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The standard (Bose-Einstein/Fermi-Dirac or Maxwell-Boltzmann) distributionfrom the relativistic ideal gas model is used to study the transverse momentum($p_{T}$) spectra of identified charged hadrons ($\pi^-$, $\pi^+$, $K^-$,$K^+$, $\bar p$, and $p$) with different rapidities produced in inelasticproton-proton ($pp$) collisions at the Super Proton Synchrotron (SPS). Theexperimental data measured by the NA61/SHINE Collaboration at thecenter-of-mass (c.m.) energies $\sqrt{s}=6.3$, 7.7, 8.8, 12.3, and 17.3 GeV arefitted well by the distribution. It is shown that the effective temperature($T_{eff}$ or $T$), kinetic freeze-out temperature ($T_{0}$), and initialtemperature ($T_{i}$) decrease with the increase in rapidity and increase withthe increase in c.m. energy. The kinetic freeze-out volume ($V$) extracted fromthe $\pi^-$, $\pi^+$, $K^-$, $K^+$, and $\bar p$ spectra decreases with therapidity and increase with the c.m. energy. The opposite tendency of $V$,extracted from the $p$ spectra, is observed to be increasing with the rapidityand decreasing with the c.m. energy due to the effect of leading protons.

entropy

Rapidity and Energy Dependences of Temperatures and Volume Extracted  from Identified Charged Hadron Spectra in Proton-Proton Collisions at a Super  Proton Synchrotron (SPS)