The $\gamma \gamma n$ Events

The single photon energy spectra of the measured 635 events is plotted in Figure 6.9 and the two-photon sum energy is plotted in Figure 6.10 as open circles. The Theoretical calculation is convoluted with the response function of the RMC spectrometer and the contribution from the $\pi\pi$ annihilation process, the $NN$ bremsstrahlung process, and the full calculation are plotted as dashed, dotted and solid curves respectively. The background two-photon events from the random coincident multi-$\pi$ accidentals are clearly seen above 150 MeV in Figure 6.10.

Figure 6.9: Comparison of the single photon energy distributions from the experimental data (open circles) and the theoretical calculation (curves). The dashed curve is the $\pi\pi$ annihilation process, the dotted curve is the $NN$ bremsstrahlung process, and the solid curve is the full calculation. These curves are convoluted with the response function of the RMC spectrometer.

Figure 6.10: Comparison of the two-photon sum energy distributions from the experimental data (open circles) and the theoretical calculation (curves). The dashed curve is the $\pi\pi$ annihilation process, the dotted curve is the $NN$ bremsstrahlung process, and the solid curve is the full calculation. These curves are convoluted with the response function of the RMC spectrometer.

In Figure 6.11, we compare the two-photon angular distribution of our measured data with Beder's calculation (7). The Theoretical calculation is convoluted with the response function of the RMC spectrometer and the contribution from the $\pi\pi$ annihilation process, the $NN$ bremsstrahlung process, and the full calculation are plotted as dashed, dotted and solid curves respectively. The background contributions of 53 $\pm$ 30 ($8.3 \pm 4.8$)% from $\pi ^o$ decay events and 100 $\pm$ 16 ($15.7 \pm 2.5$)% from multi-$\pi$ stop events have been subtracted from the measured data and the final 635 - 53 - 100 = 482 signal events are plotted as open circles. The theoretical curves in Figure 6.11 are normalized to the measured data.

Figure 6.11: Comparison of the opening angle distributions from the background subtracted experimental data (open circles) and the theoretical calculation (curves). The dashed curve is the $\pi\pi$ annihilation process, the dotted curve is the $NN$ bremsstrahlung process, and the solid curve is the full calculation. These curves are convoluted with the response function of the RMC spectrometer.

The error in the final 482 signal events is estimated from the statistical error including the background subtraction. Any other possible ($\leq 1$%) background contributions include two-photon events that originate from the nuclear $( \pi , 2 \gamma )$ reaction on the target walls. However, such contributions have been considered in References (12,13) and have been estimated to be negligible.

Thus the total statistical error of our measurement is estimated as,

$$N_{2\gamma} = N_{raw} - N_{\pi^o} - N_{\pi\pi}$$ (6.8)

$$482 = 635 - 53 \ (\pm 30) - 100 \ (\pm 16)$$ (6.9)

$$\begin{eqnarray*} \mbox{Stat. Error} & = & \sqrt{(635 + 30\times 30 + 16 \times ... ... & = & \sqrt{(1791)} \\ & = & 42 \quad \mbox{events, or 8.8\%} \end{eqnarray*}$$