  Using a more reasonable separate density-dependent scenario instead of the
total density-dependent scenario for in-medium $nn$, $pp$ and $np$
interactions, we examine effects of differences of in-medium nucleon-nucleon
interactions in two density-dependent scenarios on isospin-sensitive
observables in central $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon.
Moreover, to more physically detect the differences between the nucleon-nucleon
interactions in two density-dependent scenarios, we also map the
nucleon-nucleon interaction in the separate density-dependent scenario into
that in the total density-dependent scenario through fitting the identical
constraints for symmetric nuclear matter as well as the identical slope
parameter of nuclear symmetry energy at the saturation density. It is shown
that two density-dependent scenarios also lead to essentially different
symmetry potentials especially at high densities although they can lead to the
identical equation of state for the symmetry nuclear matter as well as the
identical symmetry energy for the isospin asymmetric nuclear matter.
Consequently, these isospin-sensitive observables are also appreciably affected
by the different density-dependent scenarios of in-medium nucleon-nucleon
interactions. Therefore, according to these findings, it is suggested that
effects of the separate density-dependent scenario of in-medium nucleon-nucleon
interactions should be taken into account when probing the high-density
symmetry energy using these isospin-sensitive observables in heavy-ion
collisions.
