L. W. Bruch

Quantized vortices around wavefunction nodes. II

Quantized vortices can occur around nodes of wavefunctions. This fact, discovered by Dirac (1931) but little noted since, is rederived here and examples are discussed. The derivation depends only on the wavefunction being single valued and continuous. Since the derivation does not depend upon the dynamical equations, the quantized vortices are expected to occur for many types of waves (i.e., electromagnetic, acoustic, etc.). Such vortices have appeared in the calculations (McCullough and Wyatt, Kuppermann) of the H + H2 molecular collisions and play a role in the chemical kinetics. In a companion paper, it is shown that quantized vortices occur when optical waves are internally reflected from the face of a prism or particle beams are reflected from potential energy barriers.

Semiempirical Potential and Bound State of the Helium−4 Diatom

Hybrid potentials for the 4He–4He system composed of the theoretical short‐range repulsion, an empirical potential at the minimum, and the theoretical long‐range attraction have been constructed. Second virial coefficients calculated for these potentials are in poor agreement with experimental data. A semiempirical potential is constructed which fits the data well. This potential becomes the theoretical interaction at large separations; its gross features are a core radius of 2.645 A and a potential minimum of −1.73×10−15 erg at 2.975 A. There is one weakly bound state of the helium−4 diatom with a binding energy of roughly 0.01°K. An analysis of the effect of uncertainties in the experimental data upon these results is included; the bound state remains even with the allowed uncertainties.

Calculations and estimates of the ground state energy of helium trimers

Variational calculations of the ground state energy of 4He trimers are reported and are compared with the Hall‐Post‐Stenschke lower bound on the ground state energy. The variational result for the ground state energy for a range of model pair potentials is in the range −0.05 to −0.2 K; the effect of the triplet nonadditive term is estimated to be less than 1% of the contribution of the pair potentials. A study of the variation of the ground state energy of 3 bosons with pair potential coupling constant is also reported for a Lennard‐Jones and a Morse potential model. There is no bound spin 3/2 3He trimer; a lower bound is given for the ground state energy of the spin 1/2 trimer and analogy with the boson results is used to argue that the spin 1/2 trimer is probably not bound. This paper contains computational applications of formal results derived elsewhere.

The formation of dimers and trimers in free jet 4He cryogenic expansions

The formation of dimers, trimers, and tetramers in a free jet cryogenic expansion of 4He atoms has been studied by diffraction from a nanostructure transmission grating. The final average velocities, speed ratios and ambient temperatures of the expansions for source temperatures of 30, 12, and 6 K and source pressures between 0.1 and 80 bar were determined from time-of-flight measurements of the He atoms. The final mole fractions of the He2, He3, and He4 clusters in the beam were determined from the intensities of the corresponding first-order diffraction peaks for the same range of source conditions. For each source temperature, the final mole fractions of these small clusters first rise, pass through a maximum and then decrease with increasing source pressure. The processes leading to the formation of these clusters are simulated with a kinetic model that allows for density and temperature changes in the expanding beam. The best-fit three-body recombination rate constant for dimer formation increases by...

The two‐dimensional Lennard‐Jones system: Sublimation, vaporization, and melting

The solid–vapor equilibrium line and the liquid–vapor equilibrium line near the melting region for classical two‐dimensional systems of particles interacting by Lennard‐Jones (12,6) pair potentials are determined from Monte Carlo simulations with 224 particles. Structural and thermodynamic properties are evaluated for homogeneous single phases on both sides of the melting transition. The Monte Carlo results show that a cell model approximation to the solid phase has good accuracy for most of the anharmonic 2D solid conditions of this work. Free energies for solid states are constructed starting from the low temperature quasiharmonic solid; for the 2D liquid states the starting point is the virial expansion for the dilute gas. From these free energies the triple‐point melting of the periodically extended 224‐particle system is found to be first order and the latent heat of melting is determined. Graphic displays are obtained showing the occurrence of dislocation pairs, voids, particle exchange, and mixed p...

Ground state energy and structure of physisorbed monolayers of linear molecules

Model calculations of the ground state configuration and energy of monolayers of CO2 and of N2 adsorbed on the basal plane surface of graphite are reported. The interaction models consist of atom–atom and site–site potentials and point quadrupole moments, as in models for the three‐dimensional bulk solids, supplemented by effects of static and dynamic screening of multipole fields by surface charges on the graphite. There is a good quantitative agreement with estimated zero temperature heats of adsorption for N2/Gr and the calculated ground state configuration is the √3 R 30° registered monolayer solid. For CO2/Gr, the calculated low coverage isosteric heat differs by 15% from the experimental value, but the calculated lateral energy of the monolayer solid is consistent with available experimental information. Within the uncertainty caused by this discrepancy, the calculations are consistent with a suggestion that CO2/Gr is a nonwetting system at low temperatures. The ground state configuration of monolay...

The dispersion curves of the three phonon modes of xenon, krypton, and argon monolayers on the Pt(111) surface

The dispersion curves of all three phonon modes, the shear horizontal (SH), longitudinal (LA), and perpendicular (S) vibrations of the two-dimensional monolayer inert gas solids of xenon, krypton, and argon on Pt(111) have been measured by inelastic helium atom scattering (HAS). Previous HAS measurements of xenon on other substrates revealed, in addition to the S mode, only a single dispersive mode which deviated strongly from the expected behavior of the LA branch, to which it had been assigned. The new measurements now identify this mode as the SH mode and all three modes are in excellent agreement with calculations based on the inert gas pair potentials determined from gas and bulk solid data. Possible mechanisms for the excitation of the SH branch, which should couple only very weakly to HAS on the basis of symmetry considerations, are discussed.

Dielectric properties of helium: Quantum statistical mechanics

Expressions for the second dielectric and Kerr virial coefficients and the first two moments of the associated spectral functions valid in quantum statistical mechanics are derived. Upper and lower bounds are derived for the second Kerr virial coefficient to enable an indirect evaluation when quantal effects are appreciable. Calculations of helium dielectric properties near 4 K are reported. The calculations incorporate approximations for the pair distribution function of gaseous helium and coupled Hartree‐Fock results for the diatom polarizability. Structure factors calculated from the distribution functions and the calculated anisotropy moments are in good agreement with experiment. The calculated second dielectric virial coefficient at 4 K is in order‐of‐magnitude agreement with experiment and reflects an imprecise knowledge of the incremental mean polarizability of the helium diatom.

Diamagnetism of helium

The diamagnetic susceptibility of two helium atoms is calculated as a function of atomic separation R and the spherical-average incremental susceptibility is evaluated. The Hartree–Fock approximation is used at intermediate separations and perturbation theory for the leading, 1/R6, term in the increment at large separations. The change in average atomic susceptibility in liquid helium, relative to that for isolated atoms, is estimated. It is concluded that measurements on the liquid may be used to accurately determine the isolated atom diamagnetic susceptibility.

Vibrations of the commensurate monolayer solid Xe/Pt(111)

High resolution helium atom scattering has been used to study the structure and phonons of the (√3 × √3)R30° commensurate lattice of a monolayer of xenon on Pt(111). For in-plane vibrations, the data indicate a Brillouin zone-centre gap of about 1.3 meV and a dispersion of less than 0.5 meV from the Brillouin zone centre to the zone edge along the azimuth of the Xe solid, the Pt(111) direction. The data are consistent with a model of top-site adsorption of the Xe and with lateral Xe-Xe interactions being the same as in the gas phase.