Three-body system dynamical treatment

M. Ragni, A.C.P. Bitencourt, V. Aquilanti, Hyperspherical and related types of coordinates for the dynamical treatment of three-body systems, Prog. Theor. Chem. Phys. 16 (2007) Part 1,123. 

HYPERSPHERICAL AND RELATED TYPES OF COORDINATES FOR THE DYNAMICAL TREATMENT OF THREE-BODY SYSTEMS... 

For a complete treatment of a laser-driven molecule, one must solve the many-body, multidimensional time-dependent Schrodinger equation (TDSE). This represents a tremendous task and direct wavepacket simulations of nuclear and electronic motions under an intense laser pulse is presently restricted to a few bodies (at most three or four) and/or to a model of low dimensionality [27]. For a more general treatment, an approximate separation of variables between electrons (fast subsystem) and nuclei (slow subsystem) is customarily made, in the spirit of the BO approximation. To lay out the ideas underlying this approximation as adapted to field-driven molecular dynamics, we will consider from now on a molecule consisting of Nn nuclei (labeled a, p,...) and Ne electrons (labeled /, j,...), with position vectors Ro, and r respectively, defined in the center of mass (rotating) body-fixed coordinate system, in a classical field E(f) of the form Eof t) cos cot). The full semiclassical length gauge Hamiltonian is written, for a system of electrons and nuclei, as [4]... 

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