Practical criterion for the determination of translation factors

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Abstract
Following an idea of Rankin and Thorson, a method is proposed to determine translation factors in the molecular model of atomic collisions, and for low and intermediate nuclear velocities. The method is based on the minimization of a measure of all (electrostatic and dynamical) couplings between the states included in, and those left out from, the molecular expansion. The properties of this measure are discussed. In particular, its evaluation involves the calculation of a few new matrix elements, and this can be performed analytically when Gaussian-type orbitals are used to construct the wave functions. The method also provides a comparison between all approaches that employ translation factors, and a test of the conditions that are usually enforced on these factors.