List of Figures

1. The annihilation, pion bremsstrahlung and the $NN$ bremsstrahlung graphs.
2. The photon energy and opening angle dependence of the $\pi ^-p\rightarrow \gamma \gamma n$ reaction transition probability.
3. JINR experimental set-up.
4. The opening angle spectrum for two-photon events recorded in the JINR experiment.
5. Experimental set-up for the CERN measurement of double radiative nuclear capture.
6. Two photon angular distribution from nuclear capture.
7. Experimental set-up for the TRIUMF measurement of double radiative nuclear capture.
8. Energy distribution of the two photons in the TRIUMF experiment.
9. Comparison of theoretical results of Gil and Oset with the experimental measurements of Deutsch et al. for $^9$Be.
10. Comparison of theoretical results of Gil and Oset with the experimental measurements of Deutsch et al. for $^{12}$C
11. Pion Compton scattering, annihilation and the $\gamma \gamma$ $\rightarrow \pi \pi$ graph.
12. The different kinematical regions for the two-photon reactions.
13. Layout of the TRIUMF facility.
14. Time of flight (TOF) structure of the unseparated beam.
15. The RMC photon-pair spectrometer at TRIUMF.
16. A cross-sectional view of the RMC detector.
17. The measured two-photon acceptance following $\pi ^-$ stops in a CH$_2$ target.
18. The measured two-photon trigger rates on CH$_2$ target, scaled to liquid hydrogen.
19. The drift time spectra.
20. The average $\chi ^2$ of the fitted tracks vs drift velocity.
21. $xy$ projection of a typical $\pi ^-p\rightarrow \gamma \gamma n$ event.
22. The $z$ projection of the signal event.
23. The parameter R$_{close}$.
24. Two-photon background events from random multi-$\pi$ stop, and $\pi ^o$ decay.
25. The normalized ADC pulse height spectra.
26. Two-photon energy spectrum dominated by background contributions from $\pi ^o$ decays and multi-$\pi$ stops.
27. The two-photon FBTDC time difference spectra.
28. The Monte Carlo generated spectrum for the determination of low energy cut.
29. The $\pi ^-p\rightarrow \gamma \gamma n$ two-photon energy angle distribution.
30. The multi-$\pi$ accidental two-photon opening angle, two-photon energy sharing and sum energy spectra for AHC cut(3,3).
31. The multi-$\pi$ accidental two-photon opening angle, two-photon energy sharing and sum energy spectra for AHC cut(4,6).
32. Variation of the multi-$\pi$ accidental two-photon acceptance corresponding to AHC cut(3,3).
33. Variation of the multi-$\pi$ accidental two-photon acceptance corresponding to AHC cut(4,6).
34. The RMC GEANT simulated $\pi ^-p\rightarrow \gamma \gamma n$ opening angle, two-photon energy sharing and sum energy spectra.
35. The RMC GEANT simulated two-photon phase space spectra of opening angle, two-photon energy sharing and sum energy.
36. $\pi ^o$-tail obtained from analysis of Monte Carlo generated data analyzed with the $\pi ^-p\rightarrow \gamma \gamma n$ trigger.
37. The energy sharing between two-photon events from multi-$\pi$ accidentals.
38. Comparison of the single photon energy distribution between measured data and the theoretical calculation.
39. Comparison of the two-photon energy distribution between measured data and the theoretical calculation.
40. Comparison of the two-photon angular distribution between measured data and the theoretical calculation.