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Physical Review Letters

Differences in the Detachment of Electron Bubbles from Superfluid 4He Droplets versus Nonsuperfluid 3He Droplets

Michal Fárnı́k, Ulrich Henne, B. Samelin, Jan Peter Toennies

Published Nov 2, 1998• 40 citations
Publisher

Abstract

The rate of detachment of electron bubbles inside size-selected ${}^{4}\mathrm{He}$ and ${}^{3}\mathrm{He}$ droplets ( ${10}^{5}--{10}^{7}$ atoms) has been measured. At zero electric field the lifetimes of ${}^{4}\mathrm{He}$ droplets increase with size from ${10}^{\ensuremath{-}3}$ to 0.2 s, orders of magnitude smaller than previously predicted. With increasing fields the detachment gradually increases for ${}^{4}\mathrm{He}$ droplets, whereas a sharp threshold was found at 1.45 kV/cm for ${}^{3}\mathrm{He}$ droplets, independent of size. A simple dynamical model which accounts for superfluidity in the ${}^{4}\mathrm{He}$ droplets versus a viscous dynamics in ${}^{3}\mathrm{He}$ can explain the observations.

DOI
10.1103/physrevlett.81.3892

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The rate of detachment of electron bubbles inside size-selected 4He{}^{4}\mathrm{He}4He and 3He{}^{3}\mathrm{He}3He droplets ( 105−−107{10}^{5}--{10}^{7}105−−107 atoms) has been measured. At zero electric field the lifetimes of 4He{}^{4}\mathrm{He}4He droplets increase with size from 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 to 0.2 s, orders of magnitude smaller than previously predicted. With increasing fields the detachment gradually increases for 4He{}^{4}\mathrm{He}4He droplets, whereas a sharp threshold was found at 1.45 kV/cm for 3He{}^{3}\mathrm{He}3He droplets, independent of size. A simple dynamical model which accounts for superfluidity in the 4He{}^{4}\mathrm{He}4He droplets versus a viscous dynamics in 3He{}^{3}\mathrm{He}3He can explain the observations.
The lifetimes of electron bubbles in large size selected HeN−4 droplets have been measured in a molecular beam experiment to lie between 2⋅10−3 and 0.2 s in droplets with sizes between N≈105 and 107 atoms, respectively. The dependence of the lifetimes on the electric fields used to size select the droplets, on the energies of the incident electrons, and on the infrared radiation emitted from the apparatus walls were investigated and taken into account. The experimental lifetimes are many orders of magnitude smaller than predicted by earlier theories but consistent with a recent theory published by the authors in Phys. Rev. Lett. 81, 3892 (1998).
The lifetimes of electrons injected into large (≈106 atoms) superfluid He4 droplets have been measured in the presence of different prior embedded rare gas atoms, their clusters, and the molecules O2, H2O, and SF6. For the light rare gas atoms Ne and Ar the lifetimes of about 6⋅10−2 s, found previously for pure droplets, are reduced to between 1–2⋅10−2 s. Single molecules with large electron affinities, such as SF6 and O2 and small clusters of H2O lead to a significant increase in the lifetimes. In the case of Kr and Xe, larger clusters with n̄>14 are needed before the lifetimes increase. A simple model, which takes account of the energy levels occupied by the electrons in the corresponding molecules or the clusters, assumed to be solid, can qualitatively explain the observations.
Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. However, exploring the dynamic properties of individual droplets is experimentally challenging. In this work, we used single-shot femtosecond x-ray coherent diffractive imaging to investigate the rotation of single, isolated superfluid helium-4 droplets containing ~10(8) to 10(11) atoms. The formation of quantum vortex lattices inside the droplets is confirmed by observing characteristic Bragg patterns from xenon clusters trapped in the vortex cores. The vortex densities are up to five orders of magnitude larger than those observed in bulk liquid helium. The droplets exhibit large centrifugal deformations but retain axially symmetric shapes at angular velocities well beyond the stability range of viscous classical droplets.
We report on the observation of vortices in superfluid 4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.
We present a systematic study on the excited electron-bubble states in superfluid (4)He using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allow us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable configurations above the 1P state.
We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40 m/s, respectively, induced by the long-range van der Waals attraction between the droplets.