Consistent Empirical Physical Formula Construction for Gamma Ray Angular Distribution Coefficients by Layered Feedforward Neural Network
Nihat Yıldız, Serkan Akkoyun, Hüseyin Kaya · Cumhuriyet Science Journal · 2018
Multipolarities of gamma rays and spins-parities of nuclear states are usually investigated by the angular distribution of gamma rays emitted from aligned states formed by nuclear reactions. For different multipolarities of the transitions, the distribution shows different characteristics. The distribution is obtained by using angular distribution formula which has literature tabulated coefficients for different spins and multipolarities. However, these coefficients involve -fold tensor products and they are highly nonlinear in nature. Furthermore, as the calculation of these coefficients implicitly involves highly complicated integral quantities, they are very difficult to handle explicitly for larger values. In this respect, as we theoretically proved in a previous paper, universal nonlinear function approximator layered feedforward neural network (LFNN) can be applied to construct consistent empirical physical formulas (EPFs) for nonlinear physical phenomena. In this paper, by concentrating on the integer spins of nuclear states and dipole and quadrupole type multipolarities of the transitions, we consistently estimated the coefficients by constructing suitable LFNNs. The LFNN-EPFs fitted the literature coefficient data very well. Moreover, magnificent LFNN test set forecastings over previously unseen data confirmed the consistent LFNN-EPFs for the determination of coefficients. In this sense, we can conclude that the LFNN consistently infers nonlinear physical laws governing the angular distribution of gamma rays, which are otherwise difficult to obtain by conventional coefficient calculation methods.