Anisotropic gamma -ray resonance scattering from a zinc single crystal and the uncertainty principle.

Abstract

The nuclear-resonance photon-scattering technique was used for studying the temperature dependence between 12 and 295 K of the anisotropy in the scattering cross section from the 7362-keV level in $^{68}\mathrm{Zn}$ using a single crystal of metallic zinc. The anisotropy ratio of the scattering intensities with the beam parallel and perpendicular to the hexagonal planes of Zn was found to increase strongly between 295 and 12 K. This was interpreted in terms of the anisotropic binding of the Zn atoms and was used for deducing the mean-square momenta 〈${\mathit{p}}^{2}$${\mathrm{〉}}_{\mathrm{\ensuremath{\perp}}}$ and 〈${\mathit{p}}^{2}$${\mathrm{〉}}_{\mathrm{\ensuremath{\parallel}}}$ of the Zn atoms at 0 K perpendicular and parallel to the hexagonal planes, and the corresponding Debye temperatures ${\mathit{FTHETA}}_{\mathrm{\ensuremath{\parallel}}}$ and ${\mathit{FTHETA}}_{\mathrm{\ensuremath{\perp}}}$. When these values were combined with the known values of the zero-point vibrational amplitudes 〈${\mathit{x}}^{2}$${\mathrm{〉}}_{\mathrm{\ensuremath{\perp}}}$ and 〈${\mathit{x}}^{2}$${\mathrm{〉}}_{\mathrm{\ensuremath{\parallel}}}$ obtained using the M\ossbauer effect, the theoretical lower limit of the uncertainty principle for a metallic solid was found to be reached almost accurately.