Examination of cluster production in excited light systems at Fermi energies from new experimental data and comparison with transport model calculations

Four different reactions, ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$ and ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ at 25 and 50 MeV/nucleon, have been measured with the FAZIA detector capable of full isotopic identification of most forward emitted reaction products. Fragment multiplicities, angular distributions and energy spectra have been measured and compared with Monte Carlo simulations, i.e., the antisymmetrized molecular dynamics (AMD) and the heavy-ion phase space exploration (HIPSE) models. These models are combined with two different afterburner codes (HF$\ell$ and SIMON) to describe the decay of the excited primary fragments. In the case of AMD, the effect of including the clustering and interclustering processes to form bound particles and fragments is discussed. A clear confirmation of the role of the cluster aggregation in the reaction dynamics and particle production for these light systems, for which the importance of the clustering process increases with bombarding energy, is obtained.

Figure 1

Polar view of the four FAZIA blocks in the geometry of the experiment. The beam axis passes through the center. The small detector close to the the center represents a beam monitor telescope. Within the precision of the drawing the geometrical square shape of the detectors is not deformed in the polar representation taking into account the very forward angles.

Figure 2

Experimental and model correlations, before (AMD-CC $4\pi$) and after the filter (AMD-CC), of ion charge vs parallel velocity in the laboratory frame for the $\mathrm{S}+\mathrm{C}$ reaction at 25 MeV/nucleon. The red and black arrows indicate the center-of-mass and projectile velocities, respectively. Counts are normalized to unity (i.e., total number of events) for a better yield comparison.

Figure 3

Charge probability distributions for the four reactions (indicated in each panel). Black points show the experimental data while continuous lines represent the AMD-CC model and HIPSE calculations, respectively.

Figure 4

Velocity probability distributions of $Z>5$ fragments along the beam axis in the laboratory reference frame for the four reactions (indicated in each panel). Black points show the experimental data while continuous lines represent the AMD-CC model and HIPSE calculations, respectively. Arrows indicate the center-of-mass velocity (red) and beam velocity (black).

Figure 5

Proton and cluster multiplicities $(Z<6)$, after the secondary decay, in ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ (upper panels) and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$ (bottom panels) reactions. Black points represent the experimental data while red bars represent $\mathrm{AMD}+\mathrm{HF}\ell$ with cluster formation, green bars are for $\mathrm{AMD}+\mathrm{HF}\ell$ without cluster formation, and blue bars represent $\mathrm{HIPSE}+\mathrm{SIMON}$ simulations. The horizontal bars attached to the points are drawn to guide the eye as an indicator with respect to the models' results. The $y$ errors are within the point dimension or are shown as rectangular shapes surrounding the points. Errors are the sum of the statistical contribution and of the identification procedure.

Figure 6

Ratio of model-predicted and experimental multiplicities for $Z<6$ products in ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ (upper panels) and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$ (bottom panels) reactions. Simulated data refer to the end of the evaporation phase. Errors are indicated when exceeding the point size and lines are drawn to guide the eye. The black dashed line indicates full agreement between data and model predictions.

Figure 7

LCP ($Z\le 2$) energy distribution for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$. Black points represent the experimental data while the blue, red, and green lines represent HIPSE, $\mathrm{AMD}+\mathrm{HF}\ell$ with cluster and $\mathrm{AMD}+\mathrm{HF}\ell$ without cluster calculations, respectively. Spectra are normalized to the integral for a better shape comparison.

Figure 8

LCP ($Z\le 2$) angular distribution in the c.m. reference frame for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$. Black points represent the experimental data while the blue, red, and green lines represent HIPSE, $\mathrm{AMD}+\mathrm{HF}\ell$ with cluster, and $\mathrm{AMD}+\mathrm{HF}\ell$ without cluster calculations, respectively. Spectra are normalized to the integral for a better shape comparison.

Figure 9

LCP ($Z\le 2$) energy distribution for ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$ at 25 MeV/nucleon. Solid points represent the experimental data of Fig. 7 while empty points represents the same data after a big fragment velocity cut (i.e., ${\mathrm{V}}_z<$ 55 mm/ns).

Figure 10

Model calculations. Proton energy distribution for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ at 25 MeV/nucleon in $4\pi$. The lines represent various components of the AMD-CC simulation. The red, dark blue, and light blue lines are the total ($\mathrm{AMD}+$HF$\ell$), AMD only (primary), and HF$\ell$ only (secondary) components, respectively. Primary and secondary spectra are normalized to the entries of the total events of $\mathrm{AMD}+$HF$\ell$.

Figure 11

Model calculations. Proton energy distribution for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ at 25 MeV/nucleon in $4\pi$. On top the primary component (AMD only), with cluster and no cluster, is represented while at bottom the secondary (HF$\ell$only) is shown. Spectra are normalized to the integral.

Figure 12

IMF $(2<Z\le 5)$ energy per nucleon spectra for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$. Black points represent the experimental data. Model predictions, at the end of the evaporation phase, are reported for HIPSE (blue line), $\mathrm{AMD}+$HF$\ell$ with clusterization (red lines), and $\mathrm{AMD}+$HF$\ell$ without clusterization (green lines). The black arrows indicate the beam energy position in each panel. Spectra are normalized to the integral for a better shape comparison.

Figure 13

IMF $(2<Z\le 5)$ angular distribution in the c.m. frame for ${}^{20}\mathrm{Ne}+{}^{12}\mathrm{C}$ and ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$. Black points represent the experimental data. Model predictions, at the end of the evaporation phase, are reported for HIPSE (blue line), $\mathrm{AMD}+$HF$\ell$ with clusterization (red lines), and $\mathrm{AMD}+$HF$\ell$ without clusterization (green lines). Spectra are normalized to the integral for a better shape comparison.