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

Abstract

The average-resonance method of neutron-capture $\ensuremath{\gamma}$-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 $A>100$ if the $\ensuremath{\gamma}$-ray strength function is a smooth function of $\ensuremath{\gamma}$-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 $\ensuremath{\gamma}$-ray energy and that the random fluctuations in intensity are well described by the Porter-Thomas distribution. The intensities of $E1$ transitions vary with $\ensuremath{\gamma}$-ray energy more rapidly than $E_{\ensuremath{\gamma}}^{}{}_{}{}^{3}$, as expected from a giant-resonance description of the radiative process. The intensity of $M1$ radiation was measured over a 2-MeV range for $^{106}\mathrm{Pd}$ and $^{168}\mathrm{Er}$, and the reduced $M1$ widths for $^{106}\mathrm{Pd}$ form a giant-resonance-like curve that peaks at \ensuremath{\sim}7.8 MeV. Ratios of widths for $E1$ and $M1$ radiation and for $E1$ and $E2$ 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 $\ensuremath{\gamma}$-ray lines may be used to determine the parities of final states.