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 \textit{K}-hypersatellite lines, \(Kα_2^h\), \(Kα_1^h\), and \(Kβ_{1,3}^h\), are measured as $(6143.5\pm0.5)$ eV, $(6162.1\pm1.5)$ eV and $(6811.9\pm2.6)$ eV, respectively. The relative intensities of \textit{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.