AN ACCURATE ENERGY-RANGE RELATIONSHIP FOR HIGH-ENERGY ELECTRON-BEAMS IN ARBITRARY MATERIALS

A general analytical energy-range relationship has been derived to rel ate the practical range, R(p), to the most probable energy, E(p), of i ncident electron beams in the range 1 to 50 MeV and above, for absorbe rs of any atomic number. The expression is cubic in energy and require s as input parameters the total stopping power, S0, the ratio of the s cattering power and the total specific stopping power, T0/epsilon0, bo th taken at 10 MeV, and the radiation length for the material involved , X0. In addition to these parameters, five of the derived parameters are used to 'fine tune' the equation and minimize the man square devia tion from experimental and/or Monte Carlo data by means of non-linear regression. In the present study only Monte Carlo data determined with the new ITS.3 code have been employed. The standard deviations of the mean deviation from the Monte Carlo data at any energy are about 0.10 , 0.12, 0.04, 0.11, 0.04, 0.03, 0.02 mm for Be, C, H2O, Al, Cu, Ag and U, respectively, and the relative standard deviation of the mean is a bout 0.5% for all materials. The fitting program gives some priority t o water-equivalent materials, which explains the low standard deviatio n for water. A small error in the fall-off slope can give a different value for R(p). We describe a new method which reduces the uncertainty in the R(p) determination, by fitting an odd function to the descendi ng portion of the depth-dose curve in order to accurately determine th e tangent at the inflection point, and thereby the practical range. An approximate inverse relation is given expressing the most probable en ergy of an electron beam as a function of the practical range. The res ultant relative standard error of the energy is less than 0.7%, and th e maximum energy error DELTAE(p) is less than 0.3 MeV.