Half-Space Albedo Problem for Triplet Anlı-Güngör Scattering

Abstract

Introduction The Anlı-Güngör (AG) scattering function which is written in triplet form is applied to the half-space albedo problem. The aim of the study is to compare the results of albedo between the triplet AG scattering and quadratic AG scattering. Methods The analytical calculations are performed by HN method. Since the HN method is based on the usage of the Case eigenfunctions, they should be derived for the interested in this study. The tabulated results are calculated for varying the secondary neutron number and the scattering parameter. Albedo values for the triplet anisotropic scattering are convergent. A special code is used to get the numerical values in Mathematica with high precision This code holds all numerical values and the results of all algebraic process as a rational number. Thus, the round-off errors in machine language are minimized. A second and completely different numerical process is performed with the Polynomial Regression (PR) and the Artificial Neural Network (ANN). The application of the PR and ANN algorithms are studied with the calculated albedo results in this study. This application is only data mining without performing any analytical calculation. Discussion The expectation is to get bigger albedo values than the quadratic AG scattering. But the results are surprising that the triplet and the quadratic albedo results are close to each other. The result of ANN is more successful than PR results. Moreover, the intermediate values that are not in the data set can also be successfully calculated.