The nuclear quadrupole moment (NQM) of the $I^{\pi }{=3/2\mathrm{}}^{-}$ excited nuclear state of ${}^{57}\mathrm{Fe}$ at 14.41 keV, important in Mössbauer spectroscopy, is determined from the large-scale nuclear shell-model calculations for ${}^{54}\mathrm{Fe}$, ${}^{57}\mathrm{Fe}$, and also from the electronic ab initio and density functional theory calculations including solid state and electron correlation effects for the molecules $\mathrm{Fe}(\mathrm{CO}{)}_5$ and $\mathrm{Fe}({\mathrm{C}}_5{\mathrm{H}}_5{)}_2$. Both independent methods yield very similar results. The recommended value is 0.15(2) e b. The NQM of the isomeric $10+$ in ${}^{54}\mathrm{Fe}$ has also been calculated. The new NQM values for ${}^{54}\mathrm{Fe}$ and ${}^{57}\mathrm{Fe}$ are consistent with the perturbed angular distribution data.

• Received 12 January 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.062701