Applicability of geometrical progression approximation (G-P method) of gamma-ray buildup factors

The G-P method formula Br (X) = 1 + (B-1) · (KX-1)/(K-1) (X: optical length, B: buildup factor at X = 1, K: a gamma-ray multiplication factor per one mean free path) gives an accurate representation of the buildup factor for point isotropic sources. In the present work, a fitting procedure has been developed including a new expression for K-parameter. The method is used for fitting to the buildup factors calculated by the moments method and by the PALLAS code. It improves agreement with the basic buildup factors calculated by the moments method, of air, water, concrete, and iron for the 0.015- to 15 MeV energy range and for the 0.5- to 40-mfp distance range. Furthermore, exposure, absorbed dose, and dose equivalent buildup factor approximated by the G-P fitting parameters are in good agreement with the basic data calculated by the PALLAS code, for water, concrete, iron, and lead. Good agreement is obtained even in the case of rapidly increasing buildup factors for low source energies in beryllium and boron and of that in lead, including the effects of bremsstrahlung and fluorescence. Furthermore, the G-P formula efficacy for use as an analysis and interpolation technique has been confirmed through the various tests for energetic or spatial interpolation. (author)