Electronic shielding by closed shells in salts of thulium

Electronic shielding by closed electron shells has been investigated in salts of trivalent thulium, by measuring the temperature dependence of the nuclear quadrupole splitting of the 8.42-keV gamma transition in ${\mathrm{Tm}}^{169}$. The measurements were performed by using the technique of recoilless nuclear resonance absorption. The nuclear quadrupole interaction was studied for ${\mathrm{Tm}}^{3+}$ ions in thulium ethyl sulfate, thulium oxide, and thulium trifluoride within a temperature range from 9.6 to 1970\ifmmode^\circ\else\textdegree\fi{}K. The interpretation of the experimental data in terms of the contributions of distorted closed electron shells to the quadrupole interaction yields values for electronic shielding factors. The results lead to amounts of 10% or less for the atomic Sternheimer factor ${R}_{Q}$. The experiments also reveal substantial shielding of the $4f$ electrons from the crystal electric field, expressed by the shielding factor ${\ensuremath{\sigma}}_{2}$. Values of 250 and 130 are obtained for the ratio $\frac{(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})}{(1\ensuremath{-}{\ensuremath{\sigma}}_{2})}$ for thulium ethyl sulfate and thulium oxide, respectively, where ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ is the lattice Sternheimer factor.