# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### XFEL Pump-NIR Probe Results  
Let us now focus on the results of XFEL pump-NIR probe experiments in order to investigate intermediate states of the expanding nanoplasma. Figure 5 shows the time-resolved electron energy spectra for xenon clusters with an average size of 5000 atoms, where the peak fluence of XFEL is \(\sim\)1.8 \(\upmu\)J/\(\upmu\)m\({}^{2}\) and the intensity of NIR laser is 5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\). The red and black curves illustrate the electron energy spectra irradiated by an XFEL pump-pulse and a NIR probe-pulse with the time delays of +1.3 and \(-\)4.7 ps, respectively. The meaning of positive time delays is that the NIR probe-pulses arrive at the reaction point later than the XFEL pump pulses. At the present NIR laser intensity (5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\)), the Keldysh parameter is calculated to be 4.5, meaning that the multiphoton ionization is expected to  
Figure 4: (**a**) Mean charge state of detected ions as a function of cluster size at the XFEL peak fluence of \(\sim\)4.6 \(\upmu\)J/\(\upmu\)m\({}^{2}\). (**b**) Percentages of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}_{2}^{+}\), and Xe\({}_{3}^{+}\) to the total ion yield. be dominant for individual xenon atoms. The present NIR laser intensity is too low to ionize xenon atoms via the multiphoton process; however, one can clearly observe that the additional irradiation with the weak probe laser at time delay of +1.3 ps causes a significant increase in the electron emission from the XFEL-ignited nanoplasma compared to the electron kinetic energy spectrum at \(-\)4.7 ps time delay. By subtracting the contribution of photo- and Auger electrons (depicted by the black curve in Figure 1b), the difference spectra have been obtained (see the blue and green curves in Figure 5). These difference spectra indicate that the NIR probe pulses with the positive time delays have mainly enhanced the unstructured contributions of electron spectra. The origin of the significant increase in the electron emission can be explained as follows. The quasi-free electrons within the nanoplasma can absorb energy from electric fields of the NIR laser [38, 67]. The atoms and ions within the nanoplasma are further ionized by inelastic scattering of the heated-up quasifree electrons. As a result, not only the kinetic energy but also the yield of electrons emitted from the XFEL-ignited nanoplasma are significantly enhanced by being heated up with the NIR probe pulse. The decay constant of the exponential feature at the positive time delay has been increased to \(\sim\)60 eV (see the blue curve in Figure 5), which is an evidence that the NIR probe pulses have heated up the quasi-free electrons within the XFEL-ignited nanoplasma. More evidence of the electrons heating-up with the NIR probe pulses is observed in the ion TOF spectra of xenon clusters with an average size of 5000 atoms, where the peak fluence of XFEL is \(\sim\)4.6 \(\upmu\)J/\(\upmu\)m\({}^{2}\) and the intensity of the NIR laser is 5.0 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\). The red and black curves in Figure 6a show the ion TOF spectra at the time delays of +1.5 and \(-\)1.5 ps, respectively. The enhancements in atomic ions, Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), and Xe\({}^{4+}\), can also be clearly observed. The formation of Xe\({}^{4+}\), which was not observed at the negative time delay, suggests that the electrons heating-up with the NIR laser pulse has effectively increased the cluster charge \(Q\). The increasing in \(Q\) has increased the stored energy per ion of a cluster's surface, which results in a violent Coulomb explosion, producing ions with high kinetic energies (e.g., see the broaden peak of Xe\({}^{2+}\) on the red curve in Figure 6a). Moreover, one can find a diminished number of oligomer ions, Xe\({}_{2}^{+}\) and Xe\({}_{3}^{+}\), as an inverse phenomena for the increase in the yield of multiply charged ions at the positive time delay.