In the MOD yield analysis, before comparing with the MC yield, we used a simple attenuation model to analyze our data, which gave us crude yet useful insight into the physics involved.

In the one dimensional approximation, the yield ** Y** of particles after
going through a medium of thickness

where

Fitting our data using Eq. 8.7 gave us a rather good fit
with
(confidence level 19%, ** dof=2**), which is
somewhat surprising, considering the degree of approximation
introduced

We now turn to the comparisons with the SMC simulations. Encouraged by its
success in fitting the experimental data, we apply the attenuation model
also to characterize the MC results. Figure 8.18 illustrates
our Monte Carlo analysis. Plotted with error bars are experimental data,
while crosses indicate the yield from the MC. The lines are fits to the MC
yield from which we extract the effective attenuation lengths as
above. Shown in the solid line (MC(a)) is a fit to the MC results with the
nominal input, with dotted lines indicating the variations in the slope due
to the fit uncertainty and the thickness errors, where we obtained
gcm** ^{-2}**. This is consistent at the 10% level with the
experimental value extracted above. Indeed, the same conclusion can be
made from a direct comparison of the Monte Carlo and the data without the
use of the intermediate approximation of the attenuation model.

On the other hand, given in the dot-dashed line is a
fit to the MC assuming an isotropic angular distribution in elastic scattering with the total cross section kept the
same (MC(b)), where we obtained
gcm** ^{-2}**. The Monte Carlo with an isotropic angular distribution
is in disagreement with our data. In Table 8.15 we
present the summary of our attenuation analysis. We shall defer the
discussion of the implications of these measurements to Chapter 9,
but for now it suffices to state that a reasonable agreement of our