Heavy baryonic resonances, multistrange hadrons, and equilibration at energies available at the GSI Schwerionensynchrotron, SIS18

We study the details and time dependence of particle production in nuclear collisions at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A$ GeV with the UrQMD transport model. We find that the previously proposed production mechanisms for multistrange hadrons $\varphi$ and $\mathrm{\Xi }$ are possible due to secondary interactions of incoming nuclei of the projectile and target with already created nuclear resonances, while the Fermi momenta of the nuclei play only a minor role. We also show how the centrality dependence of these particle multiplicities can be used to confirm the proposed mechanism, as it strongly depends on the number of participants in the reaction. Furthermore we investigate the time dependence of particle production in collisions of Ca + Ca at this beam energy, in order to understand the origins of the apparent chemical equilibration of the measured particle yields. We find that indeed the light hadron yields appear to be in equilibrium already from the very early stage of the collision, while in fact no local equilibration, through multicollision processes, takes place. The apparent equilibrium is reached only through the decay of the resonances according to available phase space.

Figure 1

Shown (as blue short-dashed line) is the distribution of the maximally available invariant mass for resonance creation from initial scatterings of target and projectile nucleons. Note that the peak of the distribution corresponds to the energy available in proton + proton collisions, at the same beam energy, while the Fermi momenta in the nucleus smear out the distribution. The black dashed line shows the actual invariant mass distribution of $N^{*}$ resonances from these initial nucleon + nucleon scatterings, which is shifted because the outgoing particles have finite momenta. The red solid line depicts the invariant mass distribution of all $N^{*}$ resonances which decay during the systems whole evolution. Panel (a) presents results of very peripheral collisions of $\mathrm{Ca}+\mathrm{Ca}$ at $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$, whilepanel (b) depicts results for head-on collisions. In panel (c) we show results for central $\mathrm{Be}+\mathrm{Be}$ collisions at the same beam energy.

Figure 2

Distribution of the decay times of $N^{*}$ resonances (green short dashed line). We also show the distributions of resonances with masses larger than $M_{N^{*}}$. Apparently high mass resonances decay at a later time (roughly by 1 fm/$c$) than lighter resonances, as they have to be created in secondary collisions and therefore appear at a later stage of the collision.

Figure 3

Centrality dependence of several strange particle ratios for collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$, as simulated with UrQMD. A strong centrality dependence for the ${\mathrm{\Xi }}^{-}$ and $\varphi$ is observed as they can only be created in secondary reactions. We compare the results from Ca + Ca with central collisions ($b=0$ fm) of the smaller system Be + Be (dashed lines). The ratios in the Be + Be collision system are consistent with peripheral Ca + Ca collisions, indicating a universal $N_{\mathrm{part}}$ scaling as expected for multiple-step processes.

Figure 4

Centrality dependence of the $\varphi /K^{-}$ and $\varphi /{\pi }^{+}$ ratio in collisions of Ni + Ni nuclei at a beam energy of $E_{\mathrm{lab}}=1.93A$ GeV. We compare the UrQMD results (lines) with data from the FOPI Collaboration [41]. The model results well describe the measured centrality dependence.

Figure 5

Time evolution of the number of several stable particles in central ($b<4$ fm) collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$. The number extracted refers to particles without resonance decays. It can be seen that the number increases slowly for pions and $K^{-}$, as they are usually “hidden” in resonances.

Figure 6

Time evolution of the number of several stable particles in central ($b<4$ fm) collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$. The number of extracted refers to particles after resonance decays. Even if instant resonance decays are taken into account, the number of final stable particles increases differently for different particle species. The pion number actually overshoots the final value and saturates later, while the ${\mathrm{\Xi }}^{-}$ number increases slower as it is produced in secondary interactions.

Figure 7

Time evolution of the number of inelastic collisions per participant nucleon in central ($b<4$ fm) collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$. Apparently the number of inelastic collisions saturates quickly after the interpenetration time, indicating that the chemical composition of the system is fixed rather early and is essentially only changed by secondary collisions during the penetration phase of the two nuclei.

Figure 8

Results of two SHM fits to the time-dependent stable particle yields obtained with UrQMD simulations of central ($b<4$ fm) collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$. The SHM fits were performed with the thermus package (solid lines) and the florence code (dashed lines). We show the temperature (green squares) and baryo-chemical potential (red circles) as function of time. The thermal parameters already saturate around 10 fm/$c$. We compare the fit results with the thermal parameters obtained from a coarse graining approach (black lines, see text).

Figure 9

Results of a SHM fit to the time-dependent stable particle yields obtained with UrQMD simulations of central ($b<4$ fm) collisions of Ca + Ca at a fixed target beam energy of $E_{\mathrm{lab}}=1.76A\mathrm{GeV}$. The SHM fits were performed with the thermus package (solid lines) and the florence code (dashed lines). We show in panel (a) the ratio of the strangeness canonical radius over the system radius (black squares) and the ${\gamma }_s$ parameter (black circles). Both quantities have a similar systematic behavior and can be seen as equivalent. Most interestingly, we show in panel (b) the quality of the fit as function of time. Except for the very early times, where no good fit could be obtained, the fit quality is always satisfactory.