# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### XFEL Pump-NIR Probe Results
The fact that the yields of multiply charged ions, Xe\({}^{2+}\), Xe\({}^{3+}\), and Xe\({}^{4+}\), culminate at the time delay later than 200 fs means that the quasi-free electrons have been effectively created via the collisional ionization events right after the XFEL irradiation, contributing to the formation of quasi-neutral core with a high electron density. After the formation of peaks, the increments of Xe\({}^{2+}\), Xe\({}^{3+}\), and Xe\({}^{4+}\) gradually begin to decline with the decrease in the electron density of the expanding nanoplasma. On the other hand, the yields of oligomer ions, Xe\({}_{2}^{+}\) and Xe\({}_{3}^{+}\), are slowly restored at the time delayslater than \(\sim\)2 ps; in contrast, the yields of multiply-charged ions declined. We note that the surface plasma resonance effects cause sharp drops in the oligomer ion yields around 2 ps. However, the growth rate of the oligomer ions is much slower than the decline rate of the multiply charged ones. The difference of these rates has been ascribed to the fact that dispersed oligomer fragments are dissociated by the interaction with the weak NIR pulses [37; 71]. The mean velocities of Xe\({}_{2}^{+}\) and Xe\({}_{3}^{+}\) have been estimated to be \(\sim\)1.8 \(\times\) 10\({}^{3}\) and \(\sim\)1.2 \(\times\) 10\({}^{3}\) m/s, respectively, considering their experimental mean kinetic energies of 4.6 and 3.1 eV. Even if we consider the occurrence of acceleration due to the electric fields supplied by the ion spectrometer, the ionic oligomer fragments remain in the focal spot of NIR probe pulses until \(\sim\)130 ns. Thus, the dissociation of dispersed oligomer fragments has persists until long time delays are reached. The yield of Xe\({}^{+}\) is also effectively enhanced by the surface plasma resonance effects; however, its decline after \(\sim\)2 ps time delay is slower than that of the multiply charged ions. The slower decline might be caused by the formation of Xe\({}^{+}\) due to the oligomer dissociation caused by the NIR probe pulses. Now, we focus on the kinetic energy of Xe\({}^{+}\). The red and blue curves in Figure 6c depict the yields of Xe\({}^{+}\) with low (0-15 eV) and high (15-125 eV) kinetic energies, respectively. The shape of the blue curve in Figure 6c is similar to the curves of the multiply charged ions, indicating that the Xe\({}^{+}\) ions with kinetic energies of 15 to 125 eV have been produced due to the heating up of the XFEL-ignited nanoplasma by the NIR laser fields. On the other hand, oligomer dissociation caused by NIR laser fields was expected to provide slow Xe\({}^{+}\) ions, which is supported by the fact that the yield of Xe\({}^{+}\) with kinetic energies of up to 15 eV was still enhanced at the long time delay of \(\sim\)30 ps. Moreover, another effect to increase slow Xe\({}^{+}\) ions may be the reionization of highly excited atoms produced by electron-ion recombination events during the nanoplasma expansion [72]. Let us now focus on the gradual declines in the yield of the multiply charged ions after their peaks in order to discuss the electron distribution in the XFEL-ignited nanoplasma. With the assumption, as mentioned above, that the expansion speed of nanoplasma is \(\sim\)3.5 \(\times\) 10\({}^{3}\) m/s, at \(\sim\)5 ps time-delay the electron density decreases to \(\sim\)1 % of the initial one, even if the thermal electron emission and the electron-ion recombination have been excluded. When the quasi-free electrons are homogeneously distributed in the nanoplasma, the heating efficiency of the nanoplasma with a low electron density is equal to that of IBS heating. However, the IBS heating is not expected to supply sufficient energy in the XFEL-ignited nanoplasma for creating the highly charged ions (e.g., Xe\({}^{4+}\)). Recent molecular dynamics simulations reported the collective excitation modes of a nanoplasma with an inhomogeneous electron density [73; 74; 75].