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.
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