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Precision Measurement of the Radiative $\Beta$ Decay of the Free Neutron

The standard model predicts that, in addition to a proton, an electron, and an antineutrino, a continuous spectrum of photons is emitted in the $β$ decay of the free neutron. We report on the RDK II experiment which measured the photon spectrum using two different detector arrays. An annular array of bismuth germanium oxide scintillators detected photons from 14 to 782~keV. The spectral shape was consistent with theory, and we determined a branching ratio of 0.00335 $\pm$ 0.00005 [stat] $\pm$ 0.00015 [syst]. A second detector array of large area avalanche photodiodes directly detected photons from 0.4 to 14~keV. For this array, the spectral shape was consistent with theory, and the branching ratio was determined to be 0.00582 $\pm$ 0.00023 [stat] $\pm$ 0.00062 [syst]. We report the first precision test of the shape of the photon energy spectrum from neutron radiative decay and a substantially improved determination of the branching ratio over a broad range of photon energies.