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It can be concluded that a proper measurement of the velocity distribution from
the muonic hydrogen transitions is absolutely necessary to reach the final goal
of the experiment. The muonic values together with the data on the kinetic energy
distribution of the 
atom at the instant of the nuclear reaction
must constrain the input values for the Doppler distributions in the pionic
case with a relative accuracy of better than 10% which seems feasible. This
goal can be reached by using the atomic cascade model available in our group
[52,55,62] tuned to reproduce the 
X-ray data and
the nToF data. In summary the following steps are necessary
for a successful experiment:
- The resolution function of the crystals have to be known with an accuracy of
about 1% in the width determination. This statement holds for the knowledge
of the resolution function for the single crystals and consequently for the
two crystal arrangement. This knowledge is the clue to the success of the experiment
and can only be reached by intensive studies of the response function of the
crystals with X-ray lines of small width as provided by an ECR source.
- The width of the central peak ( always regarding the hfs structure as well)
in the muonic hydrogen spectra has to be measured with an accuracy of 1% in
order to determine an influence of low energy (eV) components in the energy
distribution of the muonic atoms.
- A first result for the width on the level of (2.5-2.0)% can be expected from
correlated fits without invoking a detailed knowledge of acceleration mechanisms.
This statement implies that in a survey measurement with muonic hydrogen for
different pressures including liquid the required theoretical understanding
of the cascade processes is established.
- A last step in the evaluation has necessarily to rely on a proper theoretical
description of the exotic hydrogen cascade. The experimental knowledge gained
from the muonic hydrogen spectra as well as from the neutron time of flight
experiment has to be transferred to the pionic hydrogen case.
On the other hand an intensity in each of the measured spectra between 10000
and 20000 seems to be sufficient as in total 4 spectra (two transitions at two
pressures ) will be at the disposal of the evaluation. In this way an internal
consistency check of the evaluation procedure is also possible: the result for
the strong interaction width must be independent of both the transition and
pressure used.
Next: Proposals for scheduling.
Up: Results of simulation tests.
Previous: Constraints from the velocity
Contents
Pionic Hydrogen Collaboration
1998