Few-body semiclassical approach to nucleon transfer and emission reactions

Department of Information Systems & Integrated Science and Engineering Laboratory Facilities (ISELF), St. Cloud State University, St. Cloud, MN 56301-4498, USA

^a e-mail: rasultanov@stcloudstate.edu
^b e-mail: dcguster@stcloudstate.edu

Published online: 1 April 2014

Abstract

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 A₁(Z_A1, M_A1) and A₂(Z_A2, M_A2), move along classical trajectories ${\overrightarrow{R}}_1\left(t\right)$ and ${\overrightarrow{R}}_2\left(t\right)$ 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 a unified manner. In order to solve the 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 (A₁ ≡ A₂) and also the two-level approximation in the expansion over the target (subsystem) functions is used, the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic ${\overrightarrow{R}}_1\left(t\right)$ and ${\overrightarrow{R}}_2\left(t\right)$ trajectories of the nuclear cores, a self-consistent approach based on the Feynman path integral theory is applied.