Transition dipole moments (atomic units) from the core hole to the final states of CO+ (figure 1) at the equilibrium geometry computed on the MCSCF level with the cc-pvtz basis set using the MOLPRO ab initio package [18]

Table 1. Transition dipole moments (atomic units) from the core hole to the final states of CO+ (figure 1) at the equilibrium geometry computed on the MCSCF level with the cc-pvtz basis set using the MOLPRO ab initio package [18]. Abstract 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.表1 基于从头算（ab initio）软件包MOLPRO[18]，采用cc-pvtz基组，在多组态自洽场（Multiconfiguration Self-Consistent Field, MCSCF）级别下，于平衡几何构型中计算得到的、CO⁺的核心空穴到其终态的跃迁偶极矩（原子单位）（见图1）。 摘要 本研究通过X射线自由电子激光光源对碳K壳层与氧K壳层实施核心电离，从理论层面论证了CO分子实现X射线激光的可行性。我们的数值模拟基于广义麦克斯韦-布洛赫方程（generalized Maxwell–Bloch equations）的求解，同时兼顾电子与核的自由度。经放大的X射线发射脉冲具备约0.1 eV的极窄线宽，且脉冲时长短于30飞秒（fs）。我们将X射线激光跃迁与单电离CO的三个最低电子能态进行了比对分析。本研究还系统剖析了激光效率与X射线荧光谱带的光谱宽度、电子跃迁偶极矩的幅值与取向、核心激发态的寿命以及泵浦脉冲时长之间的依赖关系。采用预对齐的分子系综可显著提升放大发射的强度。此外，通过调控分子对齐度，进而调控跃迁偶极矩的偏振取向，能够实现对发射X射线辐射的精准操控。通过制备初始振动量子态，可在荧光谱带范围内对X射线发射频率进行调谐。本方案可推广至其他双原子分子体系，从而拓展了基于束缚态跃迁受激X射线发射的相干X射线辐射源的光谱覆盖范围。