Parameters of the best approximation for distribution of the reduced neutron widths. Specificity of full-scale method of analysis

The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude and its arbitrary dispersion. The possibility to obtain reliable values of distribution parameters at variation of number of resonances involved in analysis and change of registration threshold of resonances with the lowest widths is studied.

💡 Research Summary

The paper presents a comprehensive methodology for analyzing the statistical properties of reduced neutron widths (Γ₀ⁿ), addressing the limitations of the traditional Porter‑Thomas (χ²) approach. Recognizing that experimental data only capture a subset of resonances—often missing weak resonances and suffering from systematic uncertainties—the authors propose a model in which the normalized width variable X = Γ₀ⁿ/⟨Γ₀ⁿ⟩ is described as a superposition of K Gaussian components. Each component is characterized by a mean (bₖ), a standard deviation (σₖ), and a weight (Cₖ). The overall probability density function P(X) is derived from a transformed Euler gamma function, allowing for non‑zero means and arbitrary dispersions.

To compare experimental data with the model, the authors use cumulative sums S(X) = Σ_{i≤X} X_i rather than raw histograms. The cumulative sums are evaluated over the interval