Single-differential and integral cross sections for electron-impact ionization for the damage of carbon clusters irradiated with x-ray free-electron lasers

Single-differential and integral cross sections for electron-impact ionization of the C atom and its ions were calculated with the binary-encounter-dipole model [Y.-K. Kim and M.E. Rudd, Phys. Rev. A 50, 3954 (1994)] to study the distribution of free-electron energies in carbon clusters after being irradiated with an x-ray free-electron laser (XFEL). The averaged energies of the secondary electrons for the C atom, and C1+, C2+, and C3+ ions were about 20, 70, 160, and 200 eV, respectively, when incident electron energy was about 20 keV, while those energies were in the order of tens of electronvolts when the incident electron energy was about 250 eV. The damage to carbon clusters irradiated with the XFEL was also investigated with time-dependent rate equations, considering photoionization, Compton scattering, Auger decay, and electron-impact ionization of the C atom and its ions. The results show that the electron-impact ionization becomes a more important process as the x-ray flux decreases, while the effect of Auger decay gradually appears as the x-ray flux increases. The energy dependence of the incident x ray was also investigated to evaluate the resolution of the diffraction pattern. These results indicate that we should make the XFEL pulse a few fs and about 16 keV to suppress damage and obtain desired resolution of the diffraction pattern.