Common Translation Factor Research Articles

On the choice of translation factors for approximate molecular wavefunctions

A critical analysis is presented for three different methods which introduce translation factors in the molecular approach to atomic collisions. Unlike other contributions in this field, approximate one- and many-electron wavefunctions are explicitly considered from the start. The authors' conclusions are illustrated with the calculation of the charge exchange cross section for He2++H(1s) to He+(2s,2p)+H+, which exhibits a strong origin dependence in the standard perturbed stationary states (PSS) approach. The authors' main (and new) conclusions are: (i) that the Bates-McCarroll method, and the method of projection on atomic components, are not necessarily convergent, and are exceedingly time consuming for approximate wavefunctions and (ii) that the common translation factor method is the most promising approach at present. However, before it can be used systematically in molecular calculations, more research is needed regarding its sensitivity to the analytical form of the common factor-otherwise some of the defects of the PSS approach reappear (in disguise) using this method.

Common variational translation factor for low-energy atomic collisions

Proposes a single translation factor multiplying a truncated expansion on molecular orbitals to describe the collision of a slow charge with a one-electron atom in the impact parameter approximation. Proposing a quadratic polynomial dependence on electron coordinates, the translation factor reproduces the asymptotic flux of the electron density and it also generates the translation velocity of the electron associated with the state of motions of the inertial observer; transition probabilities are therefore Galilean invariant. The coefficients of the polynomial are determined by a variational procedure, which determines the field of velocities produced by the phase factor adjusted to describe both the density flux inside each state of the expansion due to its time dependence, and the flux associated with transitions between states.