Differences in electron depth-dose curves calculated with EGS and ETRAN and improved energy-range relationships

For 1-50 MeV electrons incident on a water phantom there are systematic differences in the depth-dose curves calculated by the Monte Carlo codes EGS and ETRAN (and its descendants SANDYL, CYLTRAN, ACCEPT, and the ITS system). Compared to ETRAN, the EGS code calculates a higher surface dose and a slightly slower dose falloff past the dose maximum. The discrepancy in the surface dose is shown to exist because the modified Landau energy-loss straggling distribution used in ETRAN underestimates the mean energy loss by about 10% since it underestimates the number of large energy-loss events. Comparison to experimental data shows a preference for the EGS depth-dose curves at 10 and 20 MeV. Since various dosimetry protocols assign electron beam energies based on measured depth-dose curves in water, formulas based on these more accurate EGS4 calculations are presented: relating the mean energy of an incident electron beam to R50, the depth at which the dose in a water phantom falls to 50% of its maximum value; and relating the most probable energy of the incident beam to the projected range of the depth-dose curve. A study is presented of the effects of the incident electron spectrum on the calculated depth-dose curve.