Difficulties in probing density dependent symmetry potential with the HBT interferometry

Based on the updated UrQMD transport model, the effect of the symmetry potential energy on the two-nucleon HBT correlation is investigated with the help of the coalescence program for constructing clusters, and the CRAB analyzing program of the two-particle HBT correlation. An obvious non-linear dependence of the neutron-proton (or neutron-neutron) HBT correlation function ($C_{np,nn}$) at small relative momenta on the stiffness factor $\gamma$ of the symmetry potential energy is found: when $\gamma \lesssim 0.8$, the $C_{np,nn}$ increases rapidly with increasing $\gamma$, while it starts to saturate if $\gamma \gtrsim 0.8$. It is also found that both the symmetry potential energy at low densities and the conditions of constructing clusters at the late stage of the whole process influence the two-nucleon HBT correlation with the same power.