Cluster correlation and fragment emission in ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at 95 MeV/nucleon

The impact of cluster correlations has been studied in the intermediate mass fragment (IMF) emission in ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at 95 MeV/nucleon, using antisymmetrized molecular dynamics (AMD) model simulations. In AMD, the cluster correlation is introduced as a process to form light clusters with $A\le 4$ in the final states of a collision induced by the nucleon-nucleon residual interaction. Correlations between light clusters are also considered to form light nuclei with $A\le 9$. This version of AMD, combined with GEMINI to calculate the decay of primary fragments, reproduces the experimental energy spectra of IMFs well overall with reasonable reproduction of light charged particles when we carefully analyze the excitation energies of primary fragments produced by AMD and their secondary decays. The results indicate that the cluster correlation plays a crucial role for producing fragments at relatively low excitation energies in the intermediate-energy heavy-ion collisions.

Figure 1

Comparisons of angular distributions of $A=6$–8 isotopes with impact parameter ranges $b=0$–8 fm in (a)–(d), respectively. The experimental data from Ref. [1] are shown by open circles. Inserts are the same data in $d\sigma /d\theta$, but given in a linear scale in an expanded angular range of $0^{\circ }\text{–}{11}^{\circ }$. The calculated results of AMD+GEMINI are shown by blue solid lines. Red dashed curves are those when IMFs with $E_{\text{x}}>E_{\text{pth}}$ are forced to decay. See details in Sec. 4c. For the green long-dashed histogram for ${}^6\mathrm{Li}$ see also discussion in Sec. 4.

Figure 2

Comparisons of energy spectra of $A=6$–8 isotopes at selected angles. The experimental data are shown by open circles. The calculated results of AMD+GEMINI are shown by blue solid lines.

Figure 3

Comparisons of angular distributions of $A=9$–12 isotopes in (a)–(g), respectively. See also Fig. 1 caption.

Figure 4

Comparisons of energy spectra of $A=9$–12 isotopes. Symbols and lines are same as those in Fig. 2.

Figure 5

Comparisons of angular distributions of light charged particles for $p,d,t,$ ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ in (a)–(e), respectively. Blue solid histograms are from the final products of AMD+GEMINI, the green dotted ones are from the primary products of AMD, and the red dashed ones are from the final products with the forced-decay which is discussed in Sec. 4.

Figure 6

Comparisons of energy spectra of light charged particles at selected angles. Symbols and lines are same as those in Fig. 2.

Figure 7

Comparisons of angle-integrated cross sections over the different measured angular ranges between the AMD+GEMINI calculations and the experimental data are shown for (a) all experimentally observed over $4^{\circ }$–${43}^{\circ }$ and (b) those over ${20}^{\circ }$–${43}^{\circ }$. The experimental data are shown by open circles. The calculated results of AMD+GEMINI are shown by blue solid squares.

Figure 8

Impact parameter distributions of various isotopes calculated with the AMD model for IMFs emitted at ${\theta }_{\text{lab}}>{20}^{\circ }$ with different masses of the primary fragments. In top of each figures (a)–(d), they are indicated. Red solid and blue based histograms represent the calculated results without and with taking into account the experimental energy threshold, respectively.

Figure 9

Time evolution of nuclear density distributions in the center of mass system, projected on the reaction plane ($X\text{−}Z$ plane, $Z$ being the beam direction), for calculated events for central collisions. Reaction time is indicated in unit of $\text{fm}/c$ in each panel of the left two columns. The smallest circle indicates a nucleon. See details in the text.

Figure 10

(Left) Time evolution of the momentum distribution projected in the $X\text{−}Z$ plane for the same ${}^{12}\mathrm{C}$ event in Fig. 10. (Right) Time evolution of the phase space distribution projected in the $P_z\text{−}Z$ plane for the same ${}^{12}\mathrm{C}$ event in Fig. 10.

Figure 11

Excitation energy distributions of each fragment emitted at ${\theta }_{\text{lab}}>{20}^{\circ }$ and with kinetic energies above experimental energy thresholds. Red solid and blue dashed histograms represent those for the excited primary and survived secondary fragments, respectively. The particle decay thresholds are also shown on the $X$ axis by red arrows. The green arrow in the ${}^6\mathrm{Li}$ plot, see in the text. For $SV$ and $R$ values, see also in the text.

Figure 12

Similar plots to Fig. 11, but at ${\theta }_{\text{lab}}<{20}^{\circ }$.

Figure 13

(Left) Energy spectra of the experimental data and the calculated results at $4^{\circ }$ for the primary fragments (red dashed histograms) and final secondary products (blue solid histograms). (Right) Similar plots to the left, but with calculated results for the survived primary fragments (green solid histograms) and feeding from large parents (magenta dashed histograms). The experimental data are shown by open circles.

Figure 14

Comparisons of angular distributions of typical isotopes in different switching times from AMD to GEMINI for selected IMFs, ${}^7\mathrm{Li},{}^7\mathrm{Be},{}^{11}\mathrm{B}$, and ${}^{12}\mathrm{C}$ in (a)–(d), respectively. The experimental data are shown by solid circles. The calculated results of the different switching time at 300, 1000, and 3000 $\text{fm}/c$ are shown by blue solid, red dotted, and green dashed histograms, respectively. No forced-decay is used. See details in the text.