  The finite nuclear thickness affects the energy density $\epsilon(t)$ and
conserved-charge densities such as the net-baryon density $n_B(t)$ produced in
heavy ion collisions. While the effect is small at high collision energies
where the Bjorken energy density formula for the initial state is valid, the
effect is large at low collision energies, where the nuclear crossing time is
not small compared to the parton formation time. The temperature $T(t)$ and
chemical potentials $\mu(t)$ of the dense matter can be extracted from the
densities for a given equation of state (EOS). Therefore, including the nuclear
thickness is essential for the determination of the $T$-$\mu_B$ trajectory in
the QCD phase diagram for relativistic nuclear collisions at low to moderate
energies such as the RHIC-BES energies. In this proceeding, we will first
discuss our semi-analytical method that includes the nuclear thickness effect
and 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 $\mu_S(t)$ for
a quark-gluon plasma using the ideal gas EOS with quantum or Boltzmann
statistics. Finally, we will show the results on the $T$-$\mu_B$ trajectories
in relation to the possible location of the QCD critical end point. This
semi-analytical model provides a convenient tool for exploring the trajectories
of nuclear collisions in the QCD phase diagram.
