Quantum-classical dynamics of the capture of neon atoms by superfluid helium nanodroplets

The capture of a Ne atom by a superfluid helium nanodroplet, Ne + (4He)N → Ne@(4He)N' + (N - N') 4He, was studied using a hybrid quantum (helium)-classical (Ne) approach and taking into account the angular momentum. The atom is captured by (4He)N and follows elliptical rotating trajectories, and large energy and angular momentum transfer from the atom to the nanodroplet occur. Evaporation of helium atoms from (4He)N allows removal of the excess energy and angular momentum of the doped nanodroplet. The behaviours observed for angular momentum different from zero are similar to the zero angular momentum case. The angular momentum of the Ne atom can induce vortex nucleation for high enough initial angular momentum values (∼176.3-220.3 ℏ). Vortices arise from collapse of the surface excitations (ripplons) and are long-lived under some initial conditions. Comparison with our own previous quantum dynamics study at zero angular momentum shows that quantum effects are not important under the initial conditions examined here. Besides, a comparison with the scarce information available on other systems has been performed, showing the rich variety of behaviours that can be observed in the solvation of impurities by superfluid helium. More efforts are welcome in order to obtain a deeper insight into the dynamics of the capture process, especially in the vortex formation context.

* e-mail: miguel.gonzalez@ub.edu;Fax: +34934021231 Supplementary Information Table s1.Cartesian grid parameters of helium.Table s2.Propagation time steps and final simulation times.Table s3.Angular momenta of the HeND at the final simulation times.Figure s8.Kinetic energy transferred by the Ne atom to the HeND vs. impact parameter for v0=500 m s -1 .Figure s9.Total energy of the system (ENe + EHeND) vs. time for v0=500 m s -1 .
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2018 Figure s11.Time required to evaporate each one of the evaporated He atoms from the HeND for v0=500 m s -1 .Figure s12.Snapshots of the time evolution of the helium density, velocity and wave function phase in the xyplane for v0=500 m s -1 and b=17 Å.  Movie 1.Time evolution of the helium density and helium wave function phase in the xy-plane for v0=500 m s -1 and b=0 Å.
Movie 2. Time evolution of the helium density and helium wave function phase in the xy-plane for v0=500 m s -1 and b=14 Å. Movie 3. Time evolution of the helium density and helium wave function phase in the xy-plane for v0=500 m s -1 and b=17 Å.
Movie 4. Time evolution of the helium density and helium wave function phase in the xy-plane for v0=800 m s -1 and b=14 Å. 10.4 27 9•10 -5 9.0 34 9•10 -5 8.3 a In some cases larger simulation times have been considered only in order to follow the evolution of the vortex (cf.movies 2 and 3).-58.20 -3.15 0.00 0.00 -55.05 a Helium total (LHeND), helium centre of mass (a bS ), vortex with respect to the origin (a cde ) and with respect to the centre of the vortex (a cde,bfUgef ) and other excitations angular (a dghfe ) momenta.All angular momenta of the HeND have been calculated using the quantum operator a i j except a bS that has been calculated classically using the velocity field.b See Table s2.c The vortex was not present in the nanodroplet at the final simulation times of these conditions.s2) and as a function of the impact parameter, for v0=90, 210, 500, and 800 m s -1 .
Movie 2. Time evolution of the helium density and helium wave function phase in the xy-plane for v0=500 m s -1 and b=14 Å (simulated time≈328 ps; an additional simulated time of 151 ps has been examined here in order to better observe the vortex).See the mp4 video file "Movie 2. v500_b14.mp4"(3.86 MB).

Figure s1 .
Figure s1.Maxwell-Boltzmann velocity distribution of the Ne atom at T=300 K.

Figure s2 .
Figure s2.Radial density distribution of the HeND.

Figure s3 .
Figure s3.Snapshots of the time evolution of the helium density in the xy-plane and in the x and y axes for v0=500 m s -1 and b=14 Å.

Figure s7 .
Figure s7.Energies and time derivatives of the energies vs. time for v0=500 m s -1 .

Figure s10 .
Figure s10.Norm and total energy per He atom of the HeND vs. time for v0=500 m s -1 .

Figure s14 .
Figure s14.Angular momentum radial distribution of the HeND for the final simulation times and as a function of the impact parameter for all initial velocities.

Figure s1 .
Figure s1.Maxwell-Boltzmann velocity distribution of the Ne atom at T=300 K. Blue points are the velocities considered in this work.

Figure s3 .
Figure s3.Snapshots of the time evolution of the helium density in the xy-plane (left panels) and in the x and y axes (right panels) for v0=500 m s -1 and b=14 Å.

Figure s5 .
Figure s5.Velocity components of the Ne atom vs. time for v0=500 m s -1 .Left: modulus (top), x component (middle) and y component (bottom).Right: the same as before but for the initial times.

Figure s7 .
Figure s7.Energies and time derivatives of the energies vs. time for v0=500 m s -1 .Left: (top) neon kinetic energy, HeND total energy and interaction energies; (middle) differences between the energies values and their initial values; (bottom) time derivatives of the energies.Right: time derivatives of the energies at initial times.

Figure s8 .
Figure s8.Kinetic energy transferred by the Ne atom to the HeND vs. impact parameter for v0=500 m s -1 .The atom capture is observed for b=0, 7, 14 and 17 Å only.

Figure s10 .
Figure s10.Norm (left) and total energy per He atom (right) of the HeND vs. time for v0=500 m s -1 .

Figure s12 .
Figure s12.Snapshots of the time evolution of the helium density, velocity and wave function phase in the xy-plane for v0=500 m s -1 and b=17 Å, where the vortex is clearly evident.

Figure s14 .
Figure s14.Angular momentum radial distribution of the HeND for the final simulation times (cf.Tables2) and as a function of the impact parameter, for v0=90, 210, 500, and 800 m s -1 .

Table s1 .
Cartesian grid parameters of helium.a

Table s3 .
Angular momentum of the HeND a at the final simulation times.b