Correlation forces in electron-scattering processes via density-functional theory: Electron collisions with closed-shell atoms

Polarisation potentials for positron-molecule scattering processes

“…We have shown that the treatment of such forces in the intermediate range of distances is a crucial element of the model and that we can test this region in a parameter-free fashion by using either of the possible crossing radii between the DFT-SR forces and the LR-polarisation potential. The present calculations indeed show that, contrary to what has been found for electron collisions [13,16,33], the scattering processes with positron projectiles invariably require a stronger intermediate-range potential and therefore are better described by choosing the outer cut-off radii as matching distances within the LYP formulation of the correlation forces. In other words, the present DFT model allows one to make a distinction, as is physically expected, between correlation effects from either electron or positron collisions by using a stronger DFT model of correlation forces for the latter as opposed to the former projectile.…”

“…It still considers as negligible, however, the differences in non-adiabatic, short-range effects between electron projectiles and positron projectiles. This has been a reasonable assumption when tested for atomic targets [16,17]. That it may be also plausible for the present case needs to be verified with calculations, as we shall discuss in the following Sections.…”

“…Several suggestions by various authors [14,15] produced different choicesf~(L R) and provided the correlation energy as a direct, local functional of the target electronic density. We have discussed this derivation in detail earlier on [13,16] and will not be repeating it here. Suffice it to say, however, that the evaluation of the correlation energy as a functional of the target density, and given by the specific form derived forf~ff, li) in (4) [19], is based on the following physical picture [24]:…”

“…when long-range correlation effects (static correlation) play a negligible role [14]. The conclusion drawn earlier on from the above considerations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]16] was that one could approximate the correlation energy, Ec, within the target electrons, by using an expression of the following type:…”

FERM3D: A finite element R-matrix electron molecule scattering code

“…[20], the polarisation-correlation contribution (basically the distortion-relaxation effect on the molecule generated by the incoming electron) is extremely important for an accurate description of the scattering process. We have recently added the capability of using a parameter-free correlation-polarisation potential [21,22], which is based on DFT ideas. The long-range part of this potential can be thought of as a simple multipole expansion, of which we retain only the dipole terms:…”