Introduction

Negative pions stopped in hydrogen form pionic hydrogen atoms. These atoms can disintegrate via several modes that include the well-known processes of charge exchange $\pi^- p \rightarrow \pi^o n$ (1), radiative capture $\pi^- p \rightarrow \gamma n$ (1), and pair production $\pi^- p \rightarrow e^+e^- n$ (2,3).

However, for pionic hydrogen an additional mode of capture is predicted by theory,

$$\pi^-p \rightarrow \gamma\gamma n \quad$$ (1.1)

This double-radiative process has been investigated theoretically by several authors including Ericson and Wilkin (4), Christillin and Ericson (5), Gil and Oset (6), and Beder (7). The tree-level prediction of the branching ratio is $5.06 \times 10^{-5}$ (7), with a mechanism that is dominated by the annihilation of the stopped, real $\pi ^-$ on a soft, virtual $\pi^+$, i.e. $\pi \pi \rightarrow \gamma \gamma$.

The underlying dynamics of $\pi\pi$ annihilation in double radiative capture are rather intriguing. For example, they led Ericson and Wilkin (4) and Nyman and Rho (8) to suggest the reaction as a probe of the pion field in the nucleus, and Gil and Oset (6) to suggest the reaction as a novel window on the $\pi \pi \rightarrow \gamma \gamma$ vertex. Additionally, the related $\gamma p \rightarrow \gamma \pi n$ reaction was considered by Wolfe et al. (9) and Drechsel and Fil'kov (10) as a possible probe of the pion polarizability.

The only experimental search for double radiative capture on pionic hydrogen was conducted by Vasilevsky et al. (11) at JINR, using a large-acceptance photon-pair spectrometer. It yielded a branching ratio upper limit of $5.5 \times 10^{-4}$. The nuclear double radiative capture on beryllium and carbon has been observed in experiments by Deutsch et al. (12) at CERN and Mazzucato et al. (13) at TRIUMF. In the absence of data on hydrogen however, results of these experiments were difficult to interpret due to (i) nuclear structure effects and (ii) radiative captures occurring from both the atomic $s$ and $p$ states of the $\pi$Be and $\pi$C atoms.

Thus a measurement of the double radiative capture mode in pionic hydrogen is of considerable topical interest. Our experiment, the first measurement of the double radiative capture mode of pionic hydrogen, was carried out at the TRIUMF cyclotron using the RMC spectrometer (described in Section 3.3).

The challenges in detecting the double radiative process on pionic hydrogen are due to the weak signal and strong two-photon backgrounds. The RMC pair spectrometer records photons by photon convertion in a cylindrical lead converter and charged particle tracking in a wire chamber and a large volume drift chamber. Via the large solid angle ($\sim$ 3$\pi$ sr) for charge particle tracking and the high efficiency for photon convertion (10%), the RMC set-up offers a large acceptance for photon detection (1-2%). The detection by pair convertion and particle tracking offers clear identification of photons, and thereby good discrimination from neutrons. Reconstruction of photon pairs from pair convertion also offers a good way of determining the direction of photons and thereby separating the $\pi ^-p\rightarrow \gamma \gamma n$ signal from the $\pi^o\rightarrow\gamma\gamma$ background.

This dissertation is organized as follows. The motivation for the experiment is discussed in Chapter 2. An account of the experimental set-up is given in Chapter 3. Acceptance and trigger studies done in preparation of the final measurement are presented in Chapter 4. Data analysis is described in Chapter 5. The measured $\pi ^-p\rightarrow \gamma \gamma n$ branching ratio and the two-photon energy-angle distributions are presented in Chapter 6. Finally, our conclusions are presented in Chapter 7.