Isomer-Shift Calibrations Using Multivalent States of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ in KMg${\mathrm{F}}_3$

KMg${\mathrm{F}}_3$ single crystals were doped with ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ and irradiated by ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$ $\gamma$ rays. The obtained ${\mathrm{Fe}}^{+}$, ${\mathrm{Fe}}^{++}$, and ${\mathrm{Fe}}^{+++}$ states in KMg${\mathrm{F}}_3$ were investigated by Mössbauer spectroscopy. The isomer-shift values were correlated with electron densities $\rho \mathrm{}\left(0\right)\mathrm{}$ as evaluated by using an open-shell molecular-orbital procedure. The resulting isomer-shift calibration constant $\alpha$ is $(-0.34\mathrm{}\pm 0.04){a_0}^3$ mm ${\sec }^{-1\mathrm{}}$.