$L$ x rays emitted from multiply ionized holmium atoms

Spectra of $L$ x rays emitted from Ho targets bombarded by 10 keV electrons and $6\mathrm{MeV}∕\mathrm{amu}$ C, Ne, Ar, Kr, and Xe ions were measured in high resolution using a curved crystal spectrometer. The spectra were analyzed in order to examine the systematic evolution of the $L$ x-ray satellite structure as a function of projectile atomic number. Scaling rules are established for the apparent average $M$-shell spectator vacancy fraction and apparent average double to single $L$-vacancy population ratio at the time of $L$ x-ray emission. The results are compared to those obtained for $K$-shell ionizing collisions and with predictions of the geometrical model.

Figure 1

Spectra of $L$ x rays emitted from a Ho target under bombardment by (a) 10 keV electrons and $6\mathrm{MeV}∕\mathrm{amu}$ beams of (b) C, (c) Ne, (d) Ar, and (e) Kr. The vertical dashed lines indicate the energy positions of the nine most prominent $L$ x-ray diagram lines (see Table ). The $L_3$ absorption edge is shown by the vertical solid line.

Figure 2

(Color online) Fit of the Ho $L$ x-ray spectrum excited by (a) and (b) $6\mathrm{MeV}∕\mathrm{amu}$ C ions and (c) and (d) $6\mathrm{MeV}∕\mathrm{amu}$ Ne ions showing the experimental data points (black), overall fitted curve (red), background component curve (gray), and individual $L^1\xi M^j$ satellite peaks (blue and brown). Some of the peaks are offset in the vertical direction to avoid excessive overlapping. Only one representative peak in each group is labeled in order to avoid overcrowding. The remaining curves, as labeled, represent the combined contribution from the $L$ x-ray diagram lines (magenta) and the combined contribution from the $L^2\xi M^j$ satellite peaks (green).

Figure 3

(Color online) Fit of the Ho $L$ x-ray spectrum excited by $6\mathrm{MeV}∕\mathrm{amu}$ Kr ions. The circles represent the measured data points; the solid lines represent the overall fit (red), the (combined) $L^i\xi M^j$ satellite groups [blue, green, and brown, shown separately for different numbers of initial $L$ vacancies (i), as indicated] and (combined) contribution from the $L$ x-ray diagram lines (magenta). Satellite peaks corresponding to different values of $j$ are not shown individually, although they were included in the analysis as such. The dashed line (gray) represents the background.

Figure 4

(Color online) Spectrum of $K$ x rays emitted from a thick Co target bombarded by $6\mathrm{MeV}∕\mathrm{amu}$ Kr ions. The circles represent the measured data points; the solid lines represent the overall fit (red), the contributions from $K{\alpha }_1$ and $K{\alpha }_2$ satellites (blue and brown, respectively), and the combined contribution from the $K{\alpha }_1$ and $K{\alpha }_2$ diagram lines (magenta). The dashed line (gray) represents the background.

Figure 5

(Color online) Ionization probabilities per electron (dashed curve) plotted as a function of the universal variable $\left(X_n\right)$ according to the geometrical model [27]. The data points are experimental apparent average vacancy fractions obtained in analyses of Co, Ni, and Cu $K$ x-ray spectra $\left(p_L^x\right)$ and Ho $L$ x-ray spectra ($p_M^x$ and $p_{N+}^x$). Index $N+$ refers to Ho outer shells ($N$ shell plus the shells above it). $X_n$ was determined using Eq. (2) and expressed in atomic units.

Figure 6

(Color online) Double-vacancy production to single-vacancy production cross-section ratios $({\sigma }_2∕{\sigma }_1)$, calculated using Eq. (6), plotted (a) as a function of the single-electron ionization probability at small impact parameters $\left(p_o\right)$ and (b) as a function of the corresponding universal variable $\left(X_n\right)$ determined using Eq. (3). The solid lines represent the results for the $L$-shell ionization of Ho (red) and $K$-shell ionization of Ni (blue). Also shown are the measured values of $R^L{}_{2∕1}$ (open circles) and $R^K{}_{2∕1}$ (solid circles), for which $X_n$ was determined using Eq. (2) and the corresponding values of $p_o$ were determined as $p_s^x$ using Eq. (3). The data point shown by the solid diamond (measured using a $6\mathrm{MeV}∕\mathrm{amu}$ N beam on a Ni target) was taken from Ref. 34. The dashed lines represent the universal function predicted by the geometrical model, as given by Eq. (1).