1. Introduction to the pb Experiment - 6.1 Method of the Calibration

6.1 Method of the Calibration

In the energy range of about 70 MeV, photons can be produced by stopping negative pions in a liquid hydrogen target. A fraction of the p ^_-p atoms, where R_p is the Panofski Ratio, undergo the charge exchange reaction

, ( 6.1)

whereas almost all of the remaining 40% of the p ^_-p atoms undergo radiative capture:

, (6.2)

Due to the kinetic energy of the p ^₀ from reaction (6.1), the energies of the two photons from the p ^₀-decay range from 56 MeV to 84 MeV. Showers in the crystals initiated by such photons are used to calibrate the array of 26 CsI-crystals.

If the p ^_-p atoms are at rest before reaction (6.1), energy and momentum conservation lead to the following equation for the energy :

. ( 6.3)

Here, are the masses of the charged pion, the proton, the neutron and the neutral pion, respectively. is the mean binding energy of the p ^_-p atoms just before reaction (6.1) and is [Cra 91]. From Eq. 6.3, energy, momentum and velocity of the p ^₀ are

, ( 6.4)

whereas the velocity of the neutron from reaction (6.1) is which corresponds to v_n=0.894 cm/ns [Cra 91].

Figure 6.1: Schematic diagram of the charge exchange reaction and the terms used in the text. The p ^₀ decays with a probability of 0.988 into two photons. In the rest-frame of the p ^₀, the photons are emitted with an opening angle [GreekJ]₁₂=180° isotropically in all directions with energies . In the laboratory system, the energy E_{g 2} and the opening angle q ₁₂ are calculated using a Lorenz transformation and are

Figure 6.2: E_{g 2} and q ₁₂ as a function of the angle q ₁₀ as given in eqs. 6.5 and 6.6. The marked area indicates the acceptance of the experimental apparatus (Fig. 6.4). , and ( 6.5)

, ( 6.6)

where =28.04 MeV/c (6.4) and . The uncertainty [Delta]E_{g 2} is mainly depending on the uncertainty [Delta] q ₁₀ and is

, (6.7)

with a maximum value at q ₁₀~70° of

. ( 6.8)

The aim of the calibration measurement is to detect all the decay products of the charge exchange reaction (6.1). According to (6.5), the energy E_{g 2} can be calculated from the angle q _1n between the g ₁ and the neutron, with q ₁₀=(180°- q _1n). The second photon initiates a shower in the CsI-array. Based on equation 6.5 the energy E_{g 2}( q ₁₀) is calculated and compared to the energy deposited in the CsI-array.

In the following subsections the expression "good event" is used for events with the two photons and the neutron detected, i.e. events for which all the kinematical variables can be determined.