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Physical Review Letters

Experimental Investigation of Small Helium Clusters: Magic Numbers and the Onset of Condensation

Peter W. Stephens, John Gordon King

Published Oct 24, 1983• 148 citations
Publisher

Abstract

Clusters of He atoms formed in a supersonic free jet expansion have been studied by electron-bombardment ionization and mass spectrometry. Distinct magic-number enhancements of ion intensity are observed for clusters of 7, 10, 14, and 30 atoms for both helium isotopes, and for 23 atoms of $^{4}\mathrm{He}$. Dramatic differences in the onset of cluster formation between the two isotopes may be related to the stability of $^{4}\mathrm{He}$ dimers.

DOI
10.1103/physrevlett.51.1538

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Clusters of He atoms formed in a supersonic free jet expansion have been studied by electron-bombardment ionization and mass spectrometry. Distinct magic-number enhancements of ion intensity are observed for clusters of 7, 10, 14, and 30 atoms for both helium isotopes, and for 23 atoms of 4He^{4}\mathrm{He}4He. Dramatic differences in the onset of cluster formation between the two isotopes may be related to the stability of 4He^{4}\mathrm{He}4He dimers.
The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.
Electron impact ionization of superfluid helium droplets containing several thousand atoms produces a broad distribution of Hen+ ions that peaks at n = 2 and decreases monotonically toward larger n. In larger droplets (say 105 or more atoms), however, the He4+ signal intensity is anomalously large. We have studied the mechanism for the formation of He4+ ions in large helium droplets by varying the duration of the electron impact excitation pulse. Droplets of different average sizes were generated using the expansion of helium at 20 bars and 9-20 K through a pulsed valve nozzle. The resulting ions were analyzed by time-of-flight mass spectroscopy (TOFMS) and quadrupole mass spectroscopy (QMS). The intensity distributions obtained with the TOFMS technique initially showed much smaller He4+ signals than those obtained using QMS. However, we discovered that the intensity anomaly is associated with the duration of the electron bombardment pulse in the TOFMS instrument. Measurements with different electron bombardment pulse durations enabled us to discern a characteristic time of ∼10 μs for enhanced He4+ production in large droplets under our experimental conditions. A qualitative model is presented in which metastables interact on droplet surfaces, yielding two He2+ cores that share a Rydberg electron while minimizing repulsion between the cores. This is the He4+(4A2) state suggested by Knowles and Murrell.
Abstract Small helium clusters Hen (n = 2, 3, ... , 10) in molecular beams produced by supersonic expansion of gaseous helium have been observed in several different experiments. Among these clusters the dimer, which has a single very slightly bound state, and the trimer, which could have many bound states, have especially unusual properties which QMC calculations can explain in detail. In this paper, diffusion QMC calculations were used to determine ground state properties for clusters (n = 2, ... , 10) using two accurate, but slightly different pairwise-additive potential energy expressions, a perturbation-based potential by Tang et al.a and an empirical potential (HFD-B) proposed by Aziz et al.b Trial functions for importance sampling were based on those determined earlier by Rick et alc. Expectation values and probability distributions were determined by the descendent-weighting technique to give results independent of the trial functions. As expected, a single bound state of the dimer was found, and its average internuclear distance was predicted to be 51.5 A. Energies for clusters with n = 2, 7 with the HFD-B potential were in good agreement with those of earlier calculations. Comparisons of the results for the two different potential energy expressions showed energies differing by a few percent. Tests of possible nonadditive interactions showed these to be far less important in their effects on predicted energies.
Abstract In this introductory chapter, we begin by informing the reader about the fascinating history of superfluidity in bulk liquid helium. This is followed by relating attempts in using liquid helium as a low temperature matrix for spectroscopy. After a brief review of the thermodynamic properties of helium in Sect. 1.2, the different types of free jet expansions used in experiments to produce clusters and nanodroplets of different sizes are described in Sect. 1.3. First it is shown how they depend on the nature and location in the phase diagram of the isentropes which determine the course of the expansion. Depending on the four regimes of isentropes, different number sizes and distributions are expected. Next in Sect. 1.4, the results of theoretical and, where available, experimental results on the total energies, excited states, radial density distributions, and temperatures of clusters and droplets are discussed. Finally, in Sect. 1.5 the theoretical and experimental evidence for the superfluidity of nanodroplets is briefly reviewed. For more information on the production and characteristics of nanodroplets, the reader is referred to the chapters in this book and to the reviews in Appendix.
Diffuse clusters of arbitrary numbers of helium atoms are treated in a mean-field theory of the many-body system. The nonlinear Hartree self-consistent-field equations are solved numerically to give their energy eigenvalues and eigenfunctions. Both isotopes 4He and 3He are treated according to their bosonic and fermionic statistics and symmetry requirements. Clusters of all sizes of 4He atoms are stable, but there is a minimum threshold of ∼70 atoms for the formation of 3He clusters. All the excited states in addition to the ground state were found. The wave functions are seen to have interesting differences from electronic wave functions in atoms.