Inference and visualization of nuclear magnetic moment studies with neuro-fuzzy systems

Abstract

This study aims to predict the magnetic moments of nuclei with odd-A numbers in a certain region of which the magnetic moment has not yet been calculated, using the Adaptive Neuro-Fuzzy Inference System (Anfis) method. In our Anfis model the proton number (Z), neutron number (N), and spin value (I) are used as inputs for nuclei with 1 ≤ Z ≤ 88. With 652 nuclei in the dataset, consisting of the provided input data, 528 odd-A nuclei were used for training, and 124 odd-A nuclei were used for testing. The fact that the Anfis model was closer to the experimental data in the training and testing processes than the theoretical methods encouraged us to make inferences about the nuclei of which experimental nuclear magnetic moment is unknown. Motivated by the presence of odd-A nuclei exhibiting I π = 1/2±, 3/2±, and 5/2± ground-state configurations near the doubly closed-shell, within the 1 ≤ Z ≤ 28 regions, along with the limited knowledge of nuclear properties in this range. This study has conducted magnetic moment inferences for 165 nuclei lacking experimental data. Specifically, Na, F, and P isotopes have been chosen as Magnetic moment value inferences made for these isotopes using Anfis have also been compared with the theoretical results of the Quasiparticle-Phonon Nuclear Method (QPNM) and with the Shell Model calculations. There is a satisfactory agreement between our predictions and the results of these two theories. Furthermore, it is noteworthy that within the same isotope series, nuclei with identical ground-state configurations consistently yield compatible results, irrespective of the availability of experimental magnetic moments. In addition, the fact that the values obtained from test and train operations remain within acceptable error limits, with a range of approximately 0.03%–0.04%, reveals the reliability of our system. Since the Neuro-Fuzzy system will be a first in the field of nuclear technologies, we believe that the outputs of our study will be a good reference for future studies.