Combining statistical-mechanical theories and neutron-scattering techn
iques, we show that the effective pair potential between star polymers
is exponentially decaying for large distances and crosses over, at a
density-dependent corona diameter, to an ultrasoft logarithmic repulsi
on for small distances. We also make the theoretical prediction that i
n concentrated star polymer solutions, this ultrasoft interaction indu
ces an anomalous fluid structure factor which exhibits an unusually pr
onounced second peak.