  We analyzed the transverse momentum spectra of positively and negatively
charged pions ($\pi^+$ and $\pi^-$), positively and negatively charged kaons
($K^+$ and $K^-$), protons and antiprotons ($p$ and $\bar p$), as well as
$\phi$ produced in mid-(pseudo)rapidity region in central nucleus--nucleus (AA)
collisions over a center-of-mass energy range from 2.16 to 2760 GeV per nucleon
pair. The transverse momentum of the considered particle is regarded as the
joint contribution of two participant partons which obey the modified
Tsallis-like transverse momentum distribution and have random azimuths in
superposition. The calculation of transverse momentum distribution of particles
is performed by the Monte Carlo method and compared with the experimental data
measured by international collaborations. The excitation functions of effective
temperature and other parameters are obtained in the considered energy range.
With the increase of collision energy, the effective temperature parameter
increases quickly and then slowly. The boundary appears at around 5 GeV, which
means the change of reaction mechanism and/or generated matter.
