Quantum microscopic calculations to heavy-ion fusion and quasi-fission
The fusion between two heavy ions is a complex, highly non linear, and irreversible process. It is strongly coupled to internal structures of the colliding partners resulting from their quantum nature. Moreover the path to fusion strongly depends on the mass of the nuclei. For instance, two light nuclei in contact are likely to fuse, whereas this condition is clearly not sufficient for heavy systems which exhibit a fusion hindrance due to the quasi-fission mechanism. Indeed, in the latter, a mass flow between the reactants occurs, leading to a re-separation of more symmetric fragments in the exit channel. A good understanding of the competition between fusion and quasi-fission mechanisms is expected to be of great help to optimize the formation and study of heavy and superheavy nuclei.
Modern quantum microscopic models allow for a treatment of all degrees of freedom associated to the dynamics of each nucleon in non relativistic heavy-ion collisions. This provides a description of the complex reaction mechanisms with no parameter adjusted on reaction mechanisms. Such approaches can then be used to describe various reaction mechanisms with reaction partners spanning the entire nuclear chart.
To keep the amount of work for the physicist and his computer to a reasonable level, approximations are considered rather than solving the full Schrödinger equation. The choice of the approximation depends on the particular type of observable of interest. The Balian-Vénéroni variational principle  provides a useful starting point to derive various approximations to the quantum dynamics. For example, expectation values of one-body operators, like the evolution of the nuclear density, are computed using the time-dependent Hartree-Fock (TDHF) theory. The latter assumes a motion of independent particles in the mean-field generated by the ensemble of particles. For the fluctuation of one-body operators, however, we need to include some correlations by solving an equation equivalent to the time-dependent RPA. The range of applications of these approaches is quite large, from sub-barrier heavy-ion reactions  to more violent deep-inelastic collisions .
microscopic calculations are applied to nuclear collision around
the barrier, starting from light-medium systems to heavier
systems showing fusion hindrance. The quasi-fission
mechanism is investigated and compared to recent experimental
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 C. Simenel, Phys. Rev. Lett. 105, 192701 (2010).
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