Absolute Determination of Spins of Neutron Resonances and the Hyperfine Coupling Constant in Er-167

The spins of the four lowest neutron resonances in ${\mathrm{Er}}^{167}$ have been determined by measuring the transmission of polarized neutrons through a sample of polarized erbium nuclei. The determination of the spins depends solely on the transmission effect and is independent of any assumption about the sign of the nuclear magnetic moment or the direction of the effective field at the target nuclei. The spins were found to be $J=I+\frac{1}{2}=4$ for the 0.460-eV resonance and $J=I\ensuremath{-}\frac{1}{2}=3$ for the resonances at 0.584, 6.10, and 9.6 eV. The nuclear polarization of the sample, obtained as function of the sample temperature at a fixed energy, was fitted to a theoretical curve, using the magnetic and electric hyperfine splitting constants as fitting parameters. The values found for the magnetic and electric hfs constants are, respectively, $\frac{A}{k}=\ensuremath{-}0.085\ifmmode\pm\else\textpm\fi{}0.0005$\ifmmode^\circ\else\textdegree\fi{}K and $\frac{P}{k}=\ensuremath{-}0.005\ifmmode\pm\else\textpm\fi{}0.001$\ifmmode^\circ\else\textdegree\fi{}K. Taking the nuclear magnetic moment of ${\mathrm{Er}}^{167}$ to be $\ensuremath{-}0.56{\ensuremath{\mu}}_{N}$, the corresponding effective magnetic field at the nucleus is 7.26 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$Oe.