A schematic model for the direct cross-section in reactions induced by exotic and stable projectiles

A geometric model for the direct contribution of the reaction cross section induced by light ions on different targets is presented. The model separates the total reaction cross section into two components, one for total fusion and another for direct reactions. We show that the direct part scales as $2 \pi Ra$, where $R$ is related to the nuclear radius and $a$ is the width of a ring, which is related to the nuclear diffuseness. A simple expression is presented to calculate the radius $R$ and the width parameter $a$ in terms of the masses and charges of the system. The method is applied to experimental data of exotic, weakly bound, and strongly bound projectiles on several targets. Different diffuseness parameters were obtained for different types of projectiles: exotic n-rich, stable weakly bound, stable strongly bound and exotic p-rich exotic projectiles.