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.