Neutron Resonance Spectroscopy. XII. The Separated Isotopes of W

Abstract

The results of neutron resonance time-of-flight spectroscopy measurements using the Nevis synchrocyclotron are given for the separated W isotopes (182, 184, 186) and for natural W. Almost all $s$ levels were observed to 2.65 keV, and resonance $\mathrm{}\left(g\right)\mathrm{}{\Gamma }_n^o$ values presented to ∼16 keV for the above even isotopes, and to 700 eV and 2.6 keV, respectively, for ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$. The ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$ level assignments were from levels in natural W which were not assigned to the other isotopes. A Bayes's theorem analysis shows that nearly all of the observed levels are $s$ rather than $p$ levels, since W is at a maximum for the $s$ strength function $S_0$ but not for $S_1$, and the level detection sensitivity was not sufficient to detect other than exceptionally strong $p$ levels. We were able to assign $J$ values to 14 $s$ levels of ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$. The 41 observed ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ levels to 2.65 keV and the 52 ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$ levels to 701 eV seem to be pure complete $s$ populations, being fitted excellently by the Wigner nearest neighbor spacing theory and the Porter-Thomas reduced neutron width distribution. The orthogonal ensemble (OE) theory was found to be in good agreement with the ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ and ${}_{}{}^{183}{}_{}{}^{}\mathrm{W}$ data. The ${}_{}{}^{184}{}_{}{}^{}\mathrm{W}$ level set to ∼2.6 keV also seems to be an essentially complete, pure, $s$ population sample. While it agreed within statistical limits to the above statistical theories, it gave poorer discrimination against alternate theories. Tests suggested that a few $s$ levels in ${}_{}{}^{186}{}_{}{}^{}\mathrm{W}$ had been missed to ∼2.6 keV. The ${10}^4{S}_o$ values are 2.40 ± 0.31, 1.65 ± 0.32, 2.35 ± 0.24, and 2.23 ± 0.27 for 182, 183, 184, and 186, respectively. The $〈D〉$ values for $s$ populations are 66.3 ± 3.2 eV (182), 13.2 ± 0.7 eV (183), 81.3 ± 5.1 eV (184), and 90 ± 7 eV (186). A useful and accurate method for evaluating the Doppler-broadening integrals is described.