Distribution of Partial Radiation Widths

Abstract

The gamma-ray spectra that result from the capture of neutrons in resonances of ${\mathrm{Hg}}^{199}$, ${\mathrm{Pt}}^{195}$, ${\mathrm{W}}^{183}$, and ${\mathrm{Se}}^{77}$ are measured. A least-squares fitting of the spectra gives relative values of partial widths for various sets of high-energy radiative transitions. These widths are treated as statistical samples drawn from populations governed by a ${\ensuremath{\chi}}^{2}$ distribution with $\ensuremath{\nu}$ degrees of freedom. A technique of hypothesis testing that makes use of Monte Carlo calculations is used to derive unbiased values of $\ensuremath{\nu}$ from the small samples of experimental widths. The over-all result of the analysis is $\ensuremath{\nu}=1.34\ifmmode\pm\else\textpm\fi{}0.33\ifmmode\pm\else\textpm\fi{}0.21$. The previously reported partial radiation widths for resonances of ${\mathrm{Gd}}^{155}$, ${\mathrm{Yb}}^{173}$, ${\mathrm{Hf}}^{177}$, and ${\mathrm{Hg}}^{201}$ are also analyzed. The result is $\ensuremath{\nu}=1.14\ifmmode\pm\else\textpm\fi{}0.44\ifmmode\pm\else\textpm\fi{}0.21$. Thus, both sets of data are in good agreement with the value $\ensuremath{\nu}=1$ that is expected from the Porter-Thomas description of the distribution of the widths associated with a single exit channel.