Benford's law and thermal neutron capture cross-section of A(n,γ)B reactions

This study evaluates the first-digit distribution of experimental data and semi-empirically calculated data of the thermal neutron capture cross-sections $\sigma (n,\gamma )$ for $A(n,\gamma )B$ reactions. The $\sigma (n,\gamma )$ data for 122 isotopes were analyzed, with the scope extended to a total of 558 isotopes, including both ground and isomeric states. The results demonstrate a strong agreement with Benford's law across both datasets. However, a notable deviation is observed for the digit 8, where Mughabghab's calculated values exceed theoretical expectations. This discrepancy suggests a need for further scrutiny of the $\sigma (n,\gamma )$ values for four isotopes: ¹⁷⁷Lu, ¹⁸²Ta, ⁹⁴Nb and ⁹⁹Mo need to be more carefully considered in future evaluations, due to the significant errors in the elemental concentrations of these isotopes determined by the neutron activation analysis (NAA). Additionally, the theoretical model used for thermal neutron capture cross-section calculations follows a statistical model. The findings of this study not only validate the applicability of Benford's law in nuclear physics but also provide a promising approach for verifying both experimental and theoretical datasets, which is crucial for enhancing the precision of NAA in determining elemental concentrations.