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The rapid circularization and synchronization of the stellar components in aneccentric binary system at the onset of Roche lobe overflow (RLO) is afundamental assumption common to all binary stellar evolution and populationsynthesis codes, even though the validity of this assumption is questionableboth theoretically and observationally. Here we calculate the evolution of theorbital elements of an eccentric binary through the direct three-bodyintegration of a massive particle ejected through the inner Lagrangian point ofthe donor star at periastron. The trajectory of this particle leads to threepossible outcomes: direct accretion (DA) onto the companion star within asingle orbit, self-accretion (SA) back onto the donor star within a singleorbit, or a quasi-periodic orbit around the companion star. We calculate thesecular evolution of the binary orbit in the first two cases and conclude thatDA can increase or decrease the orbital semi-major axis and eccentricity, whileSA always decreases the orbital both orbital elements. In cases where massoverflow contributes to circularizing the orbit, circularization can set in ontimescales as short as a few per cent of the mass transfer timescale. In caseswhere mass overflow increases the eccentricity, the orbital evolution isgoverned by competition between mass overflow and tidal torques. In the absenceof tidal torques, mass overflow resulting in DI can lead to substantiallysubsynchronously rotating donor stars. Contrary to common assumptions, DIfurthermore does not always provide a strong sink of orbital angular momentumin close mass-transferring binaries; in fact we instead find that a significantpart can be returned to the orbit during the particle orbit. The formulationpresented here can be combined with stellar and binary evolution codes togenerate a better picture of the evolution of eccentric, RLO binary starsystems.

Interacting Binaries with Eccentric Orbits. III. Orbital Evolution due to Direct Impact and Self-Accretion