  The transverse momentum spectra of the well-identified produced particles,
$\pi^+$, $\pi^-$, $K^+$, $K^-$, $p$, $\bar{p}$, $K_s^0$, $\Lambda$,
$\bar{\Lambda}$, $\Xi^-$, and $\Xi^+$ are analyzed in a statistical approach.
From the partition function of grand-canonical ensemble, we propose a generic
expression for the dependence of the generic chemical potential $\mu$ on the
rapidity $y$. Then, by fitting this expression to the experimental results on
the most central $p_{\perp}$ and $d^2 N/2 \pi p_{\bot} dp_{\bot} dy$, at
energies ranging from $7.7$ to $200~$GeV, we have introduced a generic
expression for the rapidity dependence of $\mu$, at different energies, namely
$\mu=a+b y^2$, where $a$ and $b$ is constants. We find that the resulting
energy dependence $\sqrt{s_{\mathtt{NN}}}=c[(\mu-a)/b]^{d/2}$ agrees well with
the statistical thermal models. We also present precise estimations of various
types of chemical potentials, $\mu_B$, $\mu_S$, and $\mu_Q$, the baryon, the
strangeness, and the charge chemical potential, respectively.
