The effect of the diffuse nuclear potential on the penetration of the potential barrier is examined using a simplified model. The transmission coefficient for slow neutrons is treated in an exact way employing an exponential diffuse potential and is found to be larger by a factor 2 than in the usual calculation. The Coulomb penetrability is investigated on the basis of the W-K-B method, and the diffuseness makes the penetration factor much larger than that obtained in the conventional calculation, An application to the evaporation process is developed, and the energy spectrum of alpha particles from the Al/ sup 27/(n, alpha ) Na/sup 24/ reaction is found to be explained by the corrected penetrability in a satisfactory way. (auth)