Suppression of Charge Equilibration leading to the Synthesis of Exotic Nuclei Yoritaka Iwata $^{1}$, Takaharu Otsuka2 , $^{3}$, Joachim A. Maruhn$^{4}$, and Naoyuki Itagaki2 $^{1}$GSI Helmholtzzentrum f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany $^{2}$Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan $^{3}$Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033, Japan and $^{4}$Institut f¨ ur Theoretische Physik, Universit¨ at Frankfurt, D-60325 Frankfurt, Germany (Dated: June 15, 2018) Charge equilibration between two colliding nuclei can take place in the early stage of heavy-ion collisions. A basic mechanism of charge equilibration is presented in terms of the extension of single- particle motion from one nucleus to the other, from which the upper energy-limit of the bombarding energy is introduced for significant charge equilibration at the early stage of the collision. The for- mula for this limit is presented, and is compared to various experimental data. It is examined also by comparison to three-dimensional time-dependent density functional calculations. The suppression of charge equilibration, which appears in collisions at the energies beyond the upper energy-limit, gives rise to remarkable effects on the synthesis of exotic nuclei with extreme proton-neutron asymmetry. PACS numbers: 21.10.Ft, 25.70.-z, 25.70.Hi Charge equilibration is a rapid process during the early stage of heavy-ion collisions with a time scale of 10 − 22 sec (for a review, see [1]). Despite many theoretical at- tempts, its mechanism has remained an open problem, where only the relation with the isovector giant dipole resonance (iv-GDR) was discussed in certain cases (for example, see [2–8]). The charge equilibration is quite important, because it naturally prevents the synthesis of exotic nuclei with extreme proton-neutron asymmetry. As there are and will be the 3rd generation RI-beam fa- cilities, it is an urgent question whether such synthesis can be enhanced with higher beam energies or not. In this Letter, we first point out that there is an upper limit of the bombarding energy for the fast and significant charge equilibration in the initial stage of the collision. Microscopic three-dimensional (time-dependent) density functional calculations are systematically performed for the purpose of examination. We actually employ Skyrme time-dependent Hartree-Fock (TDHF) theory, which is a rather unique presently feasible method for the treat- ment of non-perturbative processes such as multi-nucleon transfers in a realistic framework. The suppression of charge equilibration brings about a favorable situation for the synthesis of exotic nuclei. The evaluation of the upper limit thus can have crucial sig- nificance for experiments on nuclei with extreme proton- neutron asymmetry. We shall consider the collision of a target nucleus with mass number A$_{1}$ , neutron (proton) number N$_{1}$ ( Z$_{1}$ ), with a projectile nucleus with A$_{2}$ , N$_{2}$ , and Z$_{2}$ . The total mass, neutron, and proton numbers are denoted by A , N , Z , respectively. We look at this problem from an intuitive and basic viewpoint. We begin with a picture that the charge equilibration takes place as wave functions of nucleons propagate from their orig- inal nucleus to the other nucleus in the initial stage of the collision. Namely, the regime of individual single- particle motion spreads out following the lowering of po- tential barrier between the two nuclei after the touching. where m , e , ϵ$_{0}$ , and r$_{0}$ are the nucleon mass, the charge We can introduce an ansatz that, in order for the fast charge equilibration to occur, the relative velocity v$_{r}$ of the two nuclei at the collision must be below the velocities corresponding to the proton or neutron Fermi momenta of both nuclei. By denoting the minimum of these four velocities as v min F , the present effect can be summarized by the statement that the upper limit of the bombarding energy for charge equilibration is determined by v$_{r}$ = v min F . The upper limit of the energy in the laboratory frame for charge equilibration is expressed as the sum of the kinetic energy for velocity v min F and the Coulomb energy at touching: Because this spreading occurs as a consequence of un- blocked single-particle motion, the process can be very fast; a particle travels into the other side within ∼ 10 − 22 sec at a quarter of light velocity, which roughly corre- sponds to the Fermi energy of normal nuclear matter. On the other hand, this propagation can be prohibited by the Pauli principle, while the neutron (or proton) ex- cess weakens this effect. Another important factor is the difference of velocities of the two nuclei. Because this spreading needs a certain time, it does not lead to charge equilibration in the initial stage if the relative velocity of the colliding nuclei is too large. In the charge equilibra- tion, protons and neutrons from both nuclei, particularly those near the Fermi levels, are mixed within a certain time after the touching. arXiv:1001.0850v1 [nucl-th] 6 Jan 2010 E$_{CE}$$_{,lab}$/A [MeV] = ℏ $^{2}$(3 π $^{2}$ρ$_{min}$ ) 2 / 3 2 m + e $^{2}$Z$_{1}$ Z$_{2}$ 4 πϵ$_{0}$r$_{0}$ A$_{1}$ + A$_{2}$ A$_{1}$A$_{2}$ ( A 1 / 3 1 + A 1 / 3 2 ) , (1) ρ$_{min}$ = min i ( ρ$_{ni}$, ρ$_{zi}$ ) = min i ( N$_{i}$ ( 4 πr$_{0}$ 3 A 1 / 3 i ) $_{−}$1 (1 − 3¯ ϵ )(1+ ¯ δ ) , Z$_{i}$ ( 4 πr$_{0}$ 3 A 1 / 3 i ) $_{−}$1 (1 − 3¯ ϵ )(1 $_{−}$¯ δ ) ) , (2)