Approaches for theoretical and experimental determinations of $K$-shell decay rates and fluorescence yields in Ge

Fluorescence yields are one of the fundamental parameters in atomic physics and related areas. Despite the increase of experimental work in the last decade, to obtain values of $K$-shell fluorescence yields available data are scarce or outdated for many elements. The available theoretical results cannot fill the gap since quite often they are derived from semi-empirical calculations based on old models. This is the case of Ge that has many applications in science. In this work, we present the results of a collaboration between an experimental and a theoretical group to obtain the decay rates and fluorescence yields for Ge. The calculations were performed within the Dirac-Fock method, including relativistic and QED corrections, using a state-of-the-art approach. The experimental work was carried out at the SOLEIL synchrotron and the fluorescence yields were measured by two distinct methods: the reflection geometry method and the escape peak method. The results show a very good agreement between the experiment and theory (1.1%), well within the experimental uncertainty (2.4%).

Figure 1

Geometry of the experimental setup.

Figure 2

Spectrum obtained with 14-keV incident energy with detailed processing of the escape peak's area. Blue lines stand for the fitting contributions and red line for the fitting line.

Figure 3

Mass-attenuation coefficients of Ge measured between 7 and 35 keV (top panel) and near edge fine structures (bottom panel).

Figure 4

Relative differences $R_{\mathrm{Tab}}$ between our experimental values ${\mu }_{\mathrm{LNHB}}$ and the tabulated values [47, 48].

Figure 5

Ge partial K-shell fluorescence yields in the reflection setup measurement (top panel) and escape peak method (bottom panel). Black diamonds $⧫$ (K$\alpha$ fluorescence yields) refer to the left vertical scale and red diamonds $\diamond$ (K$\beta$ fluorescence yields) refer to the right one.