Nuclear stopping and light charged particle emission in ${}^{12}\mathbf{C}+{}^{12}\mathbf{C}$ at 95 MeV/nucleon

Detailed comparisons between the experimental data of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at $95A$ MeV and transport model simulations are presented for all charged particles and fragments. For the simulations, antisymmetrized molecular dynamics (AMD), a modified version of AMD (AMD-FM), and constrained molecular dynamics (CoMD), are used. The experimental energy spectra and angular distributions are well reproduced by the AMD-FM calculations for light charged particles with $Z\le 2$. We show that the nuclear stopping plays a key role for these observables. The production mechanisms of light charged particles are discussed. The angular distributions of isotopes with $Z>2$ are qualitatively reproduced reasonably well, but the yields are $2–10$ times smaller in the simulations for most isotopes.

Figure 1

Moving source fit results for protons on the left column and ${}^4\mathrm{He}$ particles on the right. The experimental data from Ref. [1] are shown by open circles. PLF, IV, and TLF components are shown by blue long-dashed, magenta dotted, and green dashed lines, respectively. The total sum of the calculated spectra is shown by red solid lines. Theta Laboratory angles are shown in each figure.

Figure 2

Comparisons for proton angular distribution and energy spectra at selected angles with impact parameter $b=0$–8 fm. The experimental data are shown by solid and open symbols. The calculated results of CoMD, AMD, and AMD-FM are shown by red, blue, and magenta solid histograms, respectively.

Figure 3

Similar plot as Fig. 2, but for deuteron.

Figure 4

Similar plot as Fig. 2, but for triton.

Figure 5

Similar plot as Fig. 2, but for helium3.

Figure 6

Similar plot as Fig. 2, but for ${}^4\mathrm{He}$.

Figure 7

Energy spectra of light charged particles at selected angles with impact parameter $b=0$–8 fm. Experimental data are indicated by black circles. The red dashed histograms represent the particles generated from the primary hot nuclei, the green dotted histograms represent the particles from the secondary processes, and the blue solid histograms show the total particles.

Figure 8

Angular distributions for Li and Be isotopes. The experimental data are shown by solid points. The calculated results of AMD and AMD-FM are shown by red dotted and blue solid histograms, respectively.

Figure 9

Similar plot as Fig. 8, but for B and C isotopes.

Figure 10

Energy spectra of various isotopes at selected angles with impact parameter $b=0$–8 fm. Experimental data are indicated by black circles. The red dashed histograms represent the particles generated from the primary hot nuclei, the green dotted histograms represent the particles from the secondary processes, and the blue solid histograms show the total particles.

Figure 11

Charge density distributions of ${}^{12}\mathrm{C}$. The solid curve is that of the initial nucleus calculated from the AMD coordinate $Z_i$. The dashed curve is the distribution calculated from the physical coordinate $W_i$. The dotted curve is the experimental density distribution from Ref. [43]. The root mean square radius values are also provided for each calculation.

Figure 12

Energy spectra of ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$ at selected angles with impact parameter $b=0$–2, 2–4, 4–6, and 6–8 fm, shown by black solid, red dotted, green dashed, and blue dotted-dashed histograms, respectively. Inclusive data are indicated by black circles. First and third columns represent the primary products form AMD-FM. The second and fourth columns represent the particles generated from the secondary process.

Figure 13

The number of attempted and succeed collisions as a function of time. Counts are for every 10 fm/$c$ time interval.

Figure 14

Nuclear stopping from two models with the impact range $0\le b<8\mathrm{fm}$.

Figure 15

Energy spectra of light charged particles at ${23}^{\circ }$. Open circles: experimental data. Red histograms: results of AMD-FM model.

Figure 16

Energy spectra of deuterons, tritons, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ particles at selected angles. Experimental data are indicated by black solid points. The red open circles and blue open squares are spectra predicted by the individual fit $P_0$ and average $P_0$ of the coalescence model of Eq. (19), respectively.

Figure 17

The extracted values of $P_0$ as a function of outgoing angles in the laboratory system. The open and solid points show the results by individual fit and the dash lines present the average $P_0$ used for the coalescence calculations.