Abnormal flow of $\alpha$ particles in heavy-ion collisions at intermediate energies

The experimentally observed abnormal $\alpha$ flow behavior from heavy-ion collisions at intermediate energies is investigated using the events of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at 35 MeV/nucleon simulated with an improved antisymmetrized molecular dynamics model with specific consideration of the Fermi motion in the nucleon-nucleon collision process. Its possible origins in the processes from the fragment formation to the experimental flow extraction, i.e., dynamical process, sequential decay, experimental detection, and data analysis, are closely examined. It is found that the observed abnormal $\alpha$ flow behavior originates from the reconstruction of reaction planes in the flow extraction. How the abnormal $\alpha$ flow behavior is generated from the reaction plane reconstruction procedure is discussed.

Figure 1

(a) Mass dependence of transverse flow from the ${}^{84}\mathrm{Kr}+{}^{197}\mathrm{Au}$ collisions at 200 MeV/nucleon within the two impact parameter gates, i.e., $1<b<3$ fm (filled circles) and $4<b<6$ fm (open circles), taken from Ref. [4]. Solid and dashed lines show the corresponding thermodynamic calculations to reproduce the flow values in the overall mass range. (b) The difference between the experimentally extracted flows and those from thermodynamic model calculations at given masses.

Figure 2

Comparison between the experimentally measured energy spectra for $\alpha$ particles at entire measured angles from ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at 50 MeV/nucleon taken from Ref. [48] (circles) and those from the AMD-FM+Gemini simulations (lines).

Figure 3

Average in-plane momentum per nucleon $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\text{proj}}$ for $Z=1\text{–}6$ primary fragments from the AMD-FM. Lines depict linear fits for the data in the region of $-0.3\le Y/Y_{\text{proj}}\le 0.3$.

Figure 4

Flow as a function of $Z$. Filled circles are the results from the AMD-FM calculations up to 300 fm/c, and open circles are those derived from the CTIM fits. The insert is same but for the results for the CoMD events.

Figure 5

Time evolution of the flow for $Z=1\text{–}6$ fragments. The flow values for different time are extracted using the linear fits within $-0.3\le Y/Y_{\text{proj}}\le 0.3$.

Figure 6

Same plot as Fig. 3, but for the AMD-FM+Gemini events.

Figure 7

Same plot as Fig. 4, but for the AMD-FM+Gemini events (circles), for the filtered AMD-FM+Gemini events (squares) and for the filtered AMD-FM+Gemini events where the $\langle P_x/A\rangle$ values are in the reaction planes reconstructed using the AC method (triangles). The insert shows the comparison between the theoretical flow values from the filtered AMD-FM+Gemini events with the reaction planes reconstructed using the AC method (triangles), and the experimental flow values from the events of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at 35 MeV/nucleon within the impact parameter range of 3-6 fm characterized using the charged particle multiplicity (stars). The experimental results are taken from Ref. [32].

Figure 8

Same plot as Fig. 3, but for the filtered AMD-FM+Gemini events.

Figure 9

Same plot as Fig. 3, but for the filtered AMD-FM+Gemini events where the $\langle P_x/A\rangle$ values are in the reaction planes reconstructed using the AC method.

Figure 10

(a) Flow as a function of incident energy for proton, $\alpha$, $Z$ = 3–5 and $Z\ge 6$ fragments from the Ar+Ni system. Circles represent the experimental results directly taken from Ref. [26], and lines are the corresponding quadratic polynomial fittings. (b) Flow as a function of particle type for proton, $\alpha$, $Z$ = 3–5 and $Z\ge 6$ fragments at the incident energies of 32, 40, 52, and 63 MeV/nucleon, where the incident energies decrease from top to bottom.

Figure 11

Same plots as Fig. 10, but for those after the artificial shift in the $Y$ axis to fix the negative offsets around the balance energy.

Figure 12

(a) Same plot as Fig. 10, but as a function of $Z$. (b) Same plot as Fig. 11, but as a function of $Z$. See the details in the text.