THE EGS5 CODE SYSTEM

used for medical linacs (6–50 MeV, high-Z targets) and therefore the employment of Equation 2.149seems justified. At lower energies, use of Equation 2.149 still needs to be demonstrated. At higherenergies, the constraints are not so badly violated except for the Born approximation when high-Zmaterials are used. Again, experimental data will judge the suitability of Equation 2.149 in thiscontext.Sampling procedureTo sample the photon angular distribution, a mixed sampling procedure is employed. Since it is theangular distribution that is required, the overall normalization of Equation 2.149 is unimportantincluding any overall energy-dependent factors. The following expression for p(y) is proportionalto Equation 2.149:Defining x = y 2 ,and,where,p(y)dy = f(y 2 )N r g(y 2 )dy 2 . (2.150)f(x) = 1 + 1/(πE 0) 2(x + 1) 2 , (2.151)g(x) = 3(1 + r 2 ) − 2r − [4 + ln m(x)][(1 + r 2 ) − 4xr/(x + 1) 2 ], (2.152)r = E/E 0 ; m(x) =( ) ( )1 − r2Z1/3 2+ .2E 0 r 111(x + 1)Note that 1/E 0 (high frequency limit)≤ r ≤ 1(low frequency limit). N r is a normalization constantwhich will be discussed later.The function f(x) will be used for direct sampling. It can be easily verified that this function isnormalized correctly, (i.e., ∫ (πE 0 ) 20 f(x)dx = 1) and the candidate scattering angle is easily foundby inversion to be:ˆΘ = 1 √ζE 0 1 − ζ + 1/(πE 0 ) 2 , (2.153)where ζ is a random number selected uniformly on the range (0,1) and the “hat” over Θ signifiesthat it is a quantity determined by random selection.The function g is sampled using the rejection technique. In order to employ this technique,the optimum case is to have the location of the maximum of the function, x max characterizedallowing the most efficient determination N r = g(x max ) −1 . Failing this, the next best scenario isto overestimate g(x max ). The closer this estimate is to the true maximum value, the more efficientthe rejection technique will be. Unfortunately, characterizing g in complete generality proved to bevery difficult. The following observations were made, however. The maximum value of g(x) occurs56