Development of fitting methods using geometric progression formulae of gamma-ray buildup factors

The gamma ray buildup factors are represented by an approximation method to speed up calculation using the point attenuation kernel method. The fitting parameters obtained by the GP formula and Taylor's formula are compiled in ANSI/ANS 6.4.3, available without any limitation. The GP formula featured high accuracy but required a high-level fitting technique. Thus the GP formula was divided into a curved line and a part representing the base values and used to develop the a fitting method and X-k fitting method. As a result, this methodology showed that (1) when the fitting ranges were identical, there was no change in standard deviation when the unit penetration depth was varied; (2) even with fitting up to 300 mfp, the average standard deviation of 26 materials was 2.9% and acceptable GP parameters were extracted; (3) when the same end points of the fitting were selected and the starting points of fitting were identical with the unit penetration depth, the deviation became smaller with increasing unit penetration depth; and (4) even with the deviation adjusted to the positive side from 0.5 mfp to 300 mfp, the average standard deviation of 26 materials was 5.6%, which was an acceptable value. However, the GP parameters obtained by this methodology cannot be used for direct interpolation using gamma ray energy or materials.