Nucleon number dependence of longitudinal radii in ion-ion collisions as a signature of the onset of collective expansion

In an attempt to disentangle the effects of nuclear geometry from those of expansion we study the dependence of the longitudinal radius (RL) on nuclear numbers of colliding ions within a simple model of multiple nucleonnucleon collisions.The model has built in the nuclear geometry but there is no dynamical expansion.In principle, what is significantly beyond models of this type can be considered as caused by collective expansion.Taking into account the present errors of data, oversimplified model and the absence of accurate information on RL for pp interactions it is difficult to make strong statements about collisions of induced by light ions. On the other hand Pb-Pb data give RL significantly higher than a geometrical picture could accomodate, presenting an evidence for the onset of collective expansion,or of onset of a new dynamical regime between O-Au and Pb-Pb collisions.The situation with S-Au and S-Pb collisions is less clear because of a rather large difference of data on RL in these two cases.