Direct-interaction techniques are applied to nucleusnucleus rearrangement processes in which a nucleon is transferred from one nucleus to the other during the scattering. A formal expression is derived for the transition amplitude assuming a reaction mechanism different from that usually employed in direct-interaction rearrangement processes (such as deuteron stripping). The mechanism in the usual theories is due to the potential between the transferred panticle and one of the nuclear core'' systems; the interaction between the two nuclear cores is considered responsible in first order for the rearrangement scattering. Physical arguments support this view for the nucleusnucleus scattering mechanism and are based on the overwhelming importance of the Coulomb interaction in lowenergy processes. The amplitude for the rearrangement scattering is then expressed formally in terms of the complete amplitude or T matrix for the dominant core-core interaction. The specific example of the neutron transfer process is considered in a first-order treatment, where all purely nuclear-scattering interactions are ignored, and the only scattering arises from the Coulomb potential. The matrix element for the reaction is obtained in closed form and the results are compared both with experiment and with other treatments of rearrangement scattering. (auth)