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collisions between light nuclei. Similar results are ob- tained in [2–8]. Next, we move on to collisions involving a heavier nucleus; e.g. $^{24}$Mg + $^{208}$Pb, as shown in Fig. 4 (b). Charge-equilibration dynamics is not similar to the motion of the iv-GDR in this case, because no significant oscillations of the localized charge appear. Instead a radi- ally layered structure of the composite nucleus is formed (7.5 × 10 − 22 sec), in which a relatively neutron-rich core appears in the center, a proton-rich layer surrounds it, and a neutron-rich skin is in the surface. This seems to be due to the Coulomb repulsion, hence the radial distri- bution of charge is formed. Here one can find analogous situation of isovector monopole excitation. It means that the radial flow plays a prominent role in such low energy collisions. Similar layered structures are obtained in the TDHF calculations (with both Skyrme parameter-sets) listed in Table I except for $^{24}$Mg + $^{24}$O. Consequently, charge equilibration, which is dependent on the mass, has been clarified to be related not only with the isovector gi- ant dipole excitations, but also with the isovector giant monopole excitations. 

Finally, let us comment on the diffusion-type mech- anism towards charge equilibrium. The mechanism of charge equilibration discussed in this Letter is valid at lower energies (lower than the upper energy-limit). At much higher energies, collisions between nucleons and the diffusion contribute mostly to charge equilibration (for example, see [17, 18]). As the diffusion is a slow pro- cess, it is unlikely to attain the charge equilibrium within 

the initial stage. Energy-dependent equilibration mecha- nisms of a similar kind have been reported in condensed matter physics (see [19–21]), where the equilibration is fast for lower energies (temperatures), and quite slow for higher energies. Such a similarity between completely different physical systems is interesting. 

In this Letter the mechanism of charge equilibration, in which nucleons with the Fermi velocity play a primary role, has been presented, and its validity is examined by comparison to virtually all existing relevant experimental data. This concept has been further analyzed in terms of a three-dimensional time-dependent density function for- malism. The upper energy-limit of charge equilibration has a crucial impact on the nuclear synthesis of exotic nu- clei. Properties presented in this Letter will give a sound motivation for the production of further exotic isotopes by the latest and the future RI-beam facilities. 

This work was supported in part by EMMI project of the Helmholtz Alliance, by JSPS Core-to-Core pro- gram EFES and by grant-in-aid for Scientific Research (A) 20244022. Y.I. thanks for the JSPS fellowship, and express his gratitude to Dr. C. Simenel. T.O. thanks Prof. P. Bonche for long-term valuable collaboration. 

[1] H. Freiesleben and J.V. Kratz, Phys. Rep. 106 (1984) 1. 

[2] M. Berlanger, A. Gobbi, F. Haneppe, U Lynen, C. Ngˆ o and A. Olmi, Z. Phys. A 291 (1979) 133. 

[3] E.S. Hernandez, W.D. Myers, J. Randrup and B. Re- maud, Nucl. Phys. A 361 (1981) 483. 

[4] P. Bonche and N. Ngˆ o, Phys. Lett. B 105 (1981) 17. 

[5] E. Suraud, M. Pi, and P. Schuck, Nucl. Phys. A 492 (1989) 294. 

[6] V. Baran, D.M. Brink, M. Colonna, and M. Di Toro, Phys. Rev. Lett. 87 (2007) 182501. 

[7] C. Simenel, Ph. Chomaz, and G. de France, Phys. Rev. Lett. (2001) 2971. 

[8] C. Simenel, Ph. Chomaz, and G. de France, Phys. Rev. C 76 (2007) 024609. 

[9] W.D. Myers and W.J. Swiatecki, Ann. Phys. 55 (1969) 395. 

[10] W.D. Myers, Phys. Lett. 30B (1969) 451. 

[11] B. Gatty, D. Guerreau, M. Lefort, X. Tarrago and J. Galin, Nucl. Phys. A 253 (1975) 511. 

[12] H. Breuer et. al. , Phys. Rev. Lett. 43 (1979) 191. 

[13] P. M. Milazzo et. al. , Phys. Rev. C66 (2002) 021601. 

[14] W.P. Tan et. al. , Phys. Rev. C64 (2001) 051901. 

[15] M. Mocko et. al. , Phys. Rev. C76 (2007) 014609. 

[16] M.B. Tsang et. al. , Private communication. 

[17] L. Shi and P. Danielewicz, Phys. Rev. C 68 (2003) 064604. 

[18] M.B. Tsang et. al. , Phys. Rev. Lett. 102 (2009) 122701. 

[19] L.D. Landau and Zh. Eksperim, Soviet Phys. - JETP 5 (1957) 101. 

[20] W.R. Abel, A.C. Anderson, and J.C. Wheatley, Phys. Rev. Lett. 17 2 (1966) 74. 

[21] A.J. Leggett, Rev. Mod. Phys. 47 No.2 (1975) 331. 

