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 $\beta$ 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 $0.00335\pm 0.00005[\mathrm{stat}]\pm 0.00015[\mathrm{syst}]$. 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 $0.00582\pm 0.00023[\mathrm{stat}]\pm 0.00062[\mathrm{syst}]$. 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.

Figure 1

(a) A cross sectional diagram of the RDK II detection apparatus from above. The neutron beam (pink) traveled from left to right through the active region defined by the fields (dashed lines) created by the solenoids (gold) and the electrostatic mirror (blue). Protons and electrons follow the field lines to the SBD (light blue). Radiative photons are detected by twelve BGO crystals (green) and three large area APDs. (b) Detection probability in independent arbitrary units (A.U.) for electron-proton ($ep$) and electron-proton-photon ($ep\gamma$) detection coincidence for either the BGO or direct APD detectors. This plot is approximately aligned with the diagram above.

Figure 2

The detected timing spectrum for the difference between electron and photon detection in coincidence with a delayed proton. The central peak arises from radiative photons which are detected nearly simultaneously with the electrons while the flat regions represent sources of constant, uncorrelated photon background. The response of the APD detectors was significantly faster than the BGO detectors and resulted in a sharper timing peak. Only the background and signal windows for the BGO detectors are shown.

Figure 3

Energy spectrum deposited by photons from radiative neutron decay. Plotted are the average background-corrected radiative photon counts for both BGO, (a), and APD, (b), detectors versus photon pulse height. The pulse height was scaled such that it is approximately equal to the photon energy deposited. The blue dashed line shows the theoretical spectrum scaled to the experimental data and plotted versus photon energy. The solid lines are the output of the simulation scaled to the experimental data using the theoretical spectrum as input. The simulation incorporates the coincident detection of the decay particles and the response functions for the BGO array (red) and the APD array (green). The bump seen in (a) at $\approx 80\mathrm{keV}$ is caused by the escape of bismuth $K$ x-rays from nearby crystals. The experimental data (black circles), include only the statistical uncertainty in the vertical error bars while the horizontal error bars represent the bin size. The normalized residuals (black circles) between the experiment and simulation are also shown at the top along with the results of a ${\chi }^2$ evaluation. Here, ndf is the number of degrees of freedom and $p$ is the $p$ value.