We present a theoretical approach for describing collective x-ray emission processes in extended multilevel targets, based on a combination of propagation equations for the quantum correlation functions and the semiclassical Maxwell-Bloch equations. Such a description overcomes the key deficiencies of the two constituent sets of equations, which have until now been independently used to describe these phenomena. The model developed is employed to study the spectral properties of superfluorescence of $K\alpha$ emission in zinc at $\sim 8630\mathrm{eV}$ after inner-shell photoionization with intense attosecond free-electron laser pulses. At high pump intensities, the numerical simulations predict a splitting of the $K{\alpha }_1$ emission line due to a self-induced Autler-Townes effect, which could readily be observed with standard high-resolution x-ray spectrometers. As short duration of the pump pulse is one of the crucial parameters for the manifestation of this phenomenon in the hard-x-ray regime, experimental verification could be possible due to the most recent developments of free-electron laser sources.

中文翻译：

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X射线发射线的自感应分裂

我们基于量子相关函数的传播方程和半经典的Maxwell-Bloch方程的组合，提出了一种用于描述扩展多级目标中的集体X射线发射过程的理论方法。这样的描述克服了两个组成的方程组的关键缺陷，这两个方程组迄今为止一直被独立地用来描述这些现象。建立的模型用于研究超荧光的光谱特性。$ķ\alpha$ 锌在 $〜8630\mathrm{电子伏特}$内壳用强的亚秒级自由电子激光脉冲进行光电离后。在高泵浦强度下，数值模拟可预测泵的开裂。$ķ{\alpha }_{\mathrm{1个}}$由于自感应的Autler-Townes效应而产生的发射线，可以使用标准的高分辨率X射线光谱仪轻松观察到。由于泵浦脉冲的短持续时间是在硬X射线状态下此现象表现的关键参数之一，因此由于自由电子激光源的最新发展，可能进行实验验证。