We propose an experimental scheme for performing sensitive, high-precision laser spectroscopy studies on fast exotic isotopes. By inducing a step-wise resonant ionization of the atoms travelling inside an electric field and subsequently detecting the ion and the corresponding electron, time- and position-sensitive measurements of the resulting particles can be performed. Using a Mixture Density Network (MDN), we can leverage this information to predict the initial energy of individual atoms and thus apply a Doppler correction of the observed transition frequencies on an event-by-event basis. We conduct numerical simulations of the proposed experimental scheme and show that kHz-level uncertainties can be achieved for ion beams produced at extreme temperatures ($> 10^8$ K), with energy spreads as large as $10$ keV and non-uniform velocity distributions. The ability to perform in-flight spectroscopy, directly on highly energetic beams, offers unique opportunities to studying short-lived isotopes with lifetimes in the millisecond range and below, produced in low quantities, in hot and highly contaminated environments, without the need for cooling techniques. Such species are of marked interest for nuclear structure, astrophysics, and new physics searches.

翻译：我们提出了一种实验方案，用于对快速奇异同位素进行灵敏、高精度的激光光谱研究。通过在电场中诱导原子逐步共振电离，并随后探测离子及相应电子，可实现对生成粒子的时间和位置敏感测量。利用混合密度网络（Mixture Density Network, MDN），我们能够利用这些信息预测单个原子的初始能量，从而对观测到的跃迁频率进行单事件基础上的多普勒校正。我们对所提出的实验方案进行了数值模拟，结果表明，对于在极端温度（>10^8 K）下产生、能量弥散高达10 keV且速度分布不均匀的离子束，可实现千赫兹（kHz）量级的不确定度。直接在高能束流上进行飞行中光谱测量的能力，为研究寿命短至毫秒量级及以下、产量低、处于高温强污染环境中的短寿命同位素提供了独特机遇，无需依赖冷却技术。这类同位素对核结构、天体物理学及新物理探索具有重要意义。