Multi-$\pi$ accidental Background

Another source of background was the accidental $\gamma$-$\gamma$ coincidences arising from simultaneous multiple $\pi ^-$ stops. A photon from each of the randomly coincident pions can contribute to a photon-pair via the reactions $\pi^- p \rightarrow \gamma n$ ($B.R.$= 0.39) and $\pi^-p\rightarrow\pi^0n$ ($B.R.$= 0.61). Since the incident pion beam had a micro-structure involving a pulse width of 2-4 ns and a pulse separation of 43 ns, for an incident flux of $7 \times 10^{5}$ s$^{-1}$ pions the probability for more than one pion arriving in a single beam pulse was about 1.5% (Section 6.1). Since the photon-pair is obtained from two uncorrelated pion stops, the two-photon angular distribution spans the entire opening angle region, and can have a maximum summed energy of 258 MeV from the two $\pi^- p \rightarrow \gamma n$ photons of energy 129 MeV. Thus, multiple pion stops in one beam pulse can yield a $\gamma$-ray pair with opening angles 0-180$^{\circ}$ and summed energies 106-258 MeV. Thus, the summed two-photon energy from random background events can exceed the kinematic limit for single $\pi$ capture.

Figure 5.7: The normalized ADC pulse height spectra summed from the four beam scintillation counters. The large lower energy peak corresponds to single pions traversing the counters, the smaller higher energy peak corresponds to pion pairs traversing the counters.

The multiple $\pi ^-$ stop events are distinguished from single $\pi ^-$ stop events based upon the pulse height spectra from the four beam telescopes. This is shown in Figure 5.7 - the large peak is due to single $\pi ^-$ stops and the smaller peak is due to the accidental multi-$\pi ^-$ events.