Experimental determination of the double $K$-shell vacancy creation probability in the electron-capture decay of ${}^{55}$Fe with a microcalorimeter

The probability of double $K$-shell vacancy production following electron-capture decay is determined for ${}^{55}$Fe using a high-resolution microcalorimeter. The $K$-hypersatellite lines arising from double $K$-shell-vacancy filling are directly resolved within the measured spectra of X-ray emissions which are dominated by Mn $K$-X-ray diagram lines. The energies of the Mn $\mathit{\text{K}}$-hypersatellite lines, $K{\alpha }_2^h$, $K{\alpha }_1^h$, and $K{\beta }_{1,3}^h$, are measured as $(6143.5\pm 0.5)$ eV, $(6162.1\pm 1.5)$ eV and $(6811.9\pm 2.6)$ eV, respectively. The relative intensities of $\mathit{\text{K}}$-hypersatellite to diagram X-rays are measured to be $(1.30\pm 0.07)\times {10}^{-4}$. From the relative intensities together with established fluorescence yield values, the probability of double-vacancy creation per $K$-shell capture ($P_{KK}$) is determined as $(1.22\pm 0.09)\times {10}^{-4}$. Comparisons with previous experimental results and theoretical calculations are discussed.