Abstract
It is well known that the number of π 0's in a sample of events may be determined by detecting the resulting γ-ray conversions. Using a simple model, we derive a formula for the incertainty in the total number of π 0's as a function of their total number and the gamma-ray conversion efficiency, ε γ . Data for the reaction p ̄ p→ pions at 1 GeV/ c are simulated and analyzed; results agree with the above model. δƒ 1 0, δƒ 1 −0, and δƒ 2 00 as functions of ε γ are also determined from the simulated data. It is interesting that conventional hydrogen and deuterium bubble chamber experiments ( ε γ ∼0.01) containing large numbers of events could compete favorably with smaller (e.g. ≈one-fifth the number of events) experiments having ε γ ≥0.3, as far as small δƒ 1 0 and δƒ 2 −0 are concerned. For minimal uncertainty in ƒ 2 00 (and higher moments), however, experiments with ε γ⪆0.2 will be required.
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