Excitation functions of parameters extracted from three-source (net-)proton rapidity distributions in Au-Au and Pb-Pb collisions over an energy range from AGS to RHIC

Experimental results of the rapidity spectra of protons and net-protons (protons minus antiprotons) emitted in gold-gold (Au-Au) and lead-lead (Pb-Pb) collisions, measured by a few collaborations at the alternating gradient synchrotron (AGS), super proton synchrotron (SPS), and relativistic heavy ion collider (RHIC), are described by a three-source distribution. The values of the distribution width $\sigma_C$ and contribution ratio (relative contribution) $k_C$ of the central rapidity region, and the distribution width $\sigma_F$ and rapidity shift $\Delta y$ of the forward/backward rapidity regions, are then obtained. The excitation function of $\sigma_C$ increases generally with increase of the center-of-mass energy per nucleon pair $\sqrt{s_{NN}}$. The excitation function of $\sigma_F$ shows a saturation at $\sqrt{s_{NN}}=8.8$ GeV. The excitation function of $k_C$ shows a minimum at $\sqrt{s_{NN}}=8.8$ GeV and a saturation at $\sqrt{s_{NN}}\approx 17$ GeV. The excitation function of $\Delta y$ increase monotonously with $\ln \sqrt{s_{NN}}$ in the considered energy range.