GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s54> GLYPH<s40>GLYPH<s98>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s82> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s40>GLYPH<s50> GLYPH<s46>GLYPH<s50> GLYPH<s53> GLYPH<s44>GLYPH<s32> GLYPH<s86> GLYPH<s48> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s45>GLYPH<s32>GLYPH<s48> GLYPH<s46>GLYPH<s48> GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s54> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s116> GLYPH<s32> GLYPH<s47> GLYPH<s82> GLYPH<s40> GLYPH<s82> GLYPH<s44>GLYPH<s116>GLYPH<s41> GLYPH<s82> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s40>GLYPH<s50> GLYPH<s46>GLYPH<s50> GLYPH<s53> GLYPH<s44>GLYPH<s32> GLYPH<s86> GLYPH<s48> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48> GLYPH<s46>GLYPH<s48> GLYPH<s56> GLYPH<s50> GLYPH<s48> GLYPH<s48> GLYPH<s50>GLYPH<s46>GLYPH<s48> 4 GLYPH<s45> GLYPH<s50> GLYPH<s45> GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s45> GLYPH<s50> GLYPH<s45> GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s90>GLYPH<s32>GLYPH<s45>GLYPH<s32>GLYPH<s97>GLYPH<s120>GLYPH<s105>GLYPH<s115> GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s49>GLYPH<s51>GLYPH<s55>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s50>GLYPH<s55>GLYPH<s53>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52>GLYPH<s49>GLYPH<s50>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s53>GLYPH<s53>GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s54>GLYPH<s56>GLYPH<s55>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s56>GLYPH<s50>GLYPH<s53>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s57>GLYPH<s54>GLYPH<s50>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s49>GLYPH<s48>GLYPH<s48> GLYPH<s120> GLYPH<s120> GLYPH<s120> GLYPH<s88>GLYPH<s32>GLYPH<s45> GLYPH<s32>GLYPH<s97> GLYPH<s120>GLYPH<s105>GLYPH<s115> FIG. 3: ζ ( R , t ) against t given in three selected intervals of t . R is fixed at (2 . 25 , π, 0) (i.e., R is lying along the negative Z-axis with R = 2 . 25. Meanwhile particle 3 is close to the op- posite end of the up-vertex of the initial triangle). The three curves are associated with the three choices of Δ, namely, 0, 200 , and 400. When Δ = 0, the interval of ωt is [0 , 2 π ] (solid curve). When Δ = 200, it is [200 π, 202 π ] (dash curve). When Δ = 400, it is [400 π, 402 π ] (dash-dot-dot curve). V 0 = 0 . 08 (a) and − 0 . 08 (b). The other parameters are the same as in Fig.2. (Color online) FIG. 1: Contour diagram of the one-body density ρ 1 ( r 1 ) of the initial state plotted in the X-Z plane. η = 1 . 5 and | a | = 1 . 5 are adopted. Each maximum is marked with a × . The three particles form a regular triangle with side-length ∼ 2 . 6 initially. (Color online) GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s54>GLYPH<s48> GLYPH<s57>GLYPH<s48> GLYPH<s49>GLYPH<s50>GLYPH<s48> GLYPH<s49>GLYPH<s53>GLYPH<s48> GLYPH<s49>GLYPH<s56>GLYPH<s48> GLYPH<s40>GLYPH<s99> GLYPH<s41> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52>GLYPH<s48>GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s53>GLYPH<s51>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s50>GLYPH<s54>GLYPH<s55>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s51>GLYPH<s56>GLYPH<s49>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s52>GLYPH<s57>GLYPH<s53>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s54>GLYPH<s48>GLYPH<s56>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s55>GLYPH<s50>GLYPH<s50>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s56>GLYPH<s51>GLYPH<s54>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s53>GLYPH<s48>GLYPH<s48> GLYPH<s120> GLYPH<s120> GLYPH<s120> GLYPH<s116> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s50>GLYPH<s46>GLYPH<s53> GLYPH<s51>GLYPH<s46>GLYPH<s48> GLYPH<s40>GLYPH<s98>GLYPH<s41> GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s54>GLYPH<s52>GLYPH<s55>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s50>GLYPH<s57>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s57>GLYPH<s52>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s50>GLYPH<s53>GLYPH<s57>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s51>GLYPH<s50>GLYPH<s51>GLYPH<s55> GLYPH<s48>GLYPH<s46>GLYPH<s51>GLYPH<s56>GLYPH<s56>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s52>GLYPH<s53>GLYPH<s51>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s53>GLYPH<s49>GLYPH<s56>GLYPH<s48> GLYPH<s120> GLYPH<s120> GLYPH<s120> GLYPH<s116> GLYPH<s114> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s50>GLYPH<s46>GLYPH<s53> GLYPH<s51>GLYPH<s46>GLYPH<s48> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s55>GLYPH<s52>GLYPH<s53>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s52>GLYPH<s57>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50>GLYPH<s50>GLYPH<s51>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s50>GLYPH<s57>GLYPH<s56>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s51>GLYPH<s55>GLYPH<s50>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s52>GLYPH<s52>GLYPH<s55>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53>GLYPH<s50>GLYPH<s49>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s53>GLYPH<s57>GLYPH<s54>GLYPH<s48> GLYPH<s120> GLYPH<s120> GLYPH<s120> GLYPH<s116> GLYPH<s82> function, this is also true for other two particles. Then, the above process begins to reverse. When ωt = 2 π , the system recovers its initial status nearly. If the interaction is removed, the recovery is complete and the system will undergo an exact periodic motion with the period 2 π/ω . The motion is characterized by the repeating head-on 3-body collisions. each occurs once within the interval π/ω . FIG. 2: Contour plots of ρ R ( R, t ), ρ r ( r, t ), and ρ θ ( θ, t ) given in (a), (b), and (c), respectively, with η = 1 . 5, | a | = 1 . 5, V 0 = 0 . 08 and N 0 = 20. Each maximum is marked with a × . (Color online) However, due to the interaction, the recovery is not exact. When the time goes on the effect of the weak interaction will accumulate and gradually emerge. This is shown by the dash-curve of Fig.3a which describes the behavior of ζ ( R , t ) after 200 rounds of head-on collisions. Where the peak is lower than that of the solid curve. It implies that the density is diffusing. Furthermore, the peak of the dash-curve has shifted a little right implying that the arrival is a little delayed. The diffusion and the delay will become more explicit when t is larger as shown by the dash-dot-dot curve. When the interaction is at- tractive, the above repeating 3-body collisions remain, and the densities remain to be diffusing. However, in- stead of a delay, the peak will arrive at the end earlier as shown in Fig.3b, where V$_{0}$ = − 0 . 08. Due to the diffusion of the density as shown in Fig.3, the phenomenon of re- peating 3-body collisions will become ambiguous when t is sufficiently large. When V$_{0}$ is given at a number of values and R is fixed at (2 . 25 , π, 0), ζ ( R , t ) against ωt is plotted in Fig.4, in which ωt varies in an interval close to 201 π . In this figure both the locations and the heights of the peaks depend on the strength V$_{0}$ . In general, a larger | V$_{0}$ | will cause a stronger diffusion and therefore a shorter life of the phenomenon of clear repeating 3-body collisions, and a more positive (negative) V$_{0}$ will cause a larger shift of the peak to the right (left). In addition to V$_{0}$ , the evolution depends also on the range of interaction. Therefore, by observing the time-dependent densities, information on the interaction can be obtained. 1000 × 2 π , then t is from 0 to 0 . 001 sec). When t = 0, the inter-distances among the particles are about 2 . 6 as shown in Fig.1 and 2b. When the evolution begins, the peaks of ρ$_{r}$ and ρ$_{R}$ move inward synchronously, while ρ$_{θ}$ remains to peak at 90 ◦ . It implies a contraction of the regular triangle. Accordingly, the three particles rush towards the center leading to a 3-body head-on collision. When ωt is close to π/ 2, the inter-distances become much shorter, and ρ$_{θ}$ becomes nearly uniform. It implies that the geometric character (i.e., the regular triangle) will be spoiled when the particles are close to each other. After the first collision, the particles move outward. When ωt = π , each particle will be close to the op- posite end of its initial position as shown by the solid curve of Fig.3a. Where ζ ( R , t ) is given at the point R ≡ ( R, θ$_{R}$, φ$_{R}$ ) = (2 . 25 , π, 0) and ωt is given in the interval [0 , 2 π ]. The sharp peak of the solid curve demon- strates clearly that a particle arrives at the opposite end when ωt ∼ π . Due to the symmetrization of the wave