Exercise 3: Absorption Measurement

Object: find the fraction of particles that pass through a target.

In this case, the target should be 1 mm of lead. Do this for electrons, gammas, muons, pions, and protons, at 50 MeV. Schematically, the geometry is the same as the Energy Loss exercise. Once you have finalized your code, run this for 10000 events.

In this case, the absorption is defined as the fraction of particles that are not able to continue beyond the target in approximately the same direction they entered it. This definition is clear for gamma rays, but for charged particles, remember the results of the Energy Loss exercise and consider that they inevitably lose energy and experience multiple scattering. You may have to apply some sort of condition on the enrgy of position of the particle. More importantly, remember that reaction products may increase the number of particles on right side of the above figure, some of which will be uncharged. You should study the effect of the conditions you apply.

For automatic manipulation and outputting of results at the end of a simulation, uglast.f can be modified. Remember, for interactive sessions, calling uglast.f must be forced manually. This can be done using the interactive CALL command, or by the EXIT (not QUIT) command.

The most obvious difference between this exercise and the Energy Loss one, is that this is a count rate, or "scaler" experiment rather than a spectrometry one. You might want to simply define a set of counter variables, and simply print out the quantities of interest at the end of a series of events. Or you could accumulate a histogram and extract the counts by integrating the spectrum, or part of the spectrum (Note: the PAW GRAPHICS/OPTION and GRAPHICS/SET commands can be used to turn on basic STATistics information display on the histogram, or you could use the interactive PAW LOCATE command.). Regardless, histograms play a crucial role in determining the correct conditions to apply to the counters in real experiments and in simulations.

This is a "total absorption cross section" measurement, which you may recall from one of your quantum mechanics courses. Calculate the total absorption cross section (with error propagation) and compare it to the cross section plots available through GEANT.

Finally, reduce the height and width of the target by 2, then rotate the target by 45 degrees, and run for 10000 events with gamma rays.

You will need to define a rotation matrix and apply it to the geometry definition. Compare with the unrotated gamma ray absorption, taking statistical uncertainties into account. You should see the absorption increase by about sqrt(2), within error, turning the target has increased its effective thickness, or the amount of material the beam has to go through. This should also illustrate why count rate, or at least the overall counts is important: running with 10000 events is barely sufficient for the gamma ray measurement. This also illustrates that the target alignment can be an issue if cross section measurements attempt to meet the few percent uncertainty level.

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