Nuclear-acoustic-resonance determination of the gradient-elastic tensor and indirect nuclear-spin interactions in niobium

Nuclear-acoustic-resonance studies of the absolute intensity of the signals and of the angular dependence of their second moments have been made in single crystals of niobium for the electric quadrupole transitions $\Delta m=\pm 1$ and $\Delta m=\pm 2$ as well as for the $\Delta m=\pm 1$ magnetic dipole transition. From the intensity measurements we find the two independent coefficients of the electric field gradient-elastic strain tensor to be $|S_{11}-S_{12}|=1.2\mathrm{}\times {10}^{16}$ and $\left|S_{44}\right|=2.25\mathrm{}\times {10}^{16}$ statcoulomb ${\mathrm{cm}}^{-3\mathrm{}}$. From the second-moment data we verify that the indirect effective spin Hamiltonian is the sum of an exchange and dipolar term. The pseudodipolar coefficients for the first and second nearest neighbors are equal to $B_i=180\mathrm{} or -800\mathrm{}$ Hz and $B_2=0\mathrm{} or -400\mathrm{}$ Hz. The pseudoexchange coefficients $A_{\mathrm{ij}}$ are such that ${\Sigma }_j{A}_{\mathrm{ij}}^2=1.14\mathrm{}$ k${\mathrm{Hz}}^2$ corresponding to a first-nearest-neighbor coefficient $A_1\simeq 300$ Hz. The contribution to the second moment of the indirect electric quadrupole spin Hamiltonian is also evaluated.