Background: In electron-capture decay, a second $K$-shell vacancy is eventually created with a small probability. Measurements of the double-vacancy creation probability per $K$-shell electron capture $P_{KK}$ of various nuclei undergoing electron-capture decays have already been performed, but the statistical accuracy of $P_{KK}$ of several nuclides is still not satisfying.

Purpose: The purpose of this experiment was to improve the statistical error of $P_{KK}$ in the decay of ${}^{55}\mathrm{Fe}$ and to demonstrate the possibility of detecting double-vacancy creation events with position resolving pixel detectors. This enables angle resolved measurements.

Method: For the first time, two active-pixel detectors (A,B) were used to detect satellite- and hypersatellite-line photons in coincidence either both in two clusters of triggered pixels in only one detector (A,B) or in both detectors $(\text{A}\wedge \text{B})$. $P_{KK}$ was determined for the two detectors regarded as one single, larger detector ($P_{KK}$), for each detector separately (single-sided analysis: $P_{KK,\text{A}⊻\text{B}}$), and for both detectors in coincidence (double-sided analysis: $P_{KK,\text{A}\wedge \text{B}}$).

Results: The result of the experiment is $P_{KK}=(1.531\pm 0.079)\times {10}^{-4}$ with a systematic error of ${\left(\Delta P_{KK}\right)}_{\text{syst}}=\pm 0.023\times {10}^{-4}$. This value is in agreement with the value previously measured by Campbell et al. of $P_{KK}=(1.3\pm 0.2)\times {10}^{-4}$. The discrepancy in literature between $P_{KK}$ of ${}^{54}\mathrm{Mn}$ to the expected value extrapolated from ${}^{55}\mathrm{Fe}$ almost vanished with our result. The asymmetry between the result of the single-sided analysis ($P_{KK,\text{A}⊻\text{B}}$) and the double-sided analysis ($P_{KK,\text{A}\wedge \text{B}}$) is consistent with zero: $(P_{KK,\text{A}⊻\text{B}}-P_{KK,\text{A}\wedge \text{B}})/(P_{KK,\text{A}⊻\text{B}}+P_{KK,\text{A}\wedge \text{B}})=-0.003\pm 0.051$. This supports the assumption that angular correlations between the two photons are negligible within the achieved level of statistical accuracy for the given angular acceptance of our detectors.

Conclusions: One can conclude that hybrid photon counting pixel detectors can be used to measure angular correlations between the directions of emission of satellite and hypersatellite photons. Our result supports the suspicion that the reported discrepancy between $P_{KK}$ measured for the electron-capture decays of ${}^{54}\mathrm{Mn}$ and ${}^{55}\mathrm{Fe}$ was probably due to statistical fluctuations in the measurements. Furthermore, the $Z^{-2}$ dependence of $P_{KK}$ predicted by Primakoff and Porter is supported. The improved statistical error of our measurements underlines the previously reported discrepancy between $P_{KK}$ expected for ${}^{65}\mathrm{Zn}$ if an extrapolation is carried out from our result on ${}^{55}\mathrm{Fe}$. Thus, our result strengthens the need for triple coincidence measurements of $P_{KK}$ on ${}^{65}\mathrm{Zn}$.

• Received 15 October 2013
• Revised 22 November 2013

DOI:https://doi.org/10.1103/PhysRevC.89.014609