Spectator-electron behavior during cascade decay in krypton

We report new measurements of ${\mathrm{Kr}}^{q+}$ photo-ions, coincident with $K\alpha$ or $K\beta$ fluorescence as incident-photon energy is swept through the Kr $K$-shell threshold. From the branching ratios just above threshold, we obtain measurements of the ion charge-state probabilities for decay from the Kr $\left[2p\right]$ and Kr $\left[3p\right]$ states. In the threshold region, we observe both resonant enhancement and depletion of the branching ratios. By analyzing this behavior in light of theory, we extract sticking probabilities, which we feel are a useful set of parameters for investigating the general relationship between cascade decay from resonant and nonresonant hole states. A simplified theoretical model is employed to calculate these probabilities for the ${\mathrm{Kr}}^{2+}$ and ${\mathrm{Kr}}^{3+}$ cases.

Figure 1

Kr ion time of flight spectra coincident with $K\alpha$ [panel (a)] and $K\beta$ [panel (b)] x-ray emission. These spectra were recorded with the incident-photon energy set to the inflection point of the observed $K$-shell edge $(E_{\text{edge}}=0\mathrm{eV})$. Each charge peak consists of a number of subpeaks corresponding to the various Kr isotopes.

Figure 2

Branching ratios for ${\mathrm{Kr}}^{q+}$ production in coincidence with $K\alpha$ emission, as a function of incident-photon energy. The raw data [e.g., of Fig. 1a] has been corrected for a charge-dependent ion detection probability. The data points are connected by lines to better indicate the trends.

Figure 3

Branching ratios for ${\mathrm{Kr}}^{q+}$ production in coincidence with $K\beta$ emission, as a function of incident-photon energy. The raw data [e.g., of Fig. 1b] has been corrected for a charge-dependent ion detection probability. The data points are connected by lines to better indicate the trends.

Figure 4

Comparison of above-threshold ${\mathrm{Kr}}^{q+}$ branching ratios with theoretical predictions. Panel (a) displays our experimental results (circles) for ions coincident with $K\alpha$ emission and the experimental results of Carlson et al. [16] (boxes), together with the $j$-averaged ${\mathrm{L}}_{2,3}$ probabilities calculated by Kochur et al. [14] (solid bar) and El-Shemi et al. [15] (dashed bar). Panel (b) displays our results (circles) for $K\beta$-coincident ions, together with the measured values of Matsui et al. [10] (triangles) and the calculated results of Kochur et al. [14] (solid bar) for decay from Kr ${\mathrm{M}}_{2,3}$ states.

Figure 5

Model function of Eq. (12) for the ratio of Kr $K$-shell excitation-to-total cross section. The central, solid line corresponds to an offset parameter $\mathrm{\Delta }=3.5\mathrm{eV}$. The broken lines indicate the change resulting from varying $\mathrm{\Delta }$ by $\pm 0.5\mathrm{eV}$.

Figure 6

Two examples of least-squares fits of branching ratios to Eq. (9) using the model function of Fig. 5. The triangular data points at high energy, connected by broken lines, are above threshold for multiple excitations and are excluded from the fit.

Figure 7

Flux normalized yield of ${\mathrm{Kr}}^{1+}$ ions (triangles) coincident with $K\alpha$, $K\beta$ fluorescence, as a function of incident photon energy across the $K$-shell edge. The circles connected by dotted lines are the total-ion edge ${\sigma }_T$, scaled to the ${\mathrm{Kr}}^{1+}$ yield. The dashed line is an estimate of ${\sigma }^{+}$, the ionization component of the edge. If there were no contribution from resonant $\left[2p\right]np$ and $\left[3p\right]np$ initial states, the yield would follow ${\sigma }^{+}$.