Can the nuclear symmetry potential at supra-saturation densities be negative?

In the framework of an Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, for the central $^{197}$Au+$^{197}$Au reaction at an incident beam energy of 400 MeV/nucleon, effect of nuclear symmetry potential at supra-saturation densities on the pre-equilibrium clusters emission is studied. It is found that for the positive symmetry potential at supra-saturation densities the neutron to proton ratio of lighter clusters with mass number $A\leq3$ ($(n/p)_{A\leq3}$) is larger than that of the weighter clusters with mass number $A>3$ ($(n/p)_{A>3}$), whereas for the negative symmetry potential at supra-saturation densities the $(n/p)_{A\leq3}$ is \emph{smaller} than that of the $(n/p)_{A>3}$. This may be considered as a probe of the negative symmetry potential at supra-saturation densities.