Mass dependence of transverse flow in heavy ion collisions at intermediate energies

The mass dependence of the transverse flow in the reactions of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at 35 MeV/nucleon has been determined for emitted isotopes with $Z=1$ to 9. The observed flow is compared with that calculated using a constrained molecular dynamics (CoMD) simulation. With the application of the appropriate experimental filter, the general trend of the experimental mass-dependent flow is well reproduced by the simulation employing an effective interaction corresponding to a soft equation of state $(K=200$ MeV). The CoMD events are further utilized to study the mechanism of generation of the mass-dependent flow. It is found that the mass-dependent flow is generated by the interplay between the thermal and collective motions under a momentum conservation in the fragmenting system. With the help of the collective-thermal-interplay model, the mass-dependent flow scaled by the reduced mass of fragments $A/A_{\mathrm{sys}}$ is found to be almost independent of the size of the system.

Figure 1

(a) Normalized charged-particle distribution from the filtered CoMD events (dashed line) and reduced charged-particle distribution from the experimental data (dots). (b) Extracted $b/b_{\max }$ versus $N_{\mathrm{ch}}$ from the filtered CoMD events (dashed line) and the experimental data (dots).

Figure 2

Normalized reaction plane distributions calculated from the CoMD-simulated data at 2000 fm/$c$ using the three methods mentioned in the text.

Figure 3

Average in-plane momentum $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\mathrm{proj}}$ for $\alpha$ particles from the experiment. Different symbols represent the results from different reaction plane reconstruction methods.

Figure 4

Average in-plane momentum $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\mathrm{proj}}$ for $\alpha$ particles from unfiltered CoMD events at 2000 fm/$c$. Different symbols represent the results from different reaction reconstruction methods.

Figure 5

Average in-plane momentum $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\mathrm{proj}}$ for $\alpha$ particles from filtered CoMD events at 2000 fm/$c$. Circles represent the results in which the POI recoil correction proposed in Ref. [21] is made in the reaction plane reconstructions, whereas triangles indicate results when no POI recoil correction is made.

Figure 6

Average in-plane momentum $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\mathrm{proj}}$ for $\alpha$ particles from filtered CoMD data at 2000 fm/$c$. Different symbols represent the results from filtered CoMD events (triangles), full events (dots), and events with $Y/Y_{\mathrm{proj}}>0$ (open circles). Lines depict linear fits.

Figure 7

Transverse flow extraction for $Z=1$–9 particles from the experimental data. The lines are the linear fits of the data points in $Y/Y_{\mathrm{proj}}=0.05$–0.45.

Figure 8

Flow from the experimental data and the CoMD simulations with different conditions as a function of $Z$. Dots, experiment; open circles, CoMD without the experimental filter; squares, CoMD with the experimental filter; and triangles, CoMD with the experimental filter and the $\Delta \varphi$ effect. In the panel (a) the soft EOS is used for CoMD calculations, whereas in panel (b) the hard EOS is used. The error bars are from the slope-fitting errors.

Figure 9

Flow from unfiltered CoMD data at 300 fm/$c$ as a function of particle mass number $A$. Circles and squares are results derived from the CTIM fits of CoMD flow with and without momentum conservation, respectively.

Figure 10

Apparent temperature as a function of $Y/Y_{\mathrm{proj}}$ from $Z=1$–2 particles predicted by CoMD. The dashed line corresponds to $T=5.4$ MeV.

Figure 11

Flow predicted by CTIM versus $A$. Different symbols represent different system sizes: $A_{\mathrm{sys}}=27$ (circles), 80 (squares), and 125 (triangles).

Figure 12

Flow predicted by CTIM versus $A/A_{\mathrm{sys}}$. Different symbols represent different system sizes: $A_{\mathrm{sys}}=27$ (circles), 80 (squares), and 125 (triangles).