( p e n ) is suppressed with respect to the normal pion decay by a
factor of
,
(3.8)
because the positron is emitted in the "wrong" helicity state. The kinetic
energy of the positrons from this decay is
.
(3.9)
Results of two experiments on this decay mode have been published recently,
each of them reached an overall precision of ~0.4%. One experiment [Cza 93] was
carried out at PSI the other at TRIUMPH [Bri 94]. In order to avoid pile-up,
i.e. several decay products for one trigger event, low beam intensities were
used (7·104/s for the TRIUMF experiment and
5·103/s for the PSI experiment). Due to the low rate, inorganic
scintillators with excellent energy resolution but slow decay times
[tau]d could be used (
p a g [Iota]3[tau] d ">[tau]d
~ 300 ns for BGO and [tau]d ~250 ns for
NaI(Tl) ).The main systematic errors for both experiments came from tail corrections, i.e. from the estimation of the number of events from p ->e+ n e decay below the edge of the Michel spectrum. The tail can be seen in Figure 3.5, which shows the recorded total energy spectrum for p ->e+ n e events. In the PSI experiment this tail occurred because of photo-nuclear absorption with neutron emission and could be estimated only by a Monte Carlo Simulation. In case of the TRIUMF experiment the tail was due mostly to the response function of the NaI(Tl) crystal. The response function of the crystal was measured directly in a positron beam. The result was convoluted with the response function obtained from Monte Carlo calculations.
