Schiff approximation

Schiff approximation, electron nuclear dynamics (END), molecular systems, 339—342 Schrodinger equation ... 

We have implemented semiclassical corrections via the Schiff approximation [21] for small scattering angles. The direct differential cross section in the Schiff approximation within the END approximation is given hy [22]... 

L. I. SchifF, Approximation methods for bound states, in Quantum Mechanics, McGraw-Hill, New York, 1968, pp. 279-295. 

In Section 2 we briefly outline the salient features of END theory. In Section 3, we discuss the treatment of the END trajectories and their connection to the deflection function and differential cross section, as well as the derivation of the Schiff approximation. In Section 4, we present some simple applications and results of our approach. Finally, Section 5 contains our conclusions. 

The Schiff approximation applies only to small scattering angles, such that if R is the range of the potential that contributes significantly to the scattering, then small scattering angles are those that satisfy After... 

Once the deflection function and the phase shift have been determined for a collisional system, the direct differential cross section is obtained as the classical direct differential cross section when neglecting quantum interference effects [equation (13) with Pfo = 1] or by introducing semiclassical corrections using the Schiff approximation [equation (20)]. 

The advantage of semiclassical corrections is the inclusion of quantum effects to the differential cross section in the small scattering angle, the so-called forward peak character of the differential cross section. Furthermore, in the particular case of the Schiff approximation, the glory and rainbow angle effects in the interference are accurately represented. This behavior can be observed in Fig. 3, where the absolute direct differential cross section obtained with ENDyne goes through the experimentally determined absolute cross sections. 

From the Mulliken population, we calculate the charge exchange differential cross section. For a more complex system, in Fig. 6, the preliminary results for the direct and charge transfer differential cross section are shown for protons colliding with water at 5.0 keV as obtained by the Mulliken population analysis combined with the Schiff approximation [equation (23)]. Also for comparison we present the experimental results from Lindsay et al. [29]. 

Charon J, Blanco S, Cornet JP, et al Monte Carlo implementation of SchifFs approximation for estimating radiative properties of homogeneous, simple-shaped and optically soft particles application to photosynthetic micro-organisms, J Quant Spectrosc Radiat Transf, 2015. http //dx.doi.Org/10.1016/j.jqsrt.2015.10.020 (in press). 

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