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.

该研究提出了一种新的实验方案，可以对高速异构体进行灵敏、高精度的激光光谱研究，其中利用混合密度网络（MDN）对结果进行预测和修正，在不需要冷却技术的情况下，直接在高能束流上进行原位光谱研究，是研究核结构、星际物理和新物理探索等领域中有市场价值的研究。

利用机器学习辅助单事件多普勒校正技术对快速、高温异质同位素进行精密光谱研究