The equation of state for cold nuclear matter is determined by the effectiv
e, density-dependent interaction between bound nucleons at temperature T =
0. This interaction can be probed in elastic nucleus-nucleus collisions at
various density overlaps which may extend to several times the nor mal matt
er density. For this pur pose the elastic scattering of O-16 ions on O-16 h
as been measured at incident energies from 250 to 1120 MeV with high accura
cy. From these data, which sample both diffractive and refractive scatterin
g processes, we extract the underlying scattering potentials utilizing mode
l-unrestricted analysis methods. These potentials fit very well into the sy
stematics found in light-ion scattering and compare very favorably with mic
roscopic calculations, if these are based on a weak density dependence of t
he effective NN interaction, resulting in a soft equation of state for cold
nuclear matter.