Progress Towards a Gas-Flow Standard using Microwave and Acoustic Resonances.

We describe our progress in developing a novel gas flow standard that utilizes 1) microwave resonances to measure the volume, and 2) acoustic resonances to measure the average gas density of a collection tank / pressure vessel. The collection tank is a 1.85 m, nearly-spherical, steel vessel used at pressures up to 7 MPa.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium.

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs.

Onset of Casimir-Polder retardation in a long-range molecular quantum state.

Two 4He atoms form a diatomic molecule with a significant vibrational wave function amplitude at interatomic separations R>100  Å, where the retardation switches the London R(-6) decay of the potential to the Casimir-Polder R(-7) form. It has been assumed that this effect of retardation on the long-range part of the potential is responsible for the 2 Å (4%) increase of the bond length of 4He2. We show that is, unexpectedly, insensitive to the potential at R>20  Å and its increase is due to quantum electrodynamics effects computed by us from expressions valid at short R--beyond the validity range of Casimir-Polder theory--that seamlessly extend this theory to distances relevant for properties of long molecules.

Potential energy surface for interactions between two hydrogen molecules.

Nonrelativistic clamped-nuclei energies of interaction between two ground-state hydrogen molecules with intramolecular distances fixed at their average value in the lowest rovibrational state have been computed. The calculations applied the supermolecular coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and very large orbital basis sets-up to augmented quintuple zeta size supplemented with bond functions. The same basis sets were used in symmetry-adapted perturbation theory calculations performed mainly for larger separations to provide an independent check of the supermolecular approach.

Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes.

The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 - ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε (2). The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m.

(4)He Thermophysical Properties: New Ab Initio Calculations.

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium "ab initio" potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.

Theory of the Greenspan viscometer.

We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rd. In the lowest order, eta=pi f rho(rd/Q)2, where f and Q are the frequency and quality factor of the isolated Greenspan mode, and rho is the gas density.