Double $1s$ shell ionization of Si induced in collisions with 1–3-MeV protons

The double $1s$ ionization of Si induced in collisions with protons was studied by measuring the $K$ x-ray emission of a solid Si target ionized by the impact of 1–3-MeV protons. In order to resolve the hypersatellite contributions corresponding to the radiative decay of the double $1s$ vacancy state, a high-resolution crystal spectrometer was employed yielding sub-eV energy resolution. From the intensity of the measured hypersatellite lines double $1s$ ionization cross sections for the studied collisions were determined. Experimental values were compared with the theoretical ones obtained within the independent electron framework employing single electron ionization probabilities calculated with the semiclassical approach. This comparison suggests a sequential two step model for the double $1s$ ionization which was additionally confirmed by four body classical trajectory Monte Carlo calculations.

Figure 1

High-resolution $K\beta$ x-ray spectrum of Si induced in collisions with 2-MeV protons. The structure on the high-energy side, shown enlarged in the inset, corresponds to the lines of interest, namely the $K\beta L^1$ satellite and $K{\alpha }^{\mathrm{h}}$ hypersatellite lines.

Figure 2

High-resolution spectra of the $K\beta L^1$ satellite (dotted line) and $K{\alpha }^{\mathrm{h}}$ hypersatellite lines (solid line) induced in collisions with 1-MeV (a), 2-MeV (b), and 3-MeV (c) protons, respectively. The spectra were decomposed by the fitting model explained in the text. The background described by a second-order polynomial has been substracted from the spectra before the analysis. As expected the first two lines corresponding to $K\beta L^1$ satellite line show no dependence on the proton energy, while the intensity of the third component corresponding to the hypersatellite line clearly varies with the proton energy.

Figure 3

(Color online) The single $1s$ ionization cross sections of Si bombarded with protons from Ref. 20 compared with the first-order SCA calculation of Trautmann and Rösel [21] (red line) and the SCA calculation of Šmit [22] (black line).

Figure 4

(Color online) Double $1s$ direct ionization cross sections ${\sigma }_{\mathrm{KK}}$ as a function of the proton energy. Our experimental results are compared with the theoretical calculation within the independent electron framework using single electron ionization probabilities calculated by the first-order SCA calculation of Trautmann and Rösel [21] (red line) and the SCA calculation of Šmit [22] (black line). The dashed curves represent the double ionization cross sections ${\sigma }_{\mathrm{KK}}^{*}$ calculated with the two step model where the binding energy of the second $1s$ electron is increased.

Figure 5

(Color online) Two typical trajectories for the double $1s$ ionization of Si calculated for the 3-MeV proton at an impact parameter of 0.05 atomic unit. The trajectories of projectile (straight solid line) and both $1s$ electrons together with the position of the target nucleus (solid dot) are presented in the laboratory frame and in an arbitrary plane $\left(y\text{−}z\right)$ projection. The positions of the ejection of first and second $1s$ electron along the projectile’s trajectory are indicated with arrows. Calculated trajectories demonstrate the sequential two step process leading to the ejection of both $1s$ electrons.