Neural Network Estimation for Attenuation Coefficients for Gamma-Ray Angular Distribution

Abstract

Spins of nuclear states (J) and multipolarities of gamma rays are usually investigated by the angular distribution of gamma rays emitted from aligned states formed by nuclear reactions. In the case of partial alignment, attenuation coefficients are used in angular distribution function. These coefficients are tabulated in literature for different J values. However, these coefficients involve $$r$$ -fold tensor products. Furthermore, as the calculation of these coefficients implicitly involves highly complicated integral quantities, they are very difficult to handle explicitly for larger $$r$$ values. In this respect, universal nonlinear function approximator layered feedforward neural network (LFNN) can be applied to construct consistent empirical physical formulas (EPFs) for physical phenomena. In this paper, we consistently estimated the attenuation coefficients by constructing suitable LFNNs. The LFNN-EPFs fitted the literature coefficient data very well. Moreover, magnificent LFNN test set predictionson unseen data confirmed the consistent LFNN-EPFs for the determination of coefficients.