Comparison between calculations with the AMD code and experimental data for peripheral collisions of ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}{,}^{116}\mathrm{Sn}$ at 38 MeV/nucleon

Experimental data concerning binary events in peripheral collisions for the systems ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ and ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ at 38 MeV/nucleon, collected with the Fiasco setup, are compared with calculations performed with the dynamic code AMD, coupled with the statistical code Gemini used as an afterburner. The comparison focuses on the properties of the quasiprojectile (QP) and on the total multiplicities of the emitted light charged particles. A good reproduction of the average mass ratio, charge $Z$, and center-of-mass angle of the QP is obtained in the examined impact parameter range ($b\approx 7–12\mathrm{fm}$). Concerning the light charged particles, a general agreement is found for the total emitted charge, while some discrepancy remains for the multiplicities of the various species, especially for the protons, which are always overestimated by the calculations.

Figure 1

Two-dimensional correlation of $E^{★}/A$ vs $b$ for the system ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ obtained from AMD (with $y=0.85$) at $t=200\mathrm{fm}/c$ (a) and 500 fm/c (b).

Figure 2

Results of AMD plus Gem++ calculations, with $t_{\mathrm{sw}}=500\mathrm{fm}/c$. Two-dimensional correlations $b$ vs $C_b$ for $4\pi$ data of (a) ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (screening parameter $y=0.85$) and (d) ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ ($y=0.42$); (b) mean values and (c) standard deviations of the $b$ distribution as a function of $C_b$; (e) mean values and (f) standard deviations of the $C_b$ distribution as a function of $b$. Full and open symbols are for $4\pi$ and filtered results, respectively. Circles refer to ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (black for $y=0.85$ and green for $y=0.42$) and squares to ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$.

Figure 3

Results of AMD plus Gem++ calculations, with $t_{\mathrm{sw}}=200\mathrm{fm}/c$: (a) two-dimensional distribution of $R_v$ vs $R_A$ for semiperipheral binary events with $C_b>$ 700 MeV, in the system ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ ($y=0.42$) at 38 MeV/nucleon (events filtered with the efficiency of the experimental setup); (b) average ratio $\langle R_A/R_v\rangle$ as a function of $C_b$, for both reactions ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (circles) and ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ (squares); (c) standard deviation of the distribution of $R_A/R_v$ as a function of $C_b$.

Figure 4

Diffusion plot. Results of AMD plus Gemini calculations for the reactions ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (upper panel) and ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ (lower panels) at 38 MeV/nucleon. (a) Correlation $\left(100R_v\right)$ vs. $C_b$ with model parameters $y=0.85, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (b) Mean of the $R_v$ distribution vs. $C_b$. (c) Standard deviation of the $R_v$ distribution vs. $C_b$. (d) Same as panel (a) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ with parameters $y=0.42, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (e) Same as panel (b) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. (f) Same as panel (c) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. Full (red) squares are the experimental data. Other symbols are for calculated results; they refer to filtered events, except for asterisks, which are in $4\pi$.

Figure 5

Wilczynski plot. Results of AMD plus Gemini calculations for the reactions ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (upper panels) and ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ (lower panels) at 38 MeV/nucleon. (a) Correlation ${\theta }_{\mathrm{QP}}^{\mathrm{cm}}$ vs $C_b$ with parameters $y=0.85, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (b) Mean of the ${\theta }_{\mathrm{QP}}^{\mathrm{cm}}$ distribution vs $C_b$. (c) Standard deviation of the ${\theta }_{\mathrm{QP}}^{\mathrm{cm}}$ distribution vs $C_b$. (d) Same as panel (a) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ with parameters $y=0.42, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (e) Same as panel (b) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. (f) Same as panel (c) but for ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. Full (red) squares are experimental data. Other symbols for calculated results; they refer to filtered events, except for asterisks, which are in $4\pi$.

Figure 6

Secondary charge of QP. AMD plus Gemini calculations for the reactions ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ (upper panels) and ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ (lower panels) at 38 MeV/nucleon. (a) Correlation $Z_{\mathrm{QP}}^{\sec }$ vs $C_b$, with $y=0.85, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (b) Mean of the $Z_{\mathrm{QP}}^{\sec }$ distribution vs $C_b$. (c) Standard deviation of the $Z_{\mathrm{QP}}^{\sec }$ distribution vs $C_b$. (d) Same as panel (a) but for the reaction ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$ with $y=0.42, t_{\mathrm{sw}}=500\mathrm{fm}/c$ and Gem++; filtered results. (e) Same as panel (b) but for the reaction ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. (f) Same as panel (c) but for the reaction ${}^{93}\mathrm{Nb}+{}^{116}\mathrm{Sn}$. Full (red) squares are experimental data of Ref. [29]. Other symbols are for calculated results; they refer to filtered events, except for asterisks, which are in $4\pi$.

Figure 7

Multiplicities of LCPs and IMFs ($Z=3–7$), forward emitted in the c.m. frame, as a function of $C_b$ for the system ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ at 38 MeV/nucleon: (a) protons, (b) deuterons, (c) tritons, (d) $\alpha$ particles, and (e) IMF ($Z=3–7$). Experimental data of Ref. [10] [full (red) squares] are compared with the results of calculations, all with $t_{\mathrm{sw}}=500$ fm/$c$, but different $y$ (0.85 or 0.42) or afterburner (Gem90 or Gem++). Circles correspond to AMD plus Gemini (Gem++ in black, Gem90 in green), lines to results of AMD alone, stopped at the indicated time $t$.

Figure 8

Multiplicities of LCPs, forward emitted in the c.m. frame, as a function of $C_b$ for the system ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ at 38 MeV/nucleon: (a), (d) protons; (b), (e) deuterons; (c), (f) $\alpha$ particles. Experimental data [full (red) squares] are compared with results of calculations with $y=0.85$ and different values of $t_{\mathrm{sw}}$ (in fm/$c$). Symbols correspond to AMD plus Gemini (Gem90 in upper panels, Gem++ in lower ones), black lines to results of AMD alone, stopped at the indicated time $t$.

Figure 9

Total charge of all LCPs and IMFs ($Z=3–7$) forward emitted in the c.m. reference frame of the collision for the ${}^{93}\mathrm{Nb}+{}^{93}\mathrm{Nb}$ reaction. Full (red) squares represent experimental data, the other symbols results of various calculations with Gem++ (upper) and Gem90 (lower) afterburner. Switching times are in units of fm/$c$.

Figure 10

Same as Fig. 8, but here experimental data [full (red) squares] are compared with calculations ($y=0.85$ and $t_{\mathrm{sw}}=500\mathrm{fm}/c$) performed with an asy-stiff and an asy-soft version of the equation of state in the AMD model. Lines (symbols) correspond to results of AMD without (with) afterburner. The asy-stiff results are those of Fig. 8, presented with the same lines/symbols and colors. Upper panels refer to Gem90, lower panels to Gem++.