X-ray diffractive imaging of highly ionized helium nanodroplets

Finding the lowest energy configuration of $N$ unit charges on a sphere, known as Thomson's problem, is a long-standing query which has only been studied via numerical simulations. We present its physical realization using multiply charged He nanodroplets. The charge positions are determined by x-ray coherent diffractive imaging with Xe as a contrast agent. In neutral droplets, filaments resulting from Xe atoms condensing on quantum vortices are observed. Unique to charged droplets, however, Xe clusters that condense on charges are distributed on the surface in lattice-like structures, introducing He droplets as experimental model systems for the study of Thomson's problem.

Figure 1

Schematic of the experiment. Helium droplets are ionized via electron impact and pass through plane capacitor electrostatic deflectors. Ionized helium droplets are doped with Xe atoms which cluster around the positions of the charges and serve as markers. The droplets are interrogated with the XFEL. Diffraction patterns are recorded on a pnCCD detector and processed using a phase retrieval algorithm to obtain the density profile and charge distributions. The predicted configuration for 18 charges is used as an example to simulate the displayed diffraction pattern.

Figure 2

Results for uncharged, Xe-doped ${}^4\mathrm{He}$ droplets. (1a,2a): Diffraction patterns showing the central 600 × 600 detector pixels. The vertical streak in the upper half of the patterns is caused by stray light. (1b,2b): Density reconstructions obtained with the DCDI algorithm.

Figure 3

Same as in Fig. 2, but for charged, Xe-doped ${}^4\mathrm{He}$ droplets. For droplets 1–3, the electron energy was 40 eV and emission current 30 μA, while for droplet 4, the ionizer was set to 200 eV and 1.3 mA emission current.