Double $K$-shell photoionization of silver

We have investigated double $K$-shell vacancy production in x-ray photoionization of silver. Measurements were carried out with photon energies $\left(50\text{–}90\mathrm{keV}\right)$ varying from below threshold to beyond the expected maximum of the double $K$-shell ionization cross section. The limit of asymptotically high energies was deduced from measurements of double $K$-shell ionization following $K$-electron capture by ${}^{109}\mathrm{Cd}$ nuclei. The photon energy dependence of the ratio of double to single $K$ vacancies produced is compared to similar measurements in helium and models thereof. The dependence of that ratio on atomic number is assessed by combining these data with previous experimental and theoretical estimates. The results show a clear growth in the relative importance of the dynamical electron-electron scattering contribution in heavy atoms.

Figure 1

(Color online) The upper panel shows calculated dependence on atomic number of the hypersatellite-diagram line energy shift $\left(\mathrm{\Delta }E\right)$ [38] and lifetime width $\left(\Gamma \right)$ of the single $K$ vacancy [39]. The lower panel shows the ratio of the hypersatellite yield $\left(H\right)$ to the diagram line tail $\left(T\right)$ at the position of the $K^h{\alpha }_1$ peak. The points are the result of the calculation described in text and the line shows a $1∕Z^3$ dependence fitted to those points.

Figure 2

Measurements of the absolute photopeak efficiency for one of the Ge detectors with a calibrated ${}^{241}\mathrm{Am}$ source. The line is drawn to guide the eye.

Figure 3

(Color online) A typical distribution of time difference between the two Ge detector signals for coincidence events. The regions defining the “prompt” (time difference=0) and “delayed” coincidences are shaded.

Figure 4

Prompt coincidence energy spectrum for double $K$-shell photoionization of Ag by 90-keV photons displayed as a gray scale contour plot. The axes represent the energies measured in each detector. Both the double $K$ coincidence $\left(22\text{–}25\mathrm{keV}\right)$ and the Ge escape peak regions are indicated.

Figure 5

Fluorescence energy spectrum observed in one of the detectors for coincidence events showing the regions of Ag $K\alpha \beta (\equiv K\alpha +K\beta )$ emission and Ge escape peaks (corresponding to projection on the $x$ axis for a spectrum such as shown in Fig 4). These data were taken with 61.5-keV incident photons.

Figure 6

Prompt (top) and delayed (bottom) coincidence energy spectra in the $K$ x-ray region for double $K$-shell photoionization of Ag by $90\text{−}\mathrm{keV}$ photons displayed as contour plots of the energy in one detector $\left(E_1\right)$ versus that measured in the other $\left(E_2\right)$.

Figure 7

(Color online) Prompt spectrum measured in Det. 2 in coincidence with $K$ x rays in Det. 1 for the case of ionization by 90-keV photons. The solid line is the fit to the data obtained by summing the various components shown as dashed lines for the diagram lines and a shaded peak for the $K^h\alpha$ contribution.

Figure 8

(Color online) The fluorescence energy spectra detected in one of the detectors for the case of ionization by 61.5-keV photons. Top panel is for “singles” events, middle for prompt coincidences, and bottom are true coincidences obtained by subtracting the delayed coincidence spectrum from the corresponding prompt spectrum. The two lower spectra are obtained for coincidences with $K$ x rays in the other detector. The solid lines are the fits to the data obtained by summing the various components shown as dashed lines for the diagram lines and a shaded peak for the $K^h\alpha$ contribution.

Figure 9

(Color online) The ratio of double to single $K$-shell ionization of silver as a function of incident photon energy. The upper panel shows the data on a log-log plot while the lower panel shows the same data with linear scales, for the lower-energy region covered by this experiment. The open circles are the present results while the shaded circle shows the EC result of Ko et al. [27] which represents the asymptotic limit as is indicated by the arrow in the upper panel. The various model calculations are indicated in the legend. The “Fit”, “SSO”, and “KO” curves are based on the Rost model (see text). In the lower panel, the two vertical lines indicate the thresholds $2E_{1K}$ and $E_{2K}$ described in the text. See text for explanations of the other curves.

Figure 10

(Color online) The ratio of double to single $K$-shell photoionization as a function of atomic number. The solid symbols are used for experiments carried out in the region of the predicted peak in the double photoionization cross section. The open symbols are used for measurements of the ratio in the asymptotic limit, and the corresponding theoretical prediction for the asymptote [52] is shown as a dashed curve. The ANL experiments include an interpolation of the present $Z=47$ Ag results as described in the text as well as our $Z=10$ Ne [26] and $Z=42$ Mo [22] results. Also shown (solid line) is our previous $1∕Z^{1.61}$ power-law fit.

Figure 11

The dimensionless ratio of $(Y_p-Y_a)∕Y_a$ as described in text. The $+$ symbols show that ratio computed using the power law fit for $Y_p$ and the asymptotic expression of [52] for $Y_a$. The solid line is a best fit to those points.