Hamiltonian scattering path

That is done in the penultimate section where we present some preliminary DWBA calculations of the resonances in the H+(X) -> H(X) addition reaction using a fit to an ab initio potential energy surface. A reduced-dimensionalty scattering space is derived based on a novel scattering path hamiltonian. 

There are many other approaches to obtain resonance energies and widths, many are reviewed in this volnme. One that we consider in the next two sections is the distorted wave Born approximation (DWBA). In the following section the DWBA is tested against accurate complex coordinate calcnlations reported previously for a collinear model van der Waals system(l). The DWBA is then used to obtain the resonance energies and widths for the HCO radical. A scattering path hamiltonian is developed for that system and a 2ND approximation to it is given for the J>0 state. 

To obtain the scattering path hamiltonian we would begin with the general body-fixed hamiltonian in the variables (R.v.r)(13) and simply re-express it in terms of the variables (t.n.r) using the above transformation. For simplicity we consider the zero partial wave, J 0, and we obtain... 

We have presented a sample of resonance phenomena and calculations in reactive and non-reactive three-body systems. In all cases a two-mathematical dimensional dynamical space was considered> leading to a great simplification in the computational effort. For the H-K 0 system, low-energy coupled-channel calculations are planned in the future to test the reliablity of the approximations used here, i.e., the scattering path hamiltonian as well as the distorted wave Born approximation. Hopefully these approximations will prove useful in larger systems where coupled-channel calculations would be prohibitively difficult to do. Such approximations will be necessary as resonance phenomena will continue to attract the attention of experimentalists and theorists for many years. 

Path Integral Methods Reaction Path Hamiltonian and its Use for Investigating Reaction Mechanisms Reactive Scattering of Polyatomic Molecules State to State Reactive Scattering Statistical Adiabatic Channel Models Time Correlation Functions Transition State Theory Unimolecular Reaction Dynamics. 

In the case of scattering, without electromagnetic fields, the dependence with time of the Hamiltonian comes from the classical path followed by M point-like nuclei. In such case, the external potential t) can be written ... 

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