3 N / Z 㻜 㻡 㻝㻜  A1$_{ / }$A2 =   1  10  100 㻜㻚㻡 㻝 㻝㻚㻡 㻞 (i) (ix) (viii) (vii) (ii) (iii) (iv) (v) (vi) E / A  [MeV] F P Pb + Ca 208 40 3.0  x 10  s -22 6.0  x 10  s -22 9.0  x 10  s -22 10 fm 9.0  x 10  s -22 6.0  x 10  s -22 3.0  x 10  s -22 10 fm E  / A = 3 MeV cm E  / A = 4 MeV cm FIG. 2: N/Z dependence of the upper energy-limit of charge equilibration based on Eq. (1) in the center-of-mass frame, where A 1 > A 2 is assumed without loss of generality. Values with different total masses A = 100, 200, 300, 400, and 500 are plotted for each A 1 /A 2 , which correspond to black lines from bottom to top in each group (values are too crowded to distinguish the total mass difference, for the cases of A 1 /A 2 = 10 and 100), and lines are drawn to guide eyes. Each TDHF calculation is shown as a blue bar, where the central points correspond to the value obtained by Eq. (1) for each reaction, and Roman numbers distinguish reactions shown in Table I. FIG. 3: Real-time dynamics of charge distribution for $^{208}$Pb + $^{40}$Ca (SLy4d) is shown for a fixed impact parameter 7.5 fm. The upper and the lower panels show cases with E cm /A = 3.0 MeV and 4.0 MeV, respectively. For both cases, $^{208}$Pb is coming from the left, and $^{40}$Ca from the right. The colored regions show the distribution of charge (proton-rich part), and the contours being incremented by 0.02 fm $_{−}$3 show the density. Domains with the proton-to-neutron density ratio greater than 0.78 and 0.72 are colored in red and yellow, re- spectively. the upper-limit of charge equilibration depends largely on the Fermi energy, and the proton-neutron asymmetry can contribute to the shift of the upper-limit, where the dependence of the upper-limit on the mass-asymmetry is remarkable. Let us move on to the comparison to the experiments. It can be seen that existing experimental data agrees with the present upper-limit formula. For instance, the fol- lowing experiments show charge equilibration: $^{40}$Ar + $^{58}$Ni at E$_{lab}$/A =7.0 MeV [11], and $^{56}$Fe + $^{165}$Ho ($^{209}$Bi) at E$_{lab}$/A = 8.3 MeV [12]. The following experiment shows the disappearance of charge equilibration: $^{112}$Sn + $^{124}$Sn at E$_{lab}$/A =50 MeV [13, 14]. Recently, experi- ments: 124 , $^{112}$Sn + 124 , $^{112}$Sn at E$_{lab}$/A = 35 and 50 MeV respectively was performed at Michigan State University [16]. One remarkable result here is that the final frag- ments are not so close to charge equilibrium even in lower energy collisions with E$_{lab}$/A =35 MeV. The disappear- ance of charge equilibration for this experiment has not been explained. Because the upper limit of charge equi- libration is calculated to be E$_{lab}$/A =27.6 MeV from Eq. (1), this question can be understood now. The suppression of charge equilibration contribute nat- urally to the production of exotic fragment; more ex- otic nuclei far from the equilibrated N/Z ratio are to be synthesized above the present upper-limit. Because the We now point out some interesting details of charge- equilibration dynamics for collisions below the present upper energy limit. We shall first investigate it with a focus on the iv-GDR in a collision between light nuclei. Figure 4 (a) shows the time-evolution of charge distri- bution for $^{24}$O + $^{24}$Mg. We see the appearance of the iv-GDR and the oscillation of well-localized charge (4.5, 6.0 × 10 − 22 sec). The charge equilibration is synchro- nized with the iv-GDR. This is, however, seen only for bombarding energies of the 3rd generation RI-beam facil- ities are sufficiently high to exceed the upper-limit, the present upper-limit ensures more production of further exotic isotopes by the latest and the future RI-beam fa- cilities. In fact, in the experiment of Ref. [15], the yield of exotic fragments was increased simply by putting the beam energy higher than the present upper-limit. It is also of much interest to explore the novel possibility of the synthesis of exotic nuclei by collisions including only β - stable nuclei. Such possibilities have not attracted much attention, but may emerge with various feasibilities of the production of exotic spieces, if the experiment is set for energies beyond the present upper-limit. As an ex- ample, Fig. 3 shows the real-time dynamics of $^{208}$Pb + $^{40}$Ca around the energy where the production of exotic nuclei starts; the upper energy limit is 3.66 MeV (See Table I), fusion appears at E$_{cm}$/A = 3.0 MeV (upper panels), and break-up is seen at 4.0 MeV (lower panels). β -unstable fragments are emitted only for the bombard- ing energy higher than the upper-limit; for instance, a small fragment in the lower-right panel of Fig. 3 is $^{62}$Mn (numbers of nucleon are rounded to be integer), for which the stable isotope is $^{55}$Mn.