4He Clusters Research Articles

X-ray diffraction analysis of titanium tritide film during 1600 days

The generation and accumulation of 3He by tritium decay modified the physical and chemical properties of tritides. Here the evolution of lattice defects in long-aged titanium tritide films is investigated by X-ray diffraction and changes in the positions, intensities and line shapes of diffraction peaks have been determined over a period of about 1600days (>4years). Texture effects are also observed by biased intensities in standard θ–2θ scans. The results show that the TiT1.5 film keeps an fcc structure during 1600days and reveals an hkl-dependent unit-cell expansion and line width broadening which are interpreted in terms of isolated tetrahedral interstitial 3He atoms and isolated bubble growth models by dislocation loop-punching or dislocation dipole expansion combined with Krivoglaz theory. In the first 12days of aging, isolated tetrahedral interstitial 3He atoms or 3He clusters are formed, then interstitial 3He atoms diffuse into (111) planes and precipitate into clusters. The spontaneous formation of Frenkel pairs, the self-interstitial atoms produced are built into dislocations resulting in formation platelet bubbles and dislocation dipoles between 12 and 27days. Above 27days, multiple stages of 3He bubbles growth appear: (1) between 27 and 85days platelet helium bubbles growth by dislocation dipoles expansion, (2) between 85 and 231days the transition from platelet bubbles to sphere bubbles by loop emission, (3) after 231days sphere bubbles growth by dislocation loop-punching and probably formation of sub-grain boundaries by dislocation rearrangement.

Eta meson rescattering effects in the [formula omitted] reaction near threshold

The p + Li 6 → η + Be 7 reaction has been investigated with an emphasis on the η meson and 7Be interaction in the final state. Considering the 6Li and 7Be nuclei to be α– d and α– 3He clusters respectively, the reaction is modelled to proceed via the p + d [ α ] → He 3 [ α ] + η reaction with the α remaining a spectator. The η meson interacts with 7Be via multiple scatterings on the 3He and α clusters inside 7Be. The individual η– 3He and η– α scatterings are evaluated using few body equations for the η–3 N and η–4 N systems with a coupled channel η– N interaction as an input. Calculations including four low-lying states of 7Be lead to a double hump structure in the total cross section corresponding to the L = 1 ( J = ( 1 / 2 ) − , ( 3 / 2 ) − ) and L = 3 ( J = ( 5 / 2 ) − , ( 7 / 2 ) − ) angular momentum states. The humps arise due to the off-shell rescattering of the η meson on the 7Be nucleus in the final state.

Self-consistent quantum structure of diffuse helium atom clusters

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.

Squeezing a Helium Nanodroplet with a Rydberg Electron

We have investigated, by means of density functional theory, the structure of a "scolium", that is, an electron circulating around a positively charged 4He nanodroplet, temporarily prevented from neutralization by the helium-electron repulsion. The positive ion core resides in the center of the nanodroplet where, as a consequence of electrostriction, a strong increase in the helium density with respect to its bulk value occurs. The electron enveloping the 4He cluster exerts an additional electrostatic pressure which further increases the local 4He density around the ion core. We argue that under such pressure, sufficiently small 4He nanodroplets may turn solid. The stability of a scolium with respect to electron-ion recombination is investigated.

Rotational Structure of Small 4He Clusters Seeded with HF, HCl, and HBr Molecules

Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N<or=20 and X=F, Cl, Br. The calculations are done using ab initio He-HX intermolecular potentials whose computation is described. Intermolecular energies and He radial and angular probability density distributions are computed as a function of the number of solvent atoms. Excited states are calculated using fixed-node diffusion Monte Carlo methods, and molecule-solvent angular momentum coupling is studied as a function of cluster size and potential anisotropy. Nodal surfaces of the many-body wave function are computed approximately by making an adiabatic Born-Oppenheimer-like separation of radial and angular degrees of freedom of the cluster. This procedure is extended to include radial dependencies in the adiabatic nodal function. We predict that the observed decrease in the gas-phase rotational constants for HCl and HBr in a 4He nanodroplet will be smaller than that observed for HF, despite HF's having the largest (by far) gas-phase rotational constant of the three molecules. This suggests that the specifics of the solvation dynamics of a molecule in a 4He cluster are the result of a delicate interplay between the magnitude of the gas-phase rotational constant of the molecule and the anisotropic contributions to the atom-molecule potential energy.

Microsolvation of Cationic Dimers in 4He Droplets: Geometries of (He)N (A = Li, Na, K) from Optimized Energies

Ab initio computed interaction forces are employed to describe the microsolvation of the A+2(2Sigma) (A=Li, Na, K) molecular ion in 4He clusters of small variable size. The minimum energy structures are obtained by performing energy minimization based on a genetic algorithm approach. The symmetry features of the collocation of solvent adatoms around the dimeric cation are analyzed in detail, showing that the selective growth of small clusters around the two sides of the ion during the solvation process is a feature common to all three dopants.

Solvation Structure and Rotational Dynamics of LiH in 4He Clusters

We present results of path integral Monte Carlo simulations of LiH solvated in superfluid 4He clusters of size up to N = 100. Despite the light mass of LiH and the strongly anisotropic LiH-He potential with a large repulsion at the hydrogen end, LiH is solvated inside the cluster for sufficiently large N. Using path integral correlation function analysis, we have determined the dipole (J = 1) rotational excitations of the cluster and a corresponding effective rotational constant Beff of the solvated LiH. We predict that Beff is greatly reduced with respect to the gas-phase rotational constant B, to a value of only about 6% of B. This exceptionally large reduction of the rotational constant is due to the highly anisotropic 4He solvation structure around LiH. It does not follow the previously established trend of a relatively small B reduction for light molecules, showing the strongest reduction of all molecules in 4He to date. Comparison of the calculated rotational spectra of LiH in helium obeying Bose and Boltzmann statistics, respectively, demonstrates that the Bose statistics of helium is an essential requirement for obtaining well-defined molecule rotational spectra in helium-4.

Application of scaling and kinetic equations to helium cluster size distributions: Homogeneous nucleation of a nearly ideal gas

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected.

Magic numbers, excitation levels, and other properties of small neutral He4 clusters (N⩽50)

The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expansion. These peaks appear at cluster sizes which can just accommodate one more additional stable excitation. The good agreement with experiment provides not only experimental confirmation of the energy level and the chemical potential calculations, but also evidence for a new mechanism which can lead to magic numbers in cluster size distributions. By accounting for the falloff of the radial density distributions at the surface and a size-dependent surface tension, the energy levels are demonstrated to be consistent with a modified Rayleigh model of surface excitations. The compressibility coefficient of these small clusters is found to be one order of magnitude smaller than the bulk compressibility.

Charged-particle evaporation and pre-equilibrium emission in 1.2 GeV proton-induced spallation reactions

Absolute cross sections, energy spectra, and angular distributions have been measured for 1,2,3H, 3,4,6He, 6,7,8,9Li and 7,9,10Be isotopes produced in 1.2 GeV proton-induced spallation reactions with targets between Al and Th. Results of simulation calculations with the intra-nuclear cascade code INCL2.0 coupled to the statistical model GEMINI are in good agreement with these data, as to charged-particle evaporation, mean excitation energy, and mean linear momentum transfer. The pre-equilibrium emission of composite particles, not accounted for in these simulations, however, typically contributes to the total production of composite particles by 40–60% for 2H and 3He, 20–40% for 3H, 5–20% for 4He, and about 15–25% for Li and Be. The composite pre-equilibrium particles together carry off a mean energy of up to 50 MeV, i.e., about 30% compared to the mean energy released by particle evaporation. For deuterons, pre-equilibrium emission is shown to be well described by surface coalescence while definitely other mechanisms are required for 4He and heavier clusters.

Three-centre cluster structure in 11C and 11B

Studies of the 16O(9Be,α7Be)14C, 7Li(9Be,α7Li)5He and 7Li(9Be,ααt)5He reactions at Ebeam = 70 and 55 MeV have been performed using resonant particle spectroscopy techniques. The 11C excited states decaying into α + 7Be(gs) are observed between 8.5 and 13.5 MeV. The α + 7Li(gs), α + 7Li* (4.652 MeV) and t+8Be(gs) decays of 11B excited states between 9 and 19 MeV are observed. The decay processes are used to indicate the possible three-centre 2α + 3He (2α + 3H) cluster structure of observed states. This cluster structure is more prominent in the positive-parity states, where two rotational bands with large deformations are suggested. Excitations of some of the observed T = 1/2 resonances coincide with the energies of previously measured T = 3/2 isobaric analogues of the 11Be states, indicating that these states may have mixed isospin.

Observation of Mixed Fermionic-Bosonic Helium Clusters by Transmission Grating Diffraction

Small weakly bound boson-fermion 4He(m) 3He(n) clusters formed in a free jet expansion are identified using nondestructive transmission grating diffraction. The observations confirm the existence of more than 11 very tenuous complexes including the three-body halo molecule 4He2 3He and the pseudo-Borromean complex 4He2 3He2. Effective cluster formation temperatures, extracted from a sudden freeze model for cluster growth using theoretical binding energies, increase smoothly with cluster size, thereby confirming the calculations with the possible exception of 4He2 3He2.

Br2(X) Microsolvation in Helium Clusters: Effect of the Interaction on the Quantum Solvent Density Distribution

The Born-Oppenheimer potential energy surface for the Br2(X) molecule interacting with a varying number of 4He bosons is constructed following two different schemes which employ either a full ab initio evaluation of the Br2-He interaction forces or an estimate of the latter through an empirical model. Both descriptions are employed by carrying out diffusion Monte Carlo (DMC) calculations of the ground-state energies and quantum wavefunctions for Br2-(He)n clusters with n up to 24. The results clearly indicate, for both interactions, the occurrence of the full solvation of the molecular dopant within the quantum bosonic "solvent" but also show differences between the two models in terms of the expected density distributions of the surrounding particles within the shorter-range region that makes up the clusters with smaller n values. Our calculations also show that such differences become insignificant for the larger 4He clusters surrounding the Br2 molecule, where density profiles and bulk behaviour are chiefly driven by the solvent structure, once n values reach the region of 15-20 adatoms.

Tensor Correlation in 4He and Its Effect on the Doublet Splitting in 5He

We investigate the role of tensor correlation on the structures of 4He and its effect on the doublet splitting in 5He. We perform a configuration mixing calculation in the shell model type bases to represent the tensor correlation for 4He. It is found that our model describes the characteristics of the tensor correlation, which is represented by an admixture of the 0s1/2 configuration with a spatially modified 0p1/2 orbit. For 5He, we solve a coupled OCM equation for an extended 4He+n model, while taking into account the tensor correlation in the 4He cluster. It is shown that the tensor correlation produces the Pauli blocking, in particular, for the Jπ = 1/2− state, and its effect causes about half of the p-wave doublet splitting in 5He. This indicates that the strength of the effective spin-orbit interaction should be reduced by about half from the conventional one. We obtain a reliable 4He-n interaction, including the tensor correlation, which further improves the behavior of the d- and f-wave phase shifts in the 4He+n system.

3He Impurities in 4He Systems Adsorbed on Curved Substrates

It is shown that 3 He impurities in sufficiently large 4 He systems adsorbed onto substrates with curved geometries form surface bound states, analogous to the Andreev state on a planar liquid--vapor interface. We report the analysis performed for superfluid 4 He adsorbed on the external surface of the nano-fullerene C 60 and on cylindrical nano-wires of Au. It is found that a single 3 He impurity diluted into such adsorbed structures behaves as on films on planar substrates and as on pure 4 He clusters.

The Broadening of NMR Line in Heterogeneous 3He - 4He Structures below 50 mK

The possible reasons of the previously observed low-temperature peculiarities of the NMR signal decay in phase-separated solid 3He - 4He mixtures are analyzed. It is shown that the jumps in magnetic susceptibility at the boundary between the nuclear paramagnet 3He and the diamagnetic 4He matrix (as well as a silver powder sinter) can give rise to appreciable local gradients of the external magnetic field at low temperatures in 3He clusters several microns in size. The gradients effectively broaden the NMR line. The results of the calculations give a good description of the experimental data.

The electronically excited states of helium clusters: an unusual example for the presence of Rydberg states in condensed matter

The nature of the electronically excited states of He clusters and their relaxation mechanisms are investigated by spectroscopy using monochromatized synchrotron radiation. Time correlated fluorescence excitation and energy resolved luminescence spectra of the clusters are recorded in separate wavelength ranges. The size of the clusters and the isotopic constitution is also varied. The spectral features are analysed and discussed particularly with regard to the high lying states and their possible Rydberg nature. While Rydberg states seem not to exist in the interior region of large clusters there is experimental evidence that sharp lines in the spectrum are either due to He Rydberg atoms or excimer molecules in high vibrational states bound at the surface of large clusters or due to very small positively charged clusters with the Rydberg electron outside. The spectra of large 3He clusters exhibit a larger contribution of Rydberg lines than 4He clusters. He clusters also emit fluorescence at energies above the ionization energy of He atoms. This is attributed to the barrier for the injection of electrons into the conduction band which was found to be 1.35 eV for 4He and 0.95 eV for 3He clusters, respectively.

Local Superfluidity in 4He and para-H2 Clusters

We present a new definition of local superfluidity around impurities in quantum fluids that provides a consistent analysis of the response of the inhomogeneous fluid density to the impurity rotations. This definition is based on the local decomposition of the moments of inertia of the fluid, which can be estimated from the projected area of exchange-coupled Feynman paths in path integral Monte Carlo calculations. Application to helium droplets doped with a planar phthalocyanine molecule shows that the first solvation layers parallel to the molecular plane consist of localized helium atoms that are totally inert to superfluid response, while the second solvation layers and capping regions at the end of the molecule exhibit partial and anisotropic superfluidity. Application to weakly bound complexes of the linear OCS molecule with para-hydrogen molecules shows evidence for the existence of molecular supersolids. We find that five H2 molecules constitute a single ring around OCS which possesses both a solid-like pair correlation function and a complete superfluid response to rotation around the molecular axis below T ~ 1 K.

Liquid Drop Excitations and the Size Dependent Surface Tension of Small 4He clusters

The elementary excitation levels and chemical potentials of small 4He clusters with less than N = 50 atoms have been calculated by the diffusion Monte Carlo method. The deviations of the excitation energy levels from predictions based on a simple liquid drop model are explained by the width of the density fall-off at the cluster surface and the size dependence of the surface tension.

Correlation Effects in Small 3He Clusters

We present a variational Monte Carlo calculation of a small 3He cluster within the Jastrow-Feenberg-Slater wave function approach. The trial wave function incorporates, in a progressive way, higher order correlations to elucidate at a quantitative level the relevance and possible interference of the different correlation mechanisms. As proved previously in bulk, the present results show the importance of backflow correlations to achieve a realistic description of this Fermi system. On the other hand, the introduction of three-body dynamical correlations also improves the ground-state energy, reducing appreciably the difference between this variational approach and more exact results obtained using the diffusion Monte Carlo method.