of the p -p atoms, where Rp 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 vn=0.894 cm/ns [Cra 91].
.
In the laboratory system, the energy E g 2 and the
opening angle q 12 are calculated using a Lorenz
transformation and are
,
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.