Generalization of the Runge-Lenz Vector in the Presence of an Electric Field

It is well known that the Kepler problem admits two vector constants of the motion, the angular momentum and the Runge-Lenz vector. In this paper a generalization of the Runge-Lenz vector is found when a uniform constant electric field is present. The component of this vector in the direction of the external field is a constant of the motion.