Bound state nuclear motion problem

The Solution of the Bound State Nuclear Motion Problem for Polyatomic Clusters 323... 

THE SOLUTION OF THE BOUND STATE NUCLEAR MOTION PROBLEM FOR POLYATOMIC CLUSTERS... 

This is referred as BO ansatz. This ansatz is taken as a variational trial function. Terms beyond the leading order in m/M are neglected m is the electronic and M is nuclear mass, respectively). The problem with expansion (4) is that functions /(r, R) contain except bound states also continuum function since it includes the centre of mass (COM) motion. Variation principle does not apply to continuum states. To avoid this problem we can separate COM motion. The remaining Hamiltonian for the relative motion of nuclei and electrons has then bound state solution. But there is a problem, because this separation mixes electronic with nuclear coordinates and also there is a question how to define molecule-fixed coordinate system. This is in detail discussed by Sutcliffe [5]. In the recent paper by Kutzelnigg [8] this problem is also discussed and it is shown how to derive adiabatic corrections using, as he called it, the Bom-Handy ansatz. There are few important steps to arrive at formula for a diabatic corrections. Firstly, one separates off COM motion. Secondly, (very important step) one does not specify the relative coordinates (which are to some extent arbitrary). In this way one arrives at relative Hamiltonian Hrd [8] with trial wavefunction If we make BO ansatz... 

The higher-order two-loop corrections are to be calculated within the so-called external filed approximation (i. e. neglecting by the nuclear motion), while the recoil effects require an essential two-body treatment. There are a few approaches to solve the two-body problem (see e.g. [31]). Most start with the Green function of the two-body system which has to have a pole at the energy of the bound state... 

Since nuiny processses demonstrate substantial quantum effects of tunneling, wave packet break-up and interference, and, obviously, discrete energy spectra, symmetry induced selection rules, etc., it is clearly desirable to develop meAods by which more complex dynamical problems can be solved quantum mechanically both accurately and efficiently. There is a reciprocity between the number of particles which can be treated quantum mechanically and die number of states of impcxtance. Thus the ground states of many electron systems can be determined as can the bound state (and continuum) dynamics of diatomic molecules. Our focus in this manuscript will be on nuclear dynamics of few particle systems which are not restricted to small amplitude motion. This can encompass vibrational states and isomerizations of triatomic molecules, photodissociation and exchange reactions of triatomic systems, some atom-surface collisions, etc. 

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