Precision Spectroscopy of Fast, Hot Exotic Isotopes Using Machine Learning Assisted Event-by-Event Doppler Correction

Abstract

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.

Figures (3)

• Figure 1: Illustration of the experimental setup. Highly energetic ions, $E_i\approx 1$ MeV $\pm 10$ keV, are guided towards a system of electrostatic lenses where their energy is reduced (I) to $E_f \approx 100 \pm 10$ keV. A possible, configuration of voltages as a function of the distance travelled by the ions is shown in the bottom left corner. After that, they enter the interaction region chamber (light blue), kept at a high voltage ($\sim 9\times 10^5$ V), pass through a neutralization cell (II) and are then excited to a higher-lying electronic state by a collinear laser (III). The excited atoms are then ionized by a standing-wave laser inside an optical cavity (IV). The resulting electrons are detected by a position-sensitive detector located above the ionization point (V), while the ions continue their trajectories in the electric field produced in between two parallel plates, until they reach a second position-sensitive detector (VI). For smaller initial energies, $E_i \lesssim 100$ keV, the deceleration lenses, as well as the high voltage applied to the interaction chamber can be removed from the setup.
• Figure 2: Results of the energy and frequency reconstruction. The predicted energy error for $^{120}$Sn over all events is normally distributed with a standard deviation of only $0.4$ eV (a). This corresponds to an event-by-event reconstructed rest frame transition frequency with an error around $1$ MHz when 100 target atoms events are detected, which is further decreased to only $1.3$ kHz for $10^8$ events (b). For $^{48}$Ni, an energy uncertainty of $77$ eV is obtained (c), leading to a reconstructed rest frame transition frequency uncertainty at the MHz level, for $10^6$ events (d).
• Figure 3: Results of the frequency extraction for ions with non-Gaussian distributed initial energies, for the $^{120}$Sn case. The energy histograms when the reference and target atom have the same/different initial energy distributions are shown in (a)/(c), while the associated reconstructed rest-frame frequency of the target atom using our proposed method, relative to the true rest-frame frequency, $\nu_0$, is shown in (b)/(d).