Proposal to study pi- p --> pi0n and pi- p --> eta n at high energy Page: 13 of 37
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We see that for a 100 BeV nr that S = 1.4 mr. That means that at the detector,
the two showers in the symmetrical case are separated by 2.8 cm. In the case of
asymmetrical decay the separation is greater and the energies are no longer equal,
as can be seen in the above figure. Now it is clear that if we measure the
distance between the two showers, that this does not allow us to uniquely define
the ff0 direction. In fact,we have
where 0 is the opening angle of the pair. We can combine this equation with the
@6 6 = 2
1 2 S
and we see that there is a two-fold ambiguity in the direction of the 71 .
This leads to an uncertainty in the t of the reaction that is unacceptable.
However, if we can arrange in the detector to identify which gamma ray has the
highest energy, we can resolve this two-fold ambiguity. The detector is therefore
constructed to make a rough energy measurement of the individual showers.
From the figure above that indicates how the energy of the gamma ray varies
with angle we see that we only need a rather crude energy measurement in order
to tell the two gamma rays apart, except in the region around 0S . In this region
the two gamma rays have nearly the same energy and a detector with poor resol-
ution may not be able to resolve them. On the other hand, in this region if one
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Tollestrup, A.V.; Walker, R.L. & /Caltech. Proposal to study pi- p --> pi0n and pi- p --> eta n at high energy, report, June 1, 1970; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc887653/m1/13/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.