  The theory of mirror matter predicts a hidden sector made up of a copy of the
Standard Model particles and interactions but with opposite parity. If mirror
matter interacts with ordinary matter, there could be experimentally accessible
implications in the form of neutral particle oscillations. Direct searches for
neutron oscillations into mirror neutrons in a controlled magnetic field have
previously been performed using ultracold neutrons in storage/disappearance
measurements, with some inconclusive results consistent with characteristic
oscillation time of $\tau$$\sim$10~s. Here we describe a proposed disappearance
and regeneration experiment in which the neutron oscillates to and from a
mirror neutron state. An experiment performed using the existing General
Purpose-Small Angle Neutron Scattering instrument at the High Flux Isotope
Reactor at Oak Ridge National Laboratory could have the sensitivity to exclude
up to $\tau$$<$15~s in 1 week of beamtime and at low cost.
