Double-$K$-shell ionization of Mg and Si induced in collisions with C and Ne ions

The satellite and hypersatellite $K$ x-ray emission of a thin Mg foil and thick polycrystalline Si target bombarded by $34\text{‐}\mathrm{MeV}$ C and $50\text{‐}\mathrm{MeV}$ Ne ions was measured using high-resolution crystal diffractometry. The corresponding projectile reduced velocities $v∕v_K$ were 1.09 and 0.92 for C ions and 1.02, 0.86 for Ne ions in case of Mg and Si targets, respectively. An energy resolution of approximately $0.5\mathrm{eV}$ enabled separation of contributions corresponding to states with different numbers of $K$- and $L$-shell vacancies. The relative intensities of satellite and hypersatellite lines were determined by fitting the measured spectra with line shapes calculated using the GRASP92 computer code. To determine the production yields of initial states from the measured x-ray yields, the total decay schemes of initial states were considered. The decay schemes were also used to determine the relative intensities of components contributing to the observed $K\alpha$ satellites and hypersatellites and $K\beta$ satellite intensities. Including theoretical predictions in the fitted model is crucial to analyze properly the $K\alpha$ hypersatellite region which overlaps the $K\beta$ satellites. The initial-state production yields were then used to determine the $L$-shell ionization probabilities and the double- to single-$K$-shell ionization ratio corresponding to the four investigated collisions. The experimental values were compared to the theoretical predictions obtained within the independent electron model using single-electron ionization probabilities calculated by the three-body classical trajectory Monte Carlo (CTMC) method. Since the targets used were thick enough, the equilibrium projectile charge-state distributions in the solid media were assumed. While for the double- to single-$K$-shell ionization ratios a satisfactory agreement was observed between the CTMC predictions and our experimental results, the $L$-shell ionization probabilities were found to be overestimated by the CTMC calculations by a factor of about 2.

Figure 1

Decay scheme of the Mg $K^2{L}^{3}a$ state with two $M$-shell electrons. Only transitions with probabilities greater than 5% were considered. The notation in the boxes describes transitions (first lines), their probabilities (second lines), and atomic states after the transition with the number of $M$-shell electrons shown in parentheses (third lines). The $K\alpha$ transitions (dotted boxes) are included, regardless of their probability. The first line in these boxes describes the emitted photon.

Figure 2

Top: initial values of $\eta$ (subscript 0) for the Mg metal target and the values obtained at the end of the iteration procedure for the C-induced spectrum (subscript C) and Ne-induced spectrum (subscript Ne). Bottom: the $K\alpha$ photon yield distributions for the two Mg spectra determined from $K\beta$ photon yields using decay schemes.

Figure 3

Measured $K$ x-ray spectra of Mg fitted with the model based on the calculated line shapes. The $K\alpha$ satellite and hypersatellite regions of the spectrum induced by C impact are shown in the upper and center graphs, respectively. The lower graph shows the $K\alpha$ hypersatellite region of the Ne induced spectrum. $K\alpha$ contributions are shown by solid lines and $K\beta$ by dotted lines.

Figure 4

Measured and modeled $K\alpha$ hypersatellite spectra of Si induced by C (top) and Ne (bottom) impact. The spectra were modeled with pseudo-Voigt curves, using several curves when such a need was observed in the Mg spectra. $K\alpha$ contributions are shown by solid lines and $K\beta$ by dotted lines.

Figure 5

CTMC direct ionization (DI) and electron capture (EC) single-electron probabilities calculated for $K$- (top) and $L$- (bottom) shell electrons of Mg atoms in collisions with $34\text{‐}\mathrm{MeV}$ C ions as a function of impact parameter. The corresponding $K$- and $L$-shell radii of Mg are $0.13r_B$ and $0.69r_B$, respectively. For each point plotted in the figure, 20 000 trajectories were calculated.

Figure 6

Schematic view of the two-step double-$K$-shell ionization resulting from direct ionization (DI) and electron capture (EC) into the projectile’s $K$ shell. (SI) denotes elastic scattering. The single-electron probabilities indicated in the scheme are the CTMC predictions calculated for bare projectiles. The two-step model is needed, since electron capture probabilities are inversely proportional to the number of electrons $\left(N_e\right)$ in the projectile’s $K$ shell. We must separate the case of a bare projectile $(N_e=0)$, projectile with one-$K$-shell electron $(N_e=1)$, and projectile with $K$ shell full $(N_e=2)$, where only direct ionization contributes to the double-$K$-shell ionization.

Figure 7

Contributions of different $K^X{L}^N$ states to the $K\alpha L^N$ photon yields in the $\mathrm{Ne}\text{−}\mathrm{Mg}$ collisions (top) and $\mathrm{Ne}\text{−}\mathrm{Si}$ collisions (bottom).

Figure 8

Initial vacancy production yield distributions for states with one (Sat) and two holes (Hyp) in the $K$ shell for $\mathrm{C}\text{−}\mathrm{Si}$ collisions (top) and $\mathrm{Ne}\text{−}\mathrm{Mg}$ collisions (bottom). The dotted lines correspond to the best fits to the binomial distribution.

Figure 9

Comparison of the experimental double- to single-$K$-shell ionization ratios ${\sigma }_d∕{\sigma }_s$ obtained in the present work with theoretical predictions computed in Sec. 4. Since the theoretical values depend on the projectile’s charge, the values calculated for bare projectiles $(N_e=0)$, projectiles with two $1s$ electrons $(N_e=2)$, and projectiles with the equilibrium charge in solid media $(N_e=av)$ were plotted. For Mg the ratios obtained by fixing the $K\beta L^4$ and $K\beta L^5$ intensities to the calculated values are also presented ($K\beta$ fix).

Figure 10

Schematic view of the beam-target geometry used in the present experiment.