Three pion decays of unstable particles
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cross section for a hydrogen target at this kinematical point is 1.57&& 10—"crn'/sr. ' Under the conditions of this experiment, this cross section would provide a yield for hydrogen of 0.126 IC+ mesons per monitor unit. A rough estimate of the mean free path in nuclear matter can be made by assuming that the production of E+ mesons depends only on the number of protons in the nucleus, and that the absorption depends on the distance traveled in leaving the nucleus. Accordingly, a plot of the logarithm of the yield per proton versus A'", where A is the atomic weight, would yield a straight line whose slope is inversely proportional to the mean free path. Figure 2 shows such a plot of the experimental data points with their statistical errors. The line which is drawn is a least-squares fit for the function exp[—(r/X)A't']. The resulting slope is 0.095. This yields a value for the mean free path X equal to about 10 F, assuming a value of 1 F for the nuclear radius r. However, this is only an order of magnitude estimate since a complete analysis would require consideration of eGects of nuclear motion, Coulomb scattering, and geometrical factors. The fact that some of the points .20 Be C Al Cu Ag W Pb