1. Introduction to the pb Experiment - 3.1.1 PION BETA DECAY AT REST

3.1.1 PION BETA DECAY AT REST

If the charged pion decays at rest, the kinetic energy for the decay products of 4.452 MeV is shared by the positron, the neutrino and the recoiling p ^₀. The maximum kinetic energy of the p ^₀ is

(3.1)

i.e. the p ^₀ is almost at rest. The p ^₀ has a lifetime of 8.6·10^-17s, its decay modes are shown in table 3.2.

Figure 3.2: Kinematics of the pion beta decay: Calculated spectrum of the positron (top left) and of the p ^₀ (top right). Monte Carlo Generation of the deviation from collinearity (bottom left) and energy distribution (bottom right) of the two photons from the decay of the p ^₀. The energies of the two photons from the p ^₀-> g g decay are in the following range:

. (3.2)

The two photons are not exactly collinear (Fig. 3.2 bottom left).

An experiment using the decay-at-rest technique was carried out with a beam of 77 MeV pions, produced on the internal target of the CERN synchro-cyclotron [Dep 68]. The experimental setup is shown in Fig. 3.3. The pions were degraded and stopped in the center of the target counter; the stopping rate was ~3.5·10⁴/s. The identification of the process was based on the summed energies and a prompt coincidence of the two photons and the positron. The pulses of the target counter and the summed pulses of the eight lead-glass counters have been displayed on an oscilloscope. A coincidence of two photons occurring 6 to 100 ns after a valid pion stop triggered the oscilloscope and its traces were photographed.

The p ^₀-detector consisted of an array of eight lead-glass counters, with a thickness in radial direction of 17cm (6.8 radiation lengths X₀) and a solid angle coverage of ca 60% of 4 p . For the p ^₀-detection, a coincidence of any of the eight counters with an azimuthal separation of more than 90° and a total energy of more than 14 MeV was required.

Care was taken to determine the efficiency of the p ^₀-detection with good precision, using the reaction

. (3.3)

The p ^₀ from this reaction have a kinetic energy of 2.9 MeV, the two photons have a minimum angle of 157°, and their energies lie in a box spectrum between 55 and 83 MeV as opposed to Eq. (3.2). Due to this systematic difference, the efficiency measured by reaction (3.3) had to be corrected by the calculated ratio for the efficiency of the pion beta decay and reaction (3.3).

Figure 3.3: The experimental apparatus of the decay at rest experiment. 1,3: beam counters; 2: carbon degrader; 4: target counter; 5,6: veto counters for charged particles; A-H: lead-glass counters. For the efficiency determination, the target counter was replaced by a hydrogen pressure bottle and the number of pions stopping in hydrogen was compared to the number of detected p ^₀'s. The overall efficiency for detecting p ^₀'s from pion beta decay was (3.6%). The branching ratio of the pion beta decay was calculated according to

, (3.4)

where N_p=1.742·10¹¹ was the number of triggers of which only a factor of f=0.85±0.01 were due to pions stopping in the target. The total number of N_{p b} = 332±23 (±6.9%) pion beta events was found, which lead to a branching ratio of

. (3.5)

The main difference between the result above and earlier results was the improved precision in the detection efficiency.