Berakdar, J.

This work gives a brief overview on the recent progress in the analytical treatment of correlated few-body Coulomb continuum systems. Special emphasis is put on the approximate separability of the long and short-range dynamics. This separability is exposed by expressing the total Hamiltonian of the system in appropriate curvilinear coordinates in which case the total Hamiltonian breaks down into two commuting operators: an operator whose eigenstates decay for large inter-particle distances. The states associated with the second operator posses an oscillatory behaviour in the asymptotic region and can thus be assigned to the long-range behaviour of the few-body system. At finite distances the total Hamiltonian contains in addition to these two operators a term which mixes the long and the short range dynmics. The many body wave function in the asymptotic region is derived and discussed. Methods that couple the asymptotic region to finite distances are also presented. The strength and weaknesses of the derived approximate wave functions are demonstrated by evaluating scattering transition matrix elements and comparing to available experimental data. We also discuss a recent Green function methodology that is capable of dealing with large finite and extended systems of charged particles. In addition, we give a brief account of the Green function approach as applied for the determination of the thermodynamics properties and critical phenomena of finite interacting systems.

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