Prediction of ground-state spin in odd-<i>A</i> nuclei within decision tree

Abstract

Ground-state spin, as a fundamental parameter of nucleus, has consistently been a hot topic in research on nuclear data and structure. In this paper, we extensively investigate the odd-mass nuclei (odd-<i>A</i> nuclei) on the nuclide chart by using decision trees, including odd-proton nuclei (odd-<i>Z</i> nuclei) and odd-neutron nuclei (odd-<i>N</i> nuclei), and train ground-state spin prediction models of odd-<i>Z</i> nuclei and odd-<i>N</i> nuclei. In the case of randomly dividing the training set and validation set in a ratio of 75% to 25%, the accuracy rate of the training set and validation set for odd-<i>Z</i> nuclei reach 98.9% and 79.3%, respectively. The accuracy rate of the training set and validation set for the odd-<i>N</i> nuclei reach 98.6% and 71.6%, respectively. At the same time, by 1000 random selections of training set and validation set, after being validated repetitively, the standard error of the accuracy rate obtained can be less than 5%, further verifying the reliability and generalization performance of the decision tree. On the other hand, the accuracy rate of decision tree is much higher than those of theoretical models commonly used in nuclear structure research, such as Skyrme-Hartree-Fock-Bogoliubov, covariant density functional theory, and finite range droplet model. Next, by taking all spin-determined odd-<i>Z</i> nuclei and odd-<i>N</i> nuclei as a learning set, the ground-state spin values for 254 spin undetermined but recommended odd-<i>Z</i> nuclei and 268 spin undetermined but recommended odd-<i>N</i> nuclei are predicted, with the predicted set coincidence rates reaching 68.5% and 69.0%, respectively. Finally, four odd-mass number chains, i.e. <i>Z</i> = 59, <i>Z</i> =77, <i>N</i> = 41, and <i>N</i> = 59, are selected to compare the learning (prediction) results of the decision tree with the experimental (recommended) values of the corresponding nuclei, and to discuss the differences and similarities in the results given by the three theoretical models, thereby further demonstrating the research and application value of the decision tree in the ground-state spin of nuclei.