Number of photons in the AXE pulse for channel O 1s<sup>−1</sup> → <em>A</em> (a) and O 1s<sup>−1</sup> → <em>B</em> (b) as a function of the number of photons in the incoming XFEL pulse of a duration of 50 fs

<p><strong>Figure 4.</strong> Number of photons in the AXE pulse for channel O 1s<sup>−1</sup> → <em>A</em> (a) and O 1s<sup>−1</sup> → <em>B</em> (b) as a function of the number of photons in the incoming XFEL pulse of a duration of 50 fs. Here, we compare an isotropic molecular ensemble 〈cos <sup>2</sup>ζ〉 = 0.33 () with aligned 〈cos <sup>2</sup>ζ〉 = 0.64 (▵) and anti-aligned 〈cos <sup>2</sup>ζ〉 = 0.19 () molecular ensembles.</p> <p><strong>Abstract</strong></p> <p>We theoretically demonstrate the feasibility of x-ray lasing in the CO molecule by the core ionization of the C K- and O K-shell by x-ray free-electron laser sources. Our numerical simulations are based on the solution of generalized Maxwell–Bloch equations, accounting for the electronic and nuclear degrees of freedom. The amplified x-ray emission pulses have an extremely narrow linewidth of about 0.1 eV and a pulse duration shorter than 30 fs. We compare x-ray lasing transitions to the three lowest electronic states of singly ionized CO. The dependence of the lasing efficiency on the spectral width of the x-ray fluorescence band, value and orientation of the electronic transition dipole moment, lifetime of the core-excited state and the duration of the pump pulse is analysed. Using a pre-aligned molecular ensemble substantially increases the amplified emission. Moreover, by controlling the molecular alignment and thereby the alignment of the transition dipole moment polarization, the control of the emitted x-ray radiation is achievable. Preparing the initial vibrational quantum state, the x-ray emission frequency can be tuned within the fluorescence band. The present scheme is applicable to other diatomic systems, thereby extending the spectral range of coherent x-ray radiation sources based on stimulated x-ray emission on bound transitions.</p>