# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### Electron Spectrum of Xenon Clusters Irradiated with XFEL Pulses  
To discuss the involved photo-emission and the subsequent Auger emission, which are the initial stages of cluster ignition by irradiation of hard X-ray pulses, we focus on the electron energy spectrum. The black curve in Figure 1a depicts the electron energy spectrum of xenon clusters with an average size of 5000 atoms, irradiated with an XFEL pulse with the photon energy of 5.5 keV and the peak fluence of \(\sim\)1.8 \(\upmu\)J/\(\upmu\)m\({}^{2}\). The electron spectrum exhibits four visible peaks and an unstructured contribution. The unstructured feature in the electron spectrum can be represented by the sum of two exponential functions, i.e., the high-energy contribution from \(\sim\)100 to \(\sim\)880 eV and the shoulder-like structure below \(\sim\)100 eV can be fitted by exponential decay functions with decay constants of 490 and 33 eV, respectively (see the red and green solid lines). With the present peak fluence of the XFEL pulse (\(\sim\)1.8 \(\upmu\)J/\(\upmu\)m\({}^{2}\)), the ionization probability of an individual xenon atom is \(\sim\)3.3%, and thus, \(\sim\)170 atoms in the cluster of \(\sim\)5000 atoms are core-ionized. Therefore, \(\sim\)150 fast and \(\sim\)1100 slow electrons are emitted from these core-ionized atoms. Here, it is simply assumed that fast electrons entirely fly away from the cluster but slow ones do not. Then, the charge of the spherical cluster with a radius of 44 A is initially assumed to be +150, and the electrostatic potential on the surface is 49 eV. This provisional electrostatic potential vindicates the simple assumption of ejecting fast electrons from the system but trapping slow ones, which is further supported by considering that the collisional ionization events additionally consume the kinetic energies of slow electrons. Figure 1: (a) Electron energy spectrum from Xe\({}_{5000}\) clusters at the XFEL peak fluence of 1.8 \(\upmu\)J/\(\upmu\)m\({}^{2}\). Red and green solid lines depict exponential functions with decay constants of 33 and 490 eV, respectively. A blue solid curve shows the sum of the red and green lines. (b) Residual spectrum between the experimental results and the blue solid curve. When the charge of clusters is +150, the available electron temperature is expected to be below \(\sim\)49 eV according to the electrostatic potential on the surface of Xe\({}_{5000}\). Therefore, the exponential feature with a decay constant of 33 eV (green solid line in Figure 1a) may be attributed to the thermal electron emissions from the XFEL-ignited nanoplasma. On the other hand, the other extracted decay constant (490 eV) is much higher than the expected electrostatic potential, e.g., an electrostatic potential of 490 eV requires a +2300 charge on Xe\({}_{5000}\). A number of slow electrons (\(<\)1.2 keV) can escape from the charged cluster after losing their kinetic energies via a sequence of collisional ionization events and may contribute to the exponentially decaying feature with a constant of 490 eV. The recent XMDYN simulation for krypton clusters [31] presented proof of the contribution of slow electrons to the exponentially decaying feature on the electron spectrum. A number of photo- and Auger electrons, which are decelerated via collisional ionization processes, have been observed as the peaks. Figure 1b depicts a residual spectrum between the experimental electron spectrum and the sum of two exponential decay curves (see a blue curve in Figure 1a). In the previous electron spectroscopy study of xenon clusters with an average size of 10,000 atoms, the contributions of decelerated photo- and Auger electrons were also reported as evidence of the formation of nanoplasma by XFEL irradiation [55]. \(L_{2}\) and \(L_{3}\) photo-emissions, whose kinetic energies are originally \(\sim\)400 and \(\sim\)720 eV, respectively, in atomic case, have been observed as peaks, with a tail toward the low-energy side; this indicates that their kinetic energies are lost via the collisional ionization processes.