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Few-body semiclassical approach to nucleon transfer and emission reactions

A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A$_1(Z_{A_1}, M_{A_1})$ and A$_2(Z_{A_2}, M_{A_2})$, move along classical trajectories $\vec R_1(t)$ and $\vec R_2(t)$ respectively, while the dynamics of the lighter neutron, n, is considered from a quantum mechanical point of view. Here, $M_i$ are the nucleon masses and $Z_i$ are the Coulomb charges of the heavy nuclei ($i=1,2$). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear potentials is applied so that all three channels (elastic, rearrangement and break-up) are described in an unified manner. In order to solve these time-dependent equations the Faddeev components of the total three-body wave-function are expanded in terms of the input and output channel target eigenfunctions. In the special case when the nuclear cores are identical (A$_1 \equiv$ A$_2$) and the two-level approximation in the expansion over target functions the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic $\vec R_1(t)$ and $\vec R_2(t)$ trajectories of the nuclear cores a self-consistent approach based on the Feynman path integral theory is applied.