Calculation of gamma-ray buildup factors for two layered shields made of water, concrete and iron and application of approximating formula

Gamma ray buildup factors are basic data for point kernel calculations that are widely used in shielding design for gamma rays. However, the method has not been applied well to multi-layered shields which are often encountered in realistic facility design, because of the lack of buildup factor data and suitable parameterization method for multi-layer systems. Previously we developed a new formula which can be incorporated in point kernel codes. To calculate reference data of buildup factors up to 40 mfp thickness, a special technique has been developed for the EGS4 Monte Carlo code to be applied for this purpose. The buildup factors of double-layered shields consisting of water, concrete and iron were systematically calculated by the EGS4 code using the method mentioned at gamma ray energies of 0.1, 0.3, 0.6, 1, 3, 6 and 10 MeV. The assumed shield thickness was 40 mfp monolayer, 5 mfp 1st layer + 35 mfp 2nd layer, 10 mfp 1st layer + 30 mfp 2nd layer, and 20 mfp 1st layer + 20 mfp 2nd layer. All the possible combinations of double layered shields made up of two materials from water, concrete and iron were treated. The matrixes required in the approximating formula for concrete were calculated by the EGS4 code, and the parameters of concrete to fit the reference data by the approximating formula were newly evaluated by the least squares method using the above EGS4 buildup data as the reference. The matrices and parameters for water and iron had already been obtained in previous work for double layered shields composed of water, iron and lead, and the data were used in this work. The formula reproduced the reference data very well in all cases except for 0.1 MeV, where the reason for a small disagreement is currently under investigation