Proton and pion transverse spectra at RHIC from radial flow and finite size effects

We show that the proton and pion transverse momentum distributions measured at RHIC for all collision centralities for pions and most of the collision centralities for protons, can be simultaneously described in terms of a thermal model with common values for the radial flow and temperature, when accounting for the finite size of the interaction region at the time of decoupling. We show that this description is obtained in terms of a simple scaling law of the size of the interaction region with the number of participants in the collision. The behavior of the proton to pion ratio at mid-rapidity can also be understood as a consequence of the strength of the radial flow and system size reached at RHIC energies.