  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.
