Nuclear Moments of ${\mathrm{Tb}}^{157}$, ${\mathrm{Tb}}^{158}$, and ${\mathrm{Tb}}^{160}$ by Electron Paramagnetic Resonance and Nuclear Alignment

Electron-paramagnetic-resonance experiments on yttrium ethylsulfate (YES) single crystals containing terbium isotopes in the relative abundances ${\mathrm{Tb}}^{159}$:${\mathrm{Tb}}^{157}$:${\mathrm{Tb}}^{158}$=25:1.6:1 were carried out at $Q$-band frequencies (35 GHz). The nuclear spin of ${\mathrm{Tb}}^{158}$ was found to be 3, and by comparison with the observed hyperfine structure of ${\mathrm{Tb}}^{159}$ and its known moment, a magnetic moment ${\mu }^{158}=1.740\mathrm{}\left(7\right)\mathrm{}$ nm was calculated. Transitions due to ${\mathrm{Tb}}^{157}$ were obscured by the stronger ${\mathrm{Tb}}^{159}$ lines. Assuming $I\left(157\right)=I\left(159\right)=\frac{3}{2}$, the following limits were set on the value of ${\mu }^{157}:{\mu }^{157}=2.0\mathrm{}\left(1\right)\mathrm{}$ nm. ${\mathrm{Tb}}^{160}$ lines were also observed in YES single crystals. They gave ${\mu }^{160}=1.685\mathrm{}\left(8\right)\mathrm{}$ nm. Nuclear-alignment experiments on ${\mathrm{Tb}}^{158}$ in a single crystal of neodymium ethylsulfate were also carried out in order to determine a relationship between the quadrupole coupling constant and the magnetic hyperfine structure constant. This information, as well as existing nuclear-orientation results on ${\mathrm{Tb}}^{160}$, was combined with the EPR data to obtain quadrupole coupling constants. Quadrupole moments calculated from the coupling constants were found to be $Q^{158}=+2.7\mathrm{}\mathrm{}\left(5\right)\mathrm{}$ b and $Q^{160}=+3.0\mathrm{}\mathrm{}\left(5\right)\mathrm{}$ b.