Event simulations in a transport model for intermediate energy heavy ion collisions: Applications to multiplicity distributions

We perform transport model calculations for central collisions of mass 120 on mass 120 at laboratory beam energy in the range 20 MeV/nucleon to 200 MeV/nucleon. A simplified yet accurate method allows calculation of fluctuations in systems much larger than what was considered feasible in a well-known and already existing model. The calculations produce clusters. The distribution of clusters is remarkably similar to that obtained in equilibrium statistical model.

Figure 1

Comparison of mass distribution calculated according to the prescription of Ref. [3] (blue dotted lines) and the present work (red solid lines). The average value of 5 mass units are shown. The cases are for central collision of mass 40 on mass 40 for different beam energies (a) 25, (b) 50, and (c) 100 MeV/nucleon. 500 events were chosen at each energy.

Figure 2

Mass distribution from BUU model calculation for $N_A=120$ on $N_B=120$ reaction at beam energies (a) 50 MeV/nucleon, (b) 75 MeV/nucleon, (c) 100 MeV/nucleon, and (d) 150 MeV/nucleon. The average value of 5 mass units is shown. At each energy 1000 events are chosen. Only central collisions are considered here but even at $E_p=50$ MeV/nucleon, nucleons in the peripheral region passes through and largest fragment remaining is less than the sum of the masses of the two nuclei.

Figure 3

Mass distribution from the canonical thermodynamical model (CTM) calculation for fragmentation of a system of mass $A_0=192$ at temperature (a) 6.5 MeV, (b) 7.5 MeV, (c) 10 MeV, and (d) 14 MeV.

Figure 4

Top left curve (a) is a canonical thermodynamical model (CTM) calculation for excitation $\left(E^{*}\right)$ vs. temperature $\left(T\right)$ for $A_0=192$. Between 6 MeV and 7.5 MeV temperatures, $E^{*}$ rises quickly. The $d{E}^{*}/dT$ slope increases sharply with mass size $A_0$ and is indicative of first-order phase transition. Bottom left curve (b) is also a CTM curve showing that the size of largest cluster drops sharply between 6 MeV and 7.5 MeV. Again this is a first-order liquid gas phase transition. Top right (c) is also with CTM but $A_{max}/A_0$ is plotted against excitation energy per nucleon instead of temperature. The change of liquid to gas is necessarily slower, the range of energy for the change is dictated by latent heat. Bottom right (d) is the calculation from transport model.

Figure 5

Variation of average availability factor (see text) with time (red line) for $N_A=120$ on $N_B=120$ reaction at beam energy 100 MeV/nucleon. The lower curve (black dotted line) is the average availability factor $\langle \tilde{f}\rangle$ at the phase space points of arbitrarily chosen 120 test particles in an isolated mass 120 nucleus as they move in time. The fluctuations from the value 0 reflects uncertainties, probably due to fluctuation in initial Monte Carlo simulations.