AXE gain curves (a) and AXE (full) and fluorescence (protect {----}) spectra at <em>z</em> = 5 mm computed for vibrational initial states ν<sub><em>g</em></sub> = 0 (b) and ν<sub><em>g</em></sub> = 2 (c) at the C 1s<sup>−1</sup> → <em>X</em> lasing transition, 〈cos <sup>2</sup>ζ〉 = 0.64

<p><strong>Figure 7.</strong> AXE gain curves (a) and AXE (\full) and fluorescence (\protect {----}) spectra at <em>z</em> = 5 mm computed for vibrational initial states ν<sub><em>g</em></sub> = 0 (b) and ν<sub><em>g</em></sub> = 2 (c) at the C 1s<sup>−1</sup> → <em>X</em> lasing transition, 〈cos <sup>2</sup>ζ〉 = 0.64. The XFEL pump pulse parameters are the same as in figure <a href="http://iopscience.iop.org/0953-4075/46/16/164017/article#jpb465580f5" target="_blank">5</a>.</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>