THE EGS5 CODE SYSTEM

Table 2.4: Materials used in reference tables of scattering strength vs. characteristic dimension atvarious energies.Material Z Z(Z + 1) A ρ Z(Z + 1)/ALi 3 12 6.93900 0.5340 1.7294C 6 42 12.01115 2.2600 3.4968H 2 O 10 76 18.01534 1.0000 4.2186Al 13 182 26.98150 2.7020 6.7454S 16 272 32.06435 2.0700 8.4829Ti 22 506 47.90000 4.5400 10.5637Cu 29 870 63.54000 8.9333 13.6922Ge 32 1056 72.59000 5.3600 14.5475Zr 40 1640 91.22000 6.4000 17.9785Ag 47 2256 107.87000 10.5000 20.9141La 57 3306 138.91000 6.1500 23.7996Gd 64 4160 157.25000 7.8700 26.4547Hf 72 5256 178.49000 11.4000 29.4470W 74 5550 183.85000 19.3000 30.1877Au 79 6320 196.98700 19.3000 32.0833U 92 8556 232.03600 18.9000 36.8736To generate the data sets, then, for each of the 16 reference materials, 45 reference energies,and 29 broomstick lengths and diameters (i.e., characteristic dimension) a series of Monte Carlosimulations were performed, using up to 25 different values of fractional energy loss (called EFRACHin EGS5), covering the range from 30% to 0.001% (except when such steps were less than thetheoretical lower limits of the Molière distribution). Energy loss hinges were set to the lesser ofEFRACH and 4% fractional energy loss, and 100,000 histories were simulated, resulting in relativestatistical uncertainties in the computed values of 〈r〉 at 2σ of around 0.3%. Tallies were made ofthe the average track length inside the volume, the average lateral displacement of the particlesescaping the end of the volume, the average longitudinal displacement of particles escaping thesides of the broomstick, and the fractional energy deposited, backscattered and escaping from theside of the broomstick. Computations of the number of hinges expected for the scattering strengthbeing tested given the broomstick dimension, were also made for each run, and the anticipatednumber of collisions per hinge were also determined and stored.Illustrative plots showing the divergence in the results as step-sizes are increased in Copperat 5 MeV for several different broomstick thicknesses are shown in Figures 2.17 (results of energydeposition) and 2.18 (results of lateral spread).Approximately 20,000 such plots were generated from over 500,000 simulations to encompass thedesired ranges of materials, energies, and characteristic dimensions. The data was then analyzedto determine the maximum fractional energy loss which showed convergence within the statisticaluncertainty of the data, using a least-squares fit to a line with slope zero and intercept given by the115