Discussion

The CERN synchrocyclotron and TRIUMF values for the $^{12}$C branching ratios, $(1.4 \pm 0.2) \times 10^{-5}$ and $(1.2 \pm 0.2) \times 10^{-5}$ respectively, are in reasonable agreement. They also obtain reasonably similar two-photon angular distributions. While pion capture on carbon occurs predominantly from the $p$ states (Table 2.3) the theoretical prediction (5) had been that the bremsstrahlung graphs dominate the ( $\pi^-,\gamma\gamma$) process (Figure 2.6). The two-photon energy distribution as obtained by the TRIUMF experiment (Figure 2.8) agrees well with the theoretical predictions of the authors (5). However, the experiments indicated a strong peak at large angles in the photon-pair opening angle distribution (see Figures 2.10 and 2.10). This was not explained by the theoretical calculations of Christillin and Ericson (5). One explanation for this discrepancy might be possible hydrogen contamination in these experiments, leading to the sequence $\pi^-p\rightarrow\pi^0n$ and $\pi^0\rightarrow\gamma\gamma$.

Figure 2.9: Comparison of theoretical results of Gil and Oset with the experimental measurements of Deutsch et al. for $^9$Be.

Figure 2.10: Comparison of theoretical results of Gil and Oset with the experimental measurements of Deutsch et al. (filled boxes) and Mazzucato et al. (crosses) for $^{12}$C.

Gil and Oset's calculations (6) however, reproduced this strong peak at large opening angles but disagreed with experiment in the small opening angle region. An important difference in the assumptions of Reference (6) and (5) concerns the $p$ wave pion capture which is dominated by the annihilation graph in Gil and Oset's calculation but by bremsstrahlung diagrams in Christillin and Ericson's calculation. As mentioned in the earlier section, another difference between the two calculations is the treatment of the nuclear medium effects on the elementary ($\pi ^-$,$\gamma \gamma$) reaction. The disagreement at small opening angles between the recent Oset and Gil calculation and the CERN synchrocyclotron and TRIUMF $^{12}$C results is of considerable interest as the $\pi^-\pi^+$ annihilation graph is expected to dominate at small opening angles, as predicted by Beder (7). Thus, our data on hydrogen is helpful toward understanding the underlying mechanisms of the nuclear $\gamma \gamma n$ processes as well.