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The finite nuclear thickness affects the energy density $\epsilon(t)$ andconserved-charge densities such as the net-baryon density $n_B(t)$ produced inheavy ion collisions. While the effect is small at high collision energieswhere the Bjorken energy density formula for the initial state is valid, theeffect is large at low collision energies, where the nuclear crossing time isnot small compared to the parton formation time. The temperature $T(t)$ andchemical potentials $\mu(t)$ of the dense matter can be extracted from thedensities for a given equation of state (EOS). Therefore, including the nuclearthickness is essential for the determination of the $T$-$\mu_B$ trajectory inthe QCD phase diagram for relativistic nuclear collisions at low to moderateenergies such as the RHIC-BES energies. In this proceeding, we will firstdiscuss our semi-analytical method that includes the nuclear thickness effectand its results on the densities $\epsilon(t), n_B(t), n_Q(t)$, and $n_S(t)$.Then, we will show the extracted $T(t), \mu_B(t), \mu_Q(t)$, and $\mu_S(t)$ fora quark-gluon plasma using the ideal gas EOS with quantum or Boltzmannstatistics. Finally, we will show the results on the $T$-$\mu_B$ trajectoriesin relation to the possible location of the QCD critical end point. Thissemi-analytical model provides a convenient tool for exploring the trajectoriesof nuclear collisions in the QCD phase diagram.

A Semi-analytical Method of Calculating Nuclear Collision Trajectory in the QCD Phase Diagram