  Wide-orbit exoplanets are starting to be detected, and planetary formation
models are under development to understand their properties. We propose a
population of "Oort" planets around other stars, forming by a mechanism
analogous to how the Solar System's Oort cloud of comets was populated.
Gravitational scattering among planets is inferred from the eccentricity
distribution of gas-giant exoplanets measured by the Doppler technique. This
scattering is thought to commence while the protoplanetary disk is dissipating,
$10^6-10^7$ yr after formation of the star, or perhaps soon thereafter, when
the majority of stars are expected to be part of a natal cluster. Previous
calculations of planet-planet scattering around isolated stars have one or more
planets spending $10^4-10^7$ yr at distances >100 AU before ultimately being
ejected. During that time, a close flyby of another star in the cluster may
dynamically lift the periastron of the planet, ending further scattering with
the inner planets. We present numerical simulations demonstrating this
mechanism as well as an analysis of the efficiency. We estimate an occurrence
of planets between 100 and 5000 AU by this mechanism to be <1% for gas giants
and up to a few percent for Neptunes and super-Earths.
