Static scattering potentials

Static scattering singularities are well known in atomic and nuclear physics. A prominent example is the phenomenon of orbiting, which occurs whenever the effective scattering potential exhibits a local maximum (see, e.g., Norenberg and Weidenmiiller (1976)). 

In the original Schiff treatment, the phase shift is given in terms of the static scattering potential U r) as... 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

Some allowance for the effects of distortion of the positronium and the target atom could be made by introducing the van der Waals interaction potential into the static-exchange equation for the scattering function, and Martin and Fraser (1980) and Au and Drachman (1986) calculated this potential with such an aim in mind. Its form, as determined by these latter authors, and also by Manson and Ritchie (1985), is... 

Electron scattering from molecules is receiving increasing attention, and theoretically it can be treated by calculation of the static potential (the interaction potential of an electron with the unperturbed charge distribution). Ab initio calculations for N2 using wavefunctions varying between minimal-basis and near-HF quality have been reported by Truhlar et a/.,237 and compared with semi-empirical INDO calculations. The anisotropy of the potential is only correctly described if tf-functions are included in the basis set. 

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