Transition from participant to spectator fragmentation in Au+Au reactions between $60A$ and $150A$ MeV

Using the quantum molecular dynamics approach, we analyzed the results of the recent INDRA Collaboration Au+Au experiments at GSI in the energy range between $60A$ and $150A$ MeV. It turns out that in this energy region, the transition toward a participant-spectator scenario takes place. The large Au+Au system displays, in the simulations as in the experiment, simultaneously dynamical and statistical behavior, which we analyze in detail. The composition of fragments close to midrapidity follows statistical laws, and the system shows bimodality, i.e., a sudden transition between different fragmentation patterns, as a function of centrality, as expected for a phase transition. The fragment spectra at small and large rapidities, on the other hand, are determined by dynamics, and the system as a whole does not come to equilibrium—an observation that is confirmed by FOPI Collaboration experiments for the same system.

Figure 1

Comparison of nonfiltered (top left) and filtered (top middle) QMD distributions for $Z=3$ particles for the two most central bins with experimental results (top right) for the reaction Au+Au at $60A$ MeV. To show how the filter modifies the events, we display the difference between unfiltered and filtered QMD events (bottom left), between unfiltered simulations and experiment (bottom middle), as well as between filtered simulations and experiment (bottom right).

Figure 2

Correlation between impact parameter and $E_{\mathrm{trans}12}$ for Au+Au reactions at $60A$ MeV (top) and $150A$ MeV (bottom) according to the QMD. Events above the cut in $E_{\mathrm{trans}12}$ correspond to a geometrical cross section of $\sigma =\pi (1\hspace{1em}\mathrm{fm}){}^2$.

Figure 3

Fragment yield of simulated events with $b⩽1$ fm (top) and $E_{\mathrm{trans}12}⩾1246(3313)$ MeV (bottom) for Au+Au reactions as compared with the experimental data selected by $E_{\mathrm{trans}12}$. Full (dashed) lines correspond to unfiltered (filtered) QMD events.

Figure 4

Transverse energy distribution $\mathit{dN}/E_{\mathrm{trans}12}$ for Au+Au reactions at $60A$ MeV (left) and $150A$ MeV (right). Unfiltered (solid lines) and filtered (dashed lines) QMD results are compared with the data. Vertical lines show the experimental centrality cuts for central events.

Figure 5

Multiplicity distribution of intermediate mass fragments. We compare for all events unfiltered (full line) and filtered (dashed line) QMD simulations with Au+Au data ($60A$ MeV left and $150A$ MeV right).

Figure 6

Same as Fig. 5, but for central events.

Figure 7

Fragment distribution. We compare central events unfiltered (full line) and filtered QMD (dashed) simulations with data.

Figure 8

Same as Fig. 7, but for distribution of the heaviest fragments.

Figure 9

Energy distribution of $Z=3$ and $Z=5$ fragments from central events.

Figure 10

QMD prediction of fragment composition in terms of nucleons initially in the target for $A=6$ (left) and and $A=16$ (right) in central Au+Au collisions ($b⩽3\hspace{1em}$fm). Full(dashed) line shows the distribution for $60A\hspace{1em}(150A)$ MeV.

Figure 11

Same as Fig. 10, but for midrapidity fragments.

Figure 12

QMD predictions of the correlation between the fraction of entrained target nucleons and the longitudinal fragment velocity in the center of mass for fragments with $6⩽Z⩽10$ in central Au+Au reactions.

Figure 13

$R=\frac{\langle y^{2}x\rangle }{\langle y^{2}z\rangle }$ as a function of fragment charge for central events in Au+Au reactions at $150A$ MeV measured by INDRA and FOPI collaborations [20]. Data are compared with the results of the QMD calculation.

Figure 14

$Z_{\max }$ as a function of asymmetry parameter for different experimental centrality bins for filtered QMD events at $150A$ MeV.

Figure 15

Most probable $a_2$ in unfiltered QMD simulations as a function of $E_{\mathrm{trans}12}/E_{\mathrm{c}.\mathrm{m}.}$ (left) and as a function of the impact parameter (right). As in experiment, we see in both cases a fast transition.

Figure 16

QMD predictions of the distribution of all nucleons (colors) and those nucleons which belong finally to a fragment $10⩽A⩽20$ (boxes) for collisions $6⩾b⩾8$ fm for Au+Au at $150A$ MeV (left) and $60A$ MeV (right) from $t=0$ (top) to $t=200$ fm/$c$ (bottom)

Figure 17

Same as Fig. 16, but for the momentum space distribution.

Figure 18

Momentum space distribution of all nucleons (colors) and those nucleons which belong finally to a fragment $10⩽A⩽20$ (boxes) for central collisions $0⩾b⩾4$ fm for Au+Au at $150A$ MeV (left) and $60A$ MeV (right) at $t=0$ (top) and $t=200$ fm/$c$ (bottom).

Figure 19

Multiplicity of intermediate mass fragments as a function of the impact parameter for Au+Au reactions at $60A,100A$, and $150A$ MeV. Full (dashed) line shows unfiltered (filtered) QMD events.

Figure 20

Distribution of all nucleons (colors) and those nucleons which belong finally to a fragment $6⩽A⩽10$ (boxes) for central collisions $0⩾b⩾4$ fm for Au+Au at $150A$ (left) and $60A$ MeV (right) from $t=0$ (top) to $t=200$ fm/$c$ (bottom)

Figure 21

Same as Fig. 21, but for the momentum space distribution.

Figure 22

Time evolution of central density, Δ, and binding energy $E_p$ of $Z=3$ fragments during the reaction.