Effects of mean-field momentum dependence on pion production in intermediate-energy heavy-ion collisions

Abstract

Pion production in heavy-ion collisions at intermediate energies provides an important probe of the collision dynamics and nuclear matter equation of state, especially the high-density behavior of the symmetry energy. Using the lattice Boltzmann-Uehling-Uhlenbeck transport model with a recently developed nuclear effective interaction based on the so-called N$5$LO Skyrme pseudopotential, we investigate the effects of the momentum dependence of nucleon mean-field potentials on the pion production in Au+Au collisions at a beam energy of $1.23$~GeV/nucleon. We find that a stronger momentum dependence, for which the nucleon mean-field potentials increase faster with momentum, generally suppresses pion production. This feature can be understood in terms of the mean-field-induced modification of nucleon high-momentum phase space during the compression stage: a stronger momentum dependence can reduce the relative fraction of high-momentum nucleons in heavy-ion collisions, thereby suppressing the production of $Δ$ resonances and pions.

Figures (5)

• Figure 1: Energy dependence of single-nucleon potential $U_q$ in cold nuclear matter predicted by SP$10$, SP$10$-FL and SP$10$-MID. (a) Results for symmetric nuclear matter ($\delta=0$) at saturation density $\rho_0$ are compared with the nucleon optical potential in by Hama et al.Hama:1990vr (solid stars) and its extrapolation to $1.5$ GeV (open squares), as well as with the result from Feldmeier and Linder (FL) Feldmeier:1991ey (open circles). (b) Neutron and proton potentials in asymmetric nuclear matter at density $\rho=\rho_0$ and isospin asymmetry $\delta=0.198$, a value typical for a $^{197}\text{Au}$ nucleus.
• Figure 2: Cross section for $pp \rightarrow n\Delta^{++}$ as a function of the invariant mass $\sqrt{s}$ (in GeV). Experimental data are taken from CERN8401 Flaminio:1984gr (black hollow triangles) and Landolt-Börnstein Schopper:1988hwx (Red solid dot). The solid blue line represents the parameterization given by Eq. (\ref{['eq:NNND']}). The inset provides an enlarged view of the cross section near threshold, and the black dashed line indicates $\sqrt{s}$ = 2.4 GeV.
• Figure 3: Time evolution of (a) the number of pions ($\pi^{-}, \pi^{+}$) and resonances ($\Delta^{-}$, $\Delta^{0}$, $\Delta^{+}$, $\Delta^{++}$, $N^{*}$, $\Delta^*$ ) obtained from LBUU calculation using the SP$10$ interaction, and (b) the central baryon density $\rho_{B}$ predicted by the SP$10$, SP$10$-FL and SP$10$-MID. Both panels correspond to the Au+Au collisions at $\sqrt{s_{\rm{NN}}} = 2.4 \, \text{GeV}$ and $0$-$10\%$ centrality. The vertical black dashed lines indicate $t$ = 15 fm$/c$.
• Figure 4: Rapidity distributions of pions with different momentum dependence interactions: SP$10$, SP$10$-FL, and SP$10$-MID in Au + Au collisions at $\sqrt{s_{\rm{NN}}} = 2.4 \, \text{GeV}$. Panel (a) shows the results for centrality $0-10$$\%$ and panel (b) for centrality 20-30$\%$. The solid, dashed and dotted curves represent LBUU model predictions, and the symbols represent the HADES experimental data HADES:2020ver with error bars indicating uncertainties.
• Figure 5: The averaging invariant mass $\langle\sqrt{s} \rangle$ in $N+N\rightarrow N+\Delta$ reaction as functions of baryon density $\rho_{B}$ at the evolution time of $t=15~\rm{fm}/c$ obtained from the LBUU simulations with the SP$10$, SP$10$-FL, and SP$10$-MID interactions, respectively. Statistical errors are displayed as the shaded bands.