Study of population dynamics toward the development of atomic X-ray lasers in the 3–5 keV photon energies

X-ray free-electron lasers (XFELs) are powerful tools for characterizing and probing the properties of matter at atomic resolution on the ultrafast timescale. However, they have certain limitations such as spectral fluctuation and poor temporal coherence. Atomic X-ray lasers offer the narrow bandwidth, longitudinal coherence, and spectral stability that can overcome these limitations. In this paper, we study the interaction of inner-shell vacancy states with high-intensity XFEL pulses. We show that it is possible to achieve population inversion between K-shell and L-shell vacancy states in calcium and titanium when pumped by high-intensity XFEL pulses. These states can be used to generate atomic X-ray laser emission in the 3–5 keV photon energy range.