Low-energy photoelectron dynamics in Kr $3d_{5/2}$ photoionization followed by Auger decay

The effects induced during the process of inner-shell photoionization followed by Auger decay are investigated for the photoionization of Kr $3d_{5/2}$ in an extremely low photoelectron energy regime. Both the photoelectron energy and relative angular distributions are calculated with a recently developed quantum-mechanical method where all the Coulomb interactions between each pair of particles are fully considered. The photoelectron energy distribution is asymmetric with respect to the initial photoelectron energy, and its peak shifts to a lower energy. As the absorbed photon energy is reduced, the peak of the photoelectron energy distribution moves to the negative energy range. As a manifestation of these dynamics, peak structures are observed in the relative angular distribution. We also simulate the process with a classical-trajectory Monte Carlo method, obtaining similar results to the quantum-mechanical ones.

Figure 1

The photoelectron energy distributions (normalized by dividing by the maximum probability in positive energy range) for cases (a) $E_1=1.0$ eV (dot-dashed line), 0.5 eV (dotted line), 0.25 eV (dashed line), 0.125 eV (thin solid line), and 0.1 eV (thick solid line) and (b) $E_1=0.0$ eV (thick solid line). The arrows point to the energy with maximum probability, which is 0.88 eV for the case $E_1=1.0$ eV, 0.33 eV for the case $E_1=0.5$ eV, and 0.05 eV for the case $E_1=0.25$ eV.

Figure 2

The angular probability distributions calculated by the TDSE method (normalized by dividing by the maximum probability) for cases $E_1=1.0$ eV (dot-dashed line, shifted up by 5.0), 0.5 eV (dotted line, shifted up by 4.0), 0.25 eV (dashed line, shifted up by 3.0), 0.125 eV (thin solid line, shifted up by 2.0), 0.1 eV (medium solid line, shifted up by 1.0), and 0.0 eV (thick solid line). The arrows point to the angular positions of peak(s), which are $cos{\theta }_{12}=0.74$ for the case $E_1=0.25$ eV, $cos{\theta }_{12}=0.34$ and 0.77 for the case $E_1=0.125$ eV, $cos{\theta }_{12}=0.36$ and 0.791 for the case $E_1=0.1$ eV, and $cos{\theta }_{12}=0.3$ for the case $E_1=0.0$ eV.

Figure 3

The physical quantity PED for cases (top) $E_1=0.125$ eV and (bottom) 0.0 eV.

Figure 4

The angular momentum distributions for the ionized photoelectrons (normalized by dividing by the maximum probability) of cases $E_1=1.0$ eV (red dot-dashed line), 0.5 eV (green dotted line), 0.25 eV (blue dashed line), 0.125 eV (thin solid line), 0.1 eV (medium solid line), and 0.0 eV (thick solid line). The arrows point to the angular momentum positions of the second peak, which are $\ell =6$ for the case $E_1=0.125$ eV, $\ell =7$ for the case $E_1=0.1$ eV, and $\ell =4$ for the case $E_1=0.0$ eV.

Figure 5

The angular probability distributions calculated by the CTMC method (normalized by dividing by the maximum probability) for cases $E_1=1.0$ eV (dot-dashed line, shifted up by 5.0), 0.5 eV (dotted line, shifted up by 4.0), 0.25 eV (dashed line, shifted up by 3.0), 0.125 eV (thin solid line, shifted up by 2.0), 0.1 eV (medium solid line, shifted up by 1.0), and 0.0 eV (thick solid line). The arrows point to the angular positions of the peak(s), which are $cos{\theta }_{12}=0.84$ for the case $E_1=0.25$ eV, $cos{\theta }_{12}=0.298$ and 0.88 for the case $E_1=0.125$ eV, $cos{\theta }_{12}=0.3$ and 0.89 for the case $E_1=0.1$ eV, and $cos{\theta }_{12}=0.27$ for the case $E_1=0.0$ eV.