Dependence of Freeze-Out Parameters on Collision Energies and Cross-Sections

We analyzed the transverse momentum spectra (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula>) reported by the NA61/SHINE and NA49 experiments in inelastic proton–proton (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula>) and central Lead–Lead (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>b</mi><mo>−</mo><mi>P</mi><mi>b</mi></mrow></semantics></math></inline-formula>), Argon–Scandium (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>r</mi><mo>−</mo><mi>S</mi><mi>c</mi></mrow></semantics></math></inline-formula>), and Beryllium–Beryllium (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>e</mi><mo>−</mo><mi>B</mi><mi>e</mi></mrow></semantics></math></inline-formula>) collisions with the Blast-wave model with Boltzmann–Gibbs (BWBG) statistics. The BGBW model was in good agreement with the experimental data. We were able to extract the transverse flow velocity (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>β</mi><mi>T</mi></msub></semantics></math></inline-formula>), the kinetic freeze-out temperature (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula>), and the kinetic freeze-out volume (<i>V</i>) from the <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula> spectra using the BGBW model. Furthermore, we also obtained the initial temperature (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>T</mi><mi>i</mi></msub></semantics></math></inline-formula>) and the mean transverse momentum (<<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula>>) by the alternative method. We observed that <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula> increases with increasing collision energy and collision cross-section, representing the colliding system’s size. The transverse flow velocity was observed to remain invariant with increasing collision energy, while it showed a random change with different collision cross-sections. In the same way, the kinetic freeze-out volume and mean transverse momentum increased with an increase in collision energy or collision cross-section. The same behavior was also seen in the freeze-out temperature, which increased with increasing collision cross-sections. At chemical freeze-out, we also determined both the chemical potential and temperature and compared these with the hadron resonance gas model (HRG) and different experimental data. We report that there is an excellent agreement with the HRG model and various experiments, which reveals the ability of the fit function to manifest features of the chemical freeze-out.