List of Tables

1. Energy eigenfunctions $u_{n l m}(r,\theta ,\phi )$ for a hydrogenic atom.
2. $nS$-state pion capture fractions in hydrogen (15)
3. Pion capture fractions in light nuclei.
4. Summary of Runs for E838.
5. RMC Spectrometer dimensions.
6. The four basic levels for the $\pi ^-p\rightarrow \gamma \gamma n$ trigger.
7. Definitions of the various triggers used in trigger studies.
8. The tracking cut parameters.
9. The photon cut parameters.
10. The $C$ timing, beam telescope amplitude, opening angle, and lower energy cuts.
11. The subsets of runs analyzed to obtain the two-photon acceptance from the multi-$\pi$ accidentals.
12. The final set of cuts used to obtain the signal $\pi ^-p\rightarrow \gamma \gamma n$ two-photon events from measured and Monte Carlo data.
13. The fraction of $\pi ^o$-tail background events at different opening angle cuts.
14. The random background subtraction.
15. Inventory of uncertainties in the $\pi ^-p\rightarrow \gamma \gamma n$ measurement.
16. $\pi ^-p\rightarrow \gamma \gamma n$ branching ratio for data sets AHC cut (3,3) and AHC cut (4,6).
17. The sensitivity of the $\pi ^-p\rightarrow \gamma \gamma n$ branching ratio to the cut based on beam ADC amplitude.
18. Variation of $\pi ^-p\rightarrow \gamma \gamma n$ branching ratio vs opening angle cut.
19. The sensitivity of the $\pi ^-p\rightarrow \gamma \gamma n$ branching ratio to the threshold energy $E$.