerma factors derived from the calculated results are compared with the measurements.