Based on the Monte-Carlo package G eant4 a new simulation of the complete background spectrum of the HEIDELBERG-MOSCOW experiment which operates five enriched 76 Ge detectors in a low background environment in the Gran Sasso underground laboratory was performed. The resulting background model is used to evaluate the signal of the two neutrino accompanied double beta decay with a statistical significance of 41.57 kg year resulting in a half-life of T 1/2 2ν=(1.74±0.01(stat) −0.16 +0.18(syst))×10 21 years. Using G eant4 a simulation of elastic and inelastic neutron reactions has been performed for the first time and is used to estimate the contribution of the neutron flux in the Gran Sasso underground laboratory to the experimental spectrum. The composition of the background in the energy range from 2000 to 2100 keV around the Q value for neutrinoless double beta decay is discussed in some detail.