We investigate the charged particle spectra produced in the heavy-ion collisions at nine centralities from different systems, i.e. $Pb + Pb$ $Pb + Pb$ at $\sqrt{s_{N N}} = 2.76$ $\sqrt{s_{N N}} = 2.76$ TeV and 5.02 TeV as well as $Xe + Xe$ $Xe + Xe$ at $\sqrt{s_{N N}} = 5.44$ $\sqrt{s_{N N}} = 5.44$ TeV, at Large Hadron Collider (LHC) using one empirical formula inspired by the stationary solution of the Fokker-Planck equation, dubbed as the generalized Fokker-Planck solution (GFPS). Our results show that the GFPS can reproduce the experimental particle spectrum up to transverse momentum $p_{T}$ $p_{T}$ about 45 GeV/c with the maximum discrepancy 30% covering 10 orders of magnitude. The discrepancy between the data and the results from the GFPS decreases to 15% when the maximum of the charged particle transverse momentum is cut to 20 GeV/c. We confirmed that the Tsallis distribution derived from the non-extensive statistics, which can reproduce the particle spectra produced in small collision systems, such as $p + p$ $p + p$ , up to few hundreds GeV/c, can only apply to systematically study the particle spectra up to 8 GeV/c in $A + A$ $A + A$ collisions at LHC, as pointed out in the study of identified particle spectra in $Pb + Pb$ $Pb + Pb$ collisions at $\sqrt{s_{N N}} = 2.76$ $\sqrt{s_{N N}} = 2.76$ TeV. A brief discussion on GFPS is also given.

Keywords:

PACS: 25.75.Nq, 25.75.Dw

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