Approximation formulas on buildup factors as a function of the effective atomic number, gamma-ray energy and relaxation length

Approximation formulas on energy, dose and energy absorption buildup factors were constructed to facilitate the computation of the values in a material irradiated with a point isotropic gamma-ray source. The approximation formulas were expressed as a function of the effective atomic number (Z), gamma-ray energy (E) and relaxation length in mean free path (μr), with 15 or 17 coefficients. The approximate values were compared with the buildup factors reported by Goldstein and Wilkins in the range of Z, E and μr adopted for gamma-ray irradiator design, that is in 7.42 <= Z <= 26, 0.5 <= E(MeV) <= 4 and 0 <= μr <= 10. It was shown that the maximum relative errors of the approximation formulas are +-5.2%, +-4.3% and +-3.5% for energy, dose and energy absorption buildup factor, respectively. (author)