The density effect for swift heavy ions in carbon target is analyzed from a stopping power theory point of view. This is done using our recently derived charge dependent stopping model of partially ionized heavy ions. We show that high order correction terms and partial screening by the projectile electrons reduce the charge state dependence of the stopping power. These effects are more in favor of the Bohr and Lindhard (BL) descriptions of the density effect rather than this of Betz and Grodzins (BG).