Naslov
The use of an Expanded Polynomial Orthogonal Set in Approximation to Gamma-Ray Buildup Factor Data

Autori
Michieli, Ivan

Izvornik
Nuclear Science and Engineering (0029-5639) 117 (1994), 2; 110-120

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
shielding; buildup; gamma-ray; polynomial

Sažetak
Buildup factors for various shielding materials exhibit large variations in magnitude and in curve shapes as a function of penetration depth as a result of the stohastic nature of the scattering processes for different incident photon energies. In a quest for adequate functional representation of point isotropic gamma-ray buildup factor data, a family of functions based on an expanded polynomial orthogonal set is introduced. The approximation function has the form: B(x)= 1+exp(β x)xˆ α Σ (Ai xˆ i) In the foregoing formula α and β are generally constants that differ for each material, and in that respect this formula presents a family of functions, while Ai are independent parameters of the function. This is not allways valid, and for some materials, modifications are introduced where besides Ai an additional independent parameter is β while α remains constant throughout the whole energy domain. A polynomial based function approach is validated as a possible choice (besides the well-known geometrical-progression G-P function) for point kernel calculations. Results of approximation to exposure point isotropic buildup factors for water, concrete and iron with four and for lead and beryllium with five independent parameters of presented function are in good agreement with the basic data within 4% over the standard data domain. The results are compared with five-parameter G-P function fitting on the maximum-percentage-relative-error basis. The validity of using the independent parameters of the function to interpolate buildup factors for intermediate source energies is ascertained.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Strojarstvo, Temeljne tehničke znanosti

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