Systematical law of (n, γ) reaction cross sections of odd-A nuclei

A formula for neutron radiative capture cross section is derived within the framework of compound nucleus hypothesis for incident neutron energy (EnEn) above the resonance region up to MeV. Based on this formula, we find a linear relationship between the logarithm of an (n, γ  ) cross section at fixed EnEn divided by A1.4 and the relative neutron excess of the target nucleus, and new systematics are established between the (n, γ) reaction cross section and the energy level density of a compound nucleus. The calculated (n, γ) cross sections for odd-A target nuclei from this relationship are in good agreement with the experimental data, which suggests that this new systematical law is helpful to analyze the experimental data. It would be helpful in estimating the (n, γ) cross sections of neighboring odd-A isotopes for which no experimental data are available.