Picosecond solvation dynamics of alkali cations in superfluid ${}^4\mathrm{He}$ nanodroplets

The dynamics following the photoionization of neutral Rb and Cs atoms residing in a dimple at the surface of a superfluid ${}^4\mathrm{He}_{1000}$ nanodroplet has been investigated within time-dependent density functional theory, complementing a previous study on Ba. The calculations reveal that structured high density helium solvation layers form around both the ${\mathrm{Rb}}^{+}$ and ${\mathrm{Cs}}^{+}$ cation on a picosecond time scale, forming so-called snowballs. In contrast to the ${\mathrm{Rb}}^{+}$ ion, ${\mathrm{Cs}}^{+}$ is not solvated by the ${}^4\mathrm{He}_{1000}$ droplet but rather desorbs from it as a ${\mathrm{Cs}}^{+}{\mathrm{He}}_n$ snowball. This outcome is partially related to the large size of ${\mathrm{Cs}}^{+}$ cation in relation to the helium droplet as is revealed by calculations performed using a planar helium surface. The large droplet deformations induced by the solvation of the ${\mathrm{Rb}}^{+}$ cation is found to lead to efficient nucleation of quantized vortex loops or rings.

Figure 1

Top panel: Solid line, spherically averaged helium density profile of the ${\mathrm{Rb}}^{+}@{}^4\mathrm{He}_{1000}$ complex, left scale. Dotted line, number of ${}^4\mathrm{He}$ atoms as a function of distance to the cation, right scale. Bottom panel: Solid line, ${\mathrm{Rb}}^{+}\text{−}\mathrm{He}$ pair potential of Ref. [39]; dots, pair potential calculated in this work. Next to them, the nonaveraged helium density around the cation is shown by means of surfaces of constant density $\rho =0.08$ Å${}^{-3}$. Ten isodensity contours in a plane passing through the center of the complex are shown in the 0.04–0.0218 Å${}^{-3}$ range.

Figure 2

Top panel: Solid line, spherically averaged helium density profile of the ${\mathrm{Cs}}^{+}@{}^4\mathrm{He}_{1000}$ complex, left scale. Dotted line, number of ${}^4\mathrm{He}$ atoms as a function of distance to the cation, right scale. Bottom panel: Solid line, ${\mathrm{Cs}}^{+}\text{−}\mathrm{He}$ pair potential of Ref. [39]; dots, pair potential calculated in this work. Next to them, the nonaveraged helium density around the cation is shown by means of surfaces of constant density $\rho =0.08$ Å${}^{-3}$. Ten isodensity contours in a plane passing through the center of the complex are shown in the 0.04–0.0218 Å${}^{-3}$ range.

Figure 3

Top panel: Solid line, helium density profile of the ${\mathrm{Ba}}^{+}@{}^4\mathrm{He}_{1000}$ complex, left scale. Dotted line, number of ${}^4\mathrm{He}$ atoms as a function of distance to the cation, right scale. Bottom panel: Dots, ${\mathrm{Ba}}^{+}\text{−}\mathrm{He}$ pair potential [28]. Solid line, fit to the pair potential used in this work that includes a $r^{-4}$ term appropriate for cation-atom potentials. Next to it, the helium density around the cation is shown by means of a surface of density $\rho =0.05$ Å${}^{-3}$. Ten isodensity contours in a plane passing through the center of the complex are shown in the 0.04–0.0218 Å${}^{-3}$ range.

Figure 4

Comparison between the spherically averaged DFT density profile (solid line) and QMC density profile [3] (dashed line) for the ${\mathrm{Cs}}^{+}@{}^4\mathrm{He}_{64}$ complex, left scale. Also shown is the number of ${}^4\mathrm{He}$ atoms as a function of distance to the cation, right scale.

Figure 5

Top panel: ZEKE spectrum for Ba in arbitrary units. Dashed line, experimental result for a $N=2700$ droplet [62]. Calculated spectra: solid line, ${}^4\mathrm{He}_{1000}$ droplet; squares, ${}^4\mathrm{He}_{3000}$ droplet; dotted line, helium flat surface. The ionization energy of the Ba atom is 42 034.91 ${\mathrm{cm}}^{-1}$ (vertical line) [65]. Bottom panel: Calculated ZEKE spectrum in arbitrary units for Rb (solid line) and Cs (dashed line) in a $N=1000$ droplet. In both cases, the spectrum refers to the ionization energy (vertical line), 33 690.81 ${\mathrm{cm}}^{-1}$ for Rb and 31 406.47 ${\mathrm{cm}}^{-1}$ for Cs, respectively [65].

Figure 6

Dynamic evolution of the ${\mathrm{Rb}}^{+}@{}^4\mathrm{He}_{1000}$ complex when the neutral Rb is suddenly ionized. The corresponding time is indicated in each frame. The dark spots in the $t=160$ and 200 ps frames are the cross section of nucleated vortex loops (see Fig. 12).

Figure 7

Dynamic evolution of the ${\mathrm{Cs}}^{+}@{}^4\mathrm{He}_{1000}$ complex when the neutral Cs is suddenly ionized. The corresponding time is indicated in each frame.

Figure 8

Helium atoms dynamically carried away around ${\mathrm{Cs}}^{+}$ at $t=92$ ps. The shorter horizontal dashed line indicates the number of He atoms in the first solvation shell, and the other line indicates the the total number of He atoms in the ejected, charged nanocluster. The inset shows the appearing snowball from which the distance $r$ is defined.

Figure 9

Position and speed of the alkali cation with respect to the helium center of mass as a function of time for the full calculations and for that carried out using the frozen helium density corresponding to the initial conditions. The inset shows the evolution during the first 5 ps.

Figure 10

Dynamic evolution of the ${\mathrm{Cs}}^{+}$ cation after sudden ionization of the neutral Cs atom sitting in a dimple on a planar helium surface. The corresponding time is indicated in each frame.

Figure 11

Acceleration experienced by a ${\mathrm{Cs}}^{+}$ cation during the initial phase of the solvation after its creation on a $N=1000$ helium droplet and a flat helium surface.

Figure 12

Right: Three-dimensional view of the ${\mathrm{Rb}}^{+}\text{−}\mathrm{droplet}$ complex at $t=135$ ps showing the appearance of several vortex loops attached to the droplet surface and the snowball around the cation. Left: The corresponding circulation lines on the $x\text{−}z$ plane cutting a vortex loop.