Helium Pair Research Articles

Spectrometer-sensitivity calibration in the extreme ultraviolet by means of branching ratios of magnetic-dipole lines

Relative intensity measurements of various line pairs resulting from magnetic-dipole transitions within the configurations s2p2 and s2p4, in conjunction with calculated transition probabilities, have been used to determine the wavelength dependence of the sensitivity of a grazing-incidence spectrometer in the range 400–1000 Å. Emissions from Cr xix, Fe xxi, Ni xxi, Ni xxiii, Cu xxiv, and Zr xxvii ions in Princeton Large Torus tokamak discharges were used for this purpose. Absolute sensitivity of the spectrometer at selected wavelengthshad been determined by the traditional hydrogen, helium, carbon, and oxygen electric-dipole line pairs from the same discharges. Similar attempts to use transitions in the s2p3 configurations in Cr xviii, Zr xxvi, and Mo xxviii ions resulted in significant discrepancies that are ascribed to uncertainties in the corresponding calculated transition probabilities.

Unique determination of the He2 ground state potential from experiment by use of a reliable potential model

Measured backward glory oscillations of integral 4He2 and 3He2 scattering cross sections are evaluated by use of an improved semiclassical backward glory formula yielding the energy dependence of the s phases, which allows the calculation of the He2 potential in the region 1.83–2.12 Å via Miller’s semiclassical inversion method. A physically realistic two-parameter potential model, which uses all ab initio data available with sufficient accuracy, is fitted to the inversion result, giving in a unique way the entire helium pair potential function. A well with a depth of 10.74 K at 2.975 Å is obtained, which supports a bound state for 4He2 very near to the dissociation limit. Via construction, the potential model also gives results for individual interaction energy terms in the symmetry adapted perturbation scheme for the He2 interaction. Calculations with the determined potential reproduce the various experimental data available for helium. The best ab initio He2 potentials available today converge towards that potential.

On the pair polarizability of helium

New direct CI calculations of the helium pair polarizability using a gaussian basis set are described. These calculations have been undertaken in an attempt to improve on the previous work in the light of apparent inconsistencies between the computed trace and the polarized Raman spectral lineshape. Good agreement with the spectral model for the anisotropy is obtained. A tabulation of an accurate anisotropy is proposed, together with an analytic model. The calculated trace is not in such good agreement with the trace spectral model. However it is consistent with the experimental value of the second dielectric virial coefficient. The CI contribution is found to be decomposable approximately into a dispersion term and an SCF rescaling part.

Collisional pair polarizabilities calculated by exchange perturbation theory using electric field variant basis sets

The use of exchange perturbation theory to calculate collisional pair polarizabilities is investigated. Both conventional and electric field variant basis sets are considered for the cases of helium and hydrogen atom pairs. It is shown that high quality atomic descriptions are required to obtain reliable results from the method. The inclusion of exchange is found to be important and the method leads to closer agreement with Hartree–Fock results than does dipole–induced-dipole theory. The significance of recent configuration interaction calculations for hydrogen and helium atom pairs is also discussed.

Dispersion interaction between helium pair from hydrodynamic analogy to quantum mechanics

AbstractFrequency‐dependent multipole polarizabilities of the He sequence have been calculated from a hydrodynamic model of quantum mechanics and using an independent‐particle model Hamiltonian. Our present scheme is parallel to the uncoupled Hartree–Fock approximation so our values of polarizabilities, multipole transition energies and dispersion force coefficients between the HeHe pair are comparable with earlier works using the uncoupled Hartree–Fock approximation.

Configuration interaction calculations of the helium pair potential including CI superposition corrections

Configuration interaction calculations, involving all single and double excitations, are used to calculate the He2 potential as a test of a method of calculating the CI basis superposition error. The method is also investigated using model calculations with a limited basis. For the main He2 calculations a gaussian basis (5s, 3p, 2d) is employed. This basis includes functions appropriate to the description of both intra and interatomic correlation. The effect of various changes in the basis and the effect of the addition of f orbitals is investigated. Qualitative agreement with earlier calculations which avoided the superposition error is obtained.

A calculation of the helium pair polarizability including correlation effects

Direct configuration interaction (CI) calculations, which include all single and double excitation functions, and the finite-field method have been used to calculate the polarizability of a pair of helium atoms at a number of separations in order to assess the importance of correlation effects. A limited basis set of gaussian expansions of Slater orbitals was used. The basis set located on each atom was 5s, 3p, 2d, and was chosen to provide reasonably accurate atomic wavefunctions for both zero and finite electric fields. Agreement is obtained with the long-range results of perturbation theory. For incremental and incremental mean polarizabilities it is apparent that calculation of both self-consistent field (SCF) and CI contributions is required for an accurate determination. The anisotropy, however, seems to be calculable directly from an SCF calculation provided a simple scaling procedure is adopted. Counterpoise corrections have been calculated and found to be appreciable, especially for the increment...

A high-pressure calculation used to determine the helium pair interaction

The pressures and compressibilities of solid3He and4He are calculated over the volume range 3 cm3/mole ≤V ≤ 13 cm3/mole, using a simple Heitler-London variational approach. For volumesV ≤ 8 cm3/mole, the calculation is sufficiently exact to make possible a meaningful comparison of the results, obtained using four different semiphenomenological forms for the potential, with experimental data. The results indicate that the Beck potential is the best existing representation of the helium pair potential.

Intermolecular Potentials from Crossed Beam Differential Elastic Scattering Measurements. V. The Attractive Well of He2

The van der Waals well of the helium pair potential has been studied by crossed molecular beam elastic scattering measurements. Low energy helium beams were produced by specially designed beam sources cooled with liquid hydrogen. Only five partial waves were found to contribute significantly to the differential cross section. A multiparameter potential function is used to construct the interatomic potential from experimental results. The potential parameters describing the location and depth of the attractive well are given by ε=11.0± 0.2oK, rm=2.963± 0.01 Å . The potential does not contain a bound state of zero angular momentum. Comparisons with other He2 potentials based on bulk properties and ab initio calculations are presented; the temperature dependence of the second virial coefficient is also discussed for the proposed potential.