# Ionization of Xenon Clusters by a Hard X-ray Laser Pulse
## 3 Results and Discussions
### Cluster-Size Dependence  
Figure 4a shows the mean charge state of the detected ions (Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}_{2}^{+}\), and Xe\({}_{3}^{+}\)) as a function of cluster size at the XFEL peak fluence of \(\sim\)4.6 \(\rm\upmu J/\upmu m^{2}\). Here, we have assumed that the charges of Xe\({}_{2}^{+}\) and Xe\({}_{3}^{+}\) are 1/2 and 1/3, respectively. The mean charge state of the detected ions for Xe\({}_{5000}\) is relatively higher than those for Xe\({}_{500}\) and Xe\({}_{1000}\). We note that the mean charge state has been increased by the formation of highly charge ions. Figure 4b depicts the percentages of Xe\({}^{+}\), Xe\({}^{2+}\), Xe\({}^{3+}\), Xe\({}_{2}^{+}\), and Xe\({}_{3}^{+}\) yields to total ion yield. A study using ion spectroscopy on xenon clusters with XUV pulses [66] reported that the doubly charged ions were only produced in the xenon clusters with average sizes of 10,000 and 50,000 but not 2000 atoms. This size dependence of the XUV laser can be explained by the minimum required charge to produce the doubly-charge ions on the thin spherical shell of xenon clusters [66]. Here, \(Q_{\rm min,Xe^{2+}}\), which is proportional to radii of clusters, is 28, 37, and 66 at Xe\({}_{500}\), Xe\({}_{1000}\) and Xe\({}_{5000}\) clusters, respectively. Since the number of fast electrons increasing the charge on a cluster are linearaly proportional to the number of core-ionized atoms, one can understand that in larger clusters, \(Q\) is easily greater than the minimum required charge to produce doubly-charged ions. In other words, larger clusters easily form a quasineutral core and a charged thin spherical shell.  
With the increase in the cluster size, the percentage of Xe\({}^{+}\) decreases, and the percentages of others increase, as shown in Figure 4b. The increase in the percentages of the multiply charged ions can be explained by the fact that, as mentioned above, with the increase in cluster size, the minimum required charge to produce multiply charged ions becomes smaller than the number of atoms in the cluster. The percentage of Xe\({}^{3+}\) at Xe\({}_{1000}\) is \(\sim\)1 %, which is close to at Xe\({}_{500}\); moreover, the percentage of Xe\({}^{2+}\) increases. On the other hand, the ratio of Xe\({}^{3+}\) become \(\sim\)2 % at Xe\({}_{5000}\). This fact can be understood by considering that \(Q_{\rm min,Xe^{3+}}\) is greater than \(Q_{\rm min,Xe^{2+}}\).  
The percentages of the oligomer ions rapidly increase in comparison with the percentages of the multiply charged ions, e.g., the percentage of Xe\({}_{3}^{+}\) at Xe\({}_{5000}\) becomes about 10 times greater than at Xe\({}_{500}\). With the increase in cluster size, the charges are redistributed into the thin spherical shell, that is, the average charge of the atoms in the core is expected to be reduced. As discussed in Section 3.4, a sufficient number of neutral atoms may efficiently create chemical bonding with the atomic ions. We have experimentally demonstrated that the increasing cluster size effectively enhances the oligomer formation from the XFEL-ignited nanoplasma, and thus concluded that the chemical processes are essential for the disintegration dynamics of the larger-sized clusters.