Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter

Based on the relativistic Vlasov-Uehling-Uhlenbeck transport model, which includes relativistic scalar and vector potentials on baryons, we consider an $N-\mathrm{\Delta }-\pi$ system in a box with periodic boundary conditions to study the effects of energy conservation in particle production and absorption processes on the equilibrium properties of the system. The density and temperature of the matter in the box are taken to be similar to the hot dense matter formed in heavy ion collisions at intermediate energies. We find that to maintain the equilibrium numbers of $N,\mathrm{\Delta }$, and $\pi$, which depend on the mean-field potentials of $N$ and $\mathrm{\Delta }$, we must include these potentials in the energy conservation condition that determines the momenta of outgoing particles after a scattering or decay process. We further find that the baryon scalar potentials mainly affect the $\mathrm{\Delta }$ and pion equilibrium numbers, while the baryon vector potentials have considerable effect on the effective charged pion ratio at equilibrium. Our results thus indicate that it is essential to include in the transport model the effect of potentials in the energy conservation of a scattering or decay process, which is ignored in most transport models, for studying pion production in heavy ion collisions.

Figure 1

Momentum distributions of (a) neutron, (b) ${\mathrm{\Delta }}^{-}$, and (c) ${\pi }^{-}$ in a box at $t=40$ fm/$c$. Solid lines are theoretical momentum distributions from the thermal model with the inclusion of both scalar and vector potentials at $T=60$ MeV, dash and dot lines are those in the final states of “S” and “free” cases (see text for details). Open circles are results from the RVUU model including effects of both scalar and vector potentials in the energy conservation condition of a reaction (S+V), open squares are those including only the scalar potentials (S), and open triangles are those without including any potentials (free).

Figure 2

Time evolutions of the $\mathrm{\Delta }$ numbers in box calculations in three cases (see text for details). For comparison, the thermal model results are shown as open cycles.

Figure 3

Similar to Fig. 2, but for the $\pi$ numbers.