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A class of models of a &#x201C;dark sector&#x201D; of particles consider new very weak interaction between the ordinary and dark matter transmitted by U'(1) gauge bosons A' (dark photons) mixing with ordinary photons. If such A's exist, they could be searched for in a light-shining-through-a-wall experiment in a high energy electron beam from the CERN SPS. A proposed search project suggests detection of the e+e- pairs produced in the A <sup>'</sup> -&gt; e+e - decays with a very small opening angle. Coordinate detectors based on the thin-wall drift tubes with a minimal material budget and a two-hit resolution for e+ and e- tracks separated by more than 0.5 mm are considered as an option for detecting such events.

On Detection of Narrow Angle ${\rm e}\!+\!{\rm e}- $ Pairs From Dark Photon Decays