Common translation factor method

Abstract

The basis and workings of a very useful technique in the treatment of atomic collisions is explained, which is the introduction of a common translation factor in the framework of close-coupling expansions. A historical review of the subject is presented, together with a description of the properties of the factor, and a detailed illustration of its performance.

Uncertainty estimates for theoretical atomic and molecular data

“…For more recent, but somewhat more specialized accounts we refer the reader to [149,150] These defects can be remedied by including electron translation factors (ETFs) or by using reaction coordinate techniques [151,152]. An alternative method is the hyperspherical close coupling (HSCC) approach, in which a rescaled Schrödinger equation written in terms of hyperspherical coordinates is solved (see ref.…”

Charge transfer in proton–helium collisions from low to high energy

“…In the intermediate energy range, electron translation factors (ETFs) can have a significant impact on the cross section. Their effect was included through the approximation of the common translation factor [32], in the form first introduced in [33]. In this approach, the matrix elements of the operators x 2 , xz and z 2 in the basis of the electronic wavefunctions are used to correct the radial and rotational non-adiabatic couplings.…”

Ab initiotreatment of charge transfer in ion-molecule collisions based on one-electron wave functions

“…Common translation factors have been extensively employed in previous ion-atom and ion-diatom collisional studies (see, for example, [30,31]) to ensure that a truncated expansion of the scattering wave function fulfills the boundary conditions of the system and preserve the Galilean invariance of the results. The use of a velocity field (or CTF) has been shown to be one of the most practical choices, as a correction to potential or dynamical couplings can still be written without explicit plane-wave functions in the integrands.…”