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The adiabatic nuclei approximation is used to study low energy positron collisions with hydrogen moleci~les. The interaction of the positrons with the hydrogen molecules is represented as a superposition of electrostatic and polarization potentials. Total and differential elastic and momentum transfer cross sections are calculated. The effect of small variations in the potentials, and the convergence of the partial wave expansion are discussed. The annihilation rate of the positrons is calculated with and without incorporating the effect of distortion of the electron cloud by the incoming positrons. Rotational excitation cross sections, both differential and total, are presented. The results are cornpared, where possible, to recent similar two-center calculations of Hara, and experimental results of Coleman er a/.

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