Average-Resonance Method of Neutron-Captureγ-Ray Spectroscopy: States ofPd106,Gd156,Gd158,Ho166, andEr168

The average-resonance method of neutron-capture $\gamma$-ray spectroscopy is critically examined by means of measurements on stable isotopes of palladium, gadolinium, holmium, and erbium. A mathematical model of the capture process is developed. This model shows that the intensities of the lines in average-resonance-capture spectra can yield the parities and set narrow limits on the spins of states in almost all nuclides with $A>\mathrm{}100\mathrm{}$ if the $\gamma$-ray strength function is a smooth function of $\gamma$-ray energy and if the random fluctuations in intensity result only from the Porter-Thomas distribution of partial radiation widths. The measurements give extensive data for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, and some for ${}_{}{}^{103}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{155}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{157}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$. These data are examined for information relating to the mechanisms of radiative capture. All of the data are consistent with the hypothesis that the radiation widths are a smooth function of $\gamma$-ray energy and that the random fluctuations in intensity are well described by the Porter-Thomas distribution. The intensities of $E1\mathrm{}$ transitions vary with $\gamma$-ray energy more rapidly than $E_{\gamma }^{}{}_{}{}^3$, as expected from a giant-resonance description of the radiative process. The intensity of $M1\mathrm{}$ radiation was measured over a 2-MeV range for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, and the reduced $M1\mathrm{}$ widths for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ form a giant-resonance-like curve that peaks at ∼7.8 MeV. Ratios of widths for $E1\mathrm{}$ and $M1\mathrm{}$ radiation and for $E1\mathrm{}$ and $E2\mathrm{}$ radiation are obtained for several nuclides. These properties of radiative capture are used to obtain spectroscopic information about final states. The most complete results are for ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}$, for which 16 rotational bands are identified and interpreted in terms of the collective model. Similar but less extensive data are obtained for ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{158}{}_{}{}^{}\mathrm{Gd}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$. The measurements on ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ show that the shapes of the observed $\gamma$-ray lines may be used to determine the parities of final states.