We have measured the ratio of the stopping cross sections of seven elements for helium and for hydrogen projectiles, of equal velocities upsilon(1) (between 1.1 and 2.6 a.u.). Elements with different effective plasma densities have been selected, characterized by their Fermi velocity upsilon(F) (in atomic units): Au (1.22), Cr (1.22), Ag (1.19), Al (0.89), Ge (0.91), Sn (0.84), Pb (0.83). With decreasing upsilon(1), we find that the ratio converges toward a constant constant upsilon(1) congruent-to upsilon(F), which depends on upsilon(F). This asymptotic value is in fair agreement with theoretical predictions. At high velocities a universal behavior can be found, except for Al.