Analyses of transverse momentum spectra in central C+C and C+Ta interactions at $4.2A\hspace{0.5em}\mathrm{GeV}/c$ beam momentum within a collective flow model and a boundary model

The transverse momentum spectra of secondary ${\pi }^{-}$ mesons and participant protons in central C+C and C+Ta interactions at $4.2A$ GeV/c beam momentum have been analyzed within a collective flow model and a boundary model. All the particle spectra within a collective flow model at a given beam energy can be reproduced with a single set of intensive parameters for the initial state of fireball. As typical freeze-out parameters in this beam energy region we find a freeze-out temperature $T=(55\mathrm{}–100)\hspace{0.5em}\mathrm{MeV},$ and an average transverse expansion velocity at freeze-out $〈\beta 〉=0.30\mathrm{}–\mathrm{0.39.}$ The pion spectra within a boundary model including the quantum mechanical effects can be described well. To fit the proton spectra well, within a boundary model, one will need to introduce the transverse collective expansion.