Experimental investigation of abnormal transverse flow enhancement of $\alpha$ particles in heavy-ion collisions

The mass dependence of the transverse flow for $Z=1$–5 fragments from the collisions of ${}^{40}\mathrm{Ar}+{}^{27}\mathrm{Al}, {}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$, and ${}^{40}\mathrm{Ar}+{}^{58}\mathrm{Ni}$ at 47 MeV/nucleon is investigated experimentally in this article. The transverse flow values are determined using the in-plane components of the fragment transverse momenta, where three conventional methods, i.e., the kinetic flow tensor method, the transverse momentum analysis method, and the azimuthal correlation method, are applied to reconstruct the reaction plane in an event-by-event basis. It is demonstrated from the comparison of the present experimental mass dependent flow measurements and the model simulations using an improved antisymmetrized molecular dynamics model that the experimentally observed abnormal $\alpha$ transverse flow enhancement is closely related to the reaction plane reconstruction procedure in the flow extraction. We further investigate the physical existence of the abnormal $\alpha$ flow behavior using a two-particle azimuthal correlation method, which allows us to provide the relative flow magnitude information with an identification of fragment charge number without the knowledge of the reaction plane differing from the three conventional methods. It is found that the relative flow magnitudes deduced from the two-particle azimuthal correlation functions with an identification of $Z$, with the correction for the recoil effect imposed by the momentum conservation, show a monotonically increasing trend as a function of fragment charge number, with no exception of the $\alpha$ flow enhancement. These results, in addition to those from the improved antisymmetrized molecular dynamics model simulations, definitely provide experimental evidences for the inexistence of the abnormal $\alpha$ flow behavior in the heavy-ion collisions at the present incident energy region in nature.

Figure 1

(a) Normalized charged particle multiplicity $N_{ch}$ distributions. (b) Reduced impact parameter $b/b_{max}$ versus $N_{ch}$ evaluated using Eq. (1). Left, middle, and right panels are from the systems of ${}^{40}\mathrm{Ar}+{}^{27}\mathrm{Al}, {}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$, and ${}^{40}\mathrm{Ar}+{}^{58}\mathrm{Ni}$, respectively.

Figure 2

Average in-plane momentum per nucleon $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\text{proj}}$ for $Z=1–5$ fragments from the ${}^{40}\mathrm{Ar}+{}^{27}\mathrm{Al}, {}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$, and ${}^{40}\mathrm{Ar}+{}^{58}\mathrm{Ni}$ reaction systems. Top, middle, and bottom panels in each subfigure are the results from the reaction planes reconstructed using the KFT, TMA, and AC methods as indicated on the left panels. Solid lines represent the linear fits for the data in the region of $-0.2\le Y/Y_{\text{proj}}\le 0.4$.

Figure 3

Flow as a function of $Z$ from (a) ${}^{40}\mathrm{Ar}+{}^{27}\mathrm{Al}$, (b) ${}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$, and (c) ${}^{40}\mathrm{Ar}+{}^{58}\mathrm{Ni}$. Solid dots, squares, and triangles represent the experimental results obtained from the reaction planes reconstructed using the KFT, TMA, and AC methods, respectively, whereas those from the filtered AMD-FM $+$ Gemini events are correspondingly shown by circles, open squares, and open triangles.

Figure 4

Comparison of linear fits to average in-plane momentum per nucleon $\langle P_x/A\rangle$ as a function of the scaled rapidity $Y/Y_{\text{proj}}$ for $Z=1–3$ fragments from the ${}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$ system. The results are same as those of Fig. 2, but shown in an expanded scale along the $Y$ axis. Left, middle, and right panels are those deduced using the KFT, TMA, and AC methods, respectively.

Figure 5

Flow as a function of $Z$ from the AMD-FM events of ${}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$. Dots are the results deduced without the reaction plane reconstruction process (No RP), and inverted triangles, triangles, and squares are those from the reaction planes reconstructed using the KFT, TMA, and AC methods, respectively.

Figure 6

Two-particle azimuthal correlation functions $C\left(\mathrm{\Delta }\varphi \right)$ for $Z=1–4$ pairs with (squares) and without (dots) the correction for the recoil effect from the system of ${}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$. The results shown in (a)–(d) are obtained from the experimental data, whereas those shown in (e)–(h) are from the filtered AMD-FM $+$ Gemini events. The $Z$ number for labeling each panel corresponds to the $C\left(\mathrm{\Delta }\varphi \right)$ for which both correlated particles are demanded to be with the same given $Z$ number in each of the pairs used to determine $\mathrm{\Delta }\varphi$. Solid and dashed curves in each panel represent the fits to the results with and without the correction for the recoil effect using Eq. (12).

Figure 7

Relative flow magnitude $f_1$ as a function of $Z$ extracted from the $C\left(\mathrm{\Delta }\varphi \right)$ with (squares) and without (dots) the recoil effect correction from the collision system of ${}^{40}\mathrm{Ar}+{}^{48}\mathrm{Ti}$. The results shown in (a) are obtained from the experimental data, whereas those shown in (b) are from the filtered AMD-FM $+$ Gemini events.