Permanent Quadrupole Research Articles

Polarizabilities and other properties of the tdµ molecular ion

Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+, and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the Born–Oppenheimer approximation. We tried the same approach in a muonic system, tdµ– (triton, deuteron, and muon). Improved convergence was obtained for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the two lowest J = 0 and 1 states and compared them with the best earlier calculations. Expectation values were obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with tdµ– acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results. PACS Nos.: 30.00, 36.10-k, 02.70-c

Cornell Electron Storage Ring phase-III interaction region vacuum chamber

Two 115 in. long copper ultrahigh vacuum (UHV) chambers for the Cornell Electron Storage Ring (CESR) interaction region were fabricated. These chambers are a part of the phase-III upgrade project for the CESR storage ring. They incorporate several novel features including a remotely engaging differentially pumped Viton O ring sealed UHV flange, two rf shielded bellows joints, and inner stepped masking for synchrotron radiation. The fabrication of these chambers incorporates multistage electron beam welding to maintain the strict tolerance required for installation through superconducting and permanent quadrupole magnets. Before final welding, a series of electron beam welding setup tests were done to work out a welding procedure for optimizing the welding parameters and avoiding contamination in the weld zone. In this article we will describe the design, fabrication, welding, leak checking, and final UHV performance testing of these chambers.

M + / Rg bonding: The effects of M+ permanent quadrupole moments (M+= atomic metal ion; Rg=rare gas atom)

It has been shown, using a model-potential analysis, that the large permanent quadrupole moment of the excited Mg+(3p) ion can play a significant role in the strong physical M+/Rg bonding observed for Mg+(3pπ)⋅Rg[2Π] ionic states. The four permanent quadrupole terms included in the model potential (two proportional to 1/R6, two to 1/R8) contribute substantially to Mg+(3pπ)/Rg attraction near the bond distances Re. In fact, our analysis indicates that the leading charge/induced-dipole 1/R4 attractive term contributes only ∼25–30 % to the physical bonding in the Mg+(3pπ)⋅Ar excited state, in stark contrast to the conventional wisdom that this term is usually dominant in M+/Rg bonding. Empirically derived Ae−bR repulsive terms also show that electron/electron repulsion for a given Mg+(3pπ)⋅Rg excited state is less than for the analogous Mg+(3sσ)⋅Rg ground state, consistent with the fact that the Rg atoms approach the excited 3pπ orbital of Mg+ along its nodal axis. For the Mg+(3pσ)⋅Rg[2Σ+] excited states, however, three of the permanent quadrupole terms are repulsive (with twice the magnitude) and thus contribute significantly to the extremely weak bonds and very large bond distances for the 3pσ ionic states. In contrast, the much smaller quadrupole moments of open-shell d-orbital states of transition metal M+ ions appear to have very little effect on their physical bonding with the Ar atom, at least for the few states which have been well-characterized spectroscopically. For all the M+/Rg states discussed above, our model-potential analysis indicates that no substantial chemical or charge-transfer interactions are needed to rationalize the bond strengths, the bond lengths, and the vibrational frequencies (the “shapes” of the potential curves near their minima).

Static properties and the Stark effect of the ground state of the HD molecular ion

We have calculated static properties of the ground state of the HD(+) ion and its lowest-lying P-state without making use of the Born-Oppenheimer approximation, as was done in the case of H2(+) and D2(+) [Phys. Rev. A 58, 2787 (1998)]. The ion is treated as a three-body system whose ground state is spherically symmetric. The wavefunction is of generalized Hylleraas type, but it is necessary to include high powers of the internuclear distance to localize the nuclear motion. We obtain good values of the energies of the ground S-state and lowest P-state and compare them with earlier calculations. Expectation values are obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions are also calculated. The polarizability was then calculated using second-order perturbation theory with intermediate P pseudostates. Since the nuclei in HD(+) are not of equal mass there is dipole coupling between the lowest two rotational states, which are almost degenerate. This situation is carefully analyzed, and the Stark shift is calculated variationally as a function of the applied electric field.

DIM models for RgX2− systems: suppressed influence of spin-orbit coupling and induced multipole effects for the Ar–I2− interaction

Abstract Diatomics-in-molecule models of different levels of accuracy are developed for the RgX 2 − systems, involving the complete set of X 2 − states originating from the X( 2 P 3/2,1/2 ) + X − ( 1 S 0 ) interaction, and applied to the specific case of the ArI 2 − complex. The ground and lowest excited state Ar–I 2 − potentials are found to be affected weakly by both spin-orbit coupling and mixing of different states of I 2 − by Ar. This allows for accurately reproducing the system potential energy surfaces (PES) by simple analytic functions corresponding to separate states of I 2 − treated diabatically. In addition to the standard DIM approach, interaction of the induced dipole on Ar with the induced dipole and permanent quadrupole on I is taken into account. This is found to affect significantly the Ar–I 2 − ground state PES topology by decreasing binding for both linear and T-shaped geometries, thus resulting in a single major T-well. Vibrational frequencies and electron affinity shifts are predicted. The frequencies are found to be close to those for ArI 2 in spite of about double increase of binding, and the shifts are significantly reduced relative to those for ArI. Interpretations of the obtained relations are discussed.

Many-body exchange effects in clusters of rare gases with a chromophore: He2CO2

The many-body exchange effects up to the 5-body have been analyzed in terms of possible mechanisms by which the intermolecular electron exchange is carried out. The terms corresponding to single (SE), triple (TE), double (DE), and quadruple (QE) exchanges are identified, and their diagrammatic interpretation given. It is demonstrated that they require different physical interpretations, as well as display different angular and radial behaviors. The 3-body SE and TE terms were calculated ab initio, and analyzed for a variety of geometries of the He2CO2 cluster. The anisotropy of SE over the wide range of configurations is consistent with the electrostatic model of the exchange quadrupole of He2, interacting with the permanent quadrupole of CO2. The behavior of TE may be rationalized by considering the Pauli-principle-induced distortion of the monomers involved. The influence of the CO2 asymmetric stretch on the SE, TE, and on the total exchange non-additivity has also been evaluated and discussed. The TE 4-body term in He3CO2 has been calculated and compared with the SE 3-body terms.

Properties of the ground state of the hydrogen molecular ion

The ground-state energies of the ions ${\mathrm{H}}_{2}^{+}$ and ${\mathrm{D}}_{2}^{+}$ have been calculated without making use of the Born-Oppenheimer approximation. Instead, the ions are treated as three-body systems whose ground states are spherically symmetric. The wave function of the ground state is taken to be a generalized Hylleraas form, but it is necessary to use high powers of the internuclear coordinate to simulate the localized motion of the nuclei. We obtain good values of the ground-state energies and compare them with those obtained from earlier calculations. Expectation values are calculated for various operators, the Fermi contact parameter, and the permanent quadrupole moment. The cusp condition is also calculated. The results are compared with the results of other calculations, where available.

Construction and tuning of BEPC mini-β permanent quadrupole prototype

A large aperture and good field performance permanent quadrupole prototype for the Beijing Electron Positron Collider (BEPC) luminosity upgrade was made. This paper will describe the configuration, assembly, field measurement and tuning procedure used to get the required field quality.

Phase equilibria of systems considered in supercritical fluid extraction determined from perturbation theory

The residual chemical potential of a solute, which is the main characteristic of the phase equilibrium at conditions of supercritical fluid extraction of solids, is determined from the second-order perturbation expansion proposed for mixtures of non-spherical polar molecules. Intermolecular forces are described via the generalized Kihara pair potential with a permanent point dipole or quadrupole embedded in the centre of the hard core ascribed to each molecule. General expressions for ternary systems are given first. The average and molecular distribution functions are determined on the basis of the radial distribution functions (RDFs) of the hard sphere multicomponent system; the recently proposed method for determining RDFs in the hard sphere mixture is employed. In the case of the contribution of dispersion forces, the Barker-Henderson approximation is considered for the second-order term, whereas the second-order electrostatic contributions are approximated by employing the Gaussian overlap model. Values of the calculated residual chemical potential of a solute are compared with the simulation data for the infinitely diluted binary Lennard-Jones system and infinitely diluted ternary systems; fair agreement is found. When employing parameters of the Kihara polar molecules (adjusted to experimental orthobaric data) an increase in values of the residual chemical potential is found in comparison with those for Lennard-Jones systems.

Phase equilibria of systems considered in supercritical fluid extraction determined from perturbation theory

The residual chemical potential of a solute, which is the main characteristic of the phase equilibrium at conditions of supercritical fluid extraction of solids, is determined from the second-order perturbation expansion proposed for mixtures of non-spherical polar molecules. Intermolecular forces are described via the generalized Kihara pair potential with a permanent point dipole or quadrupole embedded in the centre of the hard core ascribed to each molecule. General expressions for ternary systems are given first. The average and molecular distribution functions are determined on the basis of the radial distribution functions (RDFs) of the hard sphere multicomponent system; the recently proposed method for determining RDFs in the hard sphere mixture is employed. In the case of the contribution of dispersion forces, the Barker-Henderson approximation is considered for the second-order term, whereas the second-order electrostatic contributions are approximated by employing the Gaussian overlap model. Val...

Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. II. Ion–quadrupole capture

Classical trajectory calculations of ion–permanent quadrupole+induced dipole capture processes are performed over wide ranges of conditions. The results are expressed in two-parametric analytical form, and analyzed with respect to the transition from sudden to adiabatic dynamics. The results are compared with the statistical adiabatic channel model (SACM). For this purpose, adiabatic channel potential curves are expressed in approximate analytical form. The agreement between classical trajectory and SACM results is excellent in the range of adiabatic quasiclassical motion of the collision partners. Analytical expressions can well describe the temperature variation of the capture rate constant in the transition range between the quantum and classical limits.

Nonadditive interactions in the H2 trimer

Explicit equations for the second order nonadditive induction energy for interactions involving three linear molecules have been derived using the MAPLE symbolic computational language. This nonadditive induction energy (involving the permanent quadrupole moments and dipole polarizabilities) is compared with the triple-dipole dispersion energy for a system consisting of three hydrogen molecules, in two different configurations. It is found that for most of the orientations studied the nonadditive induction energy is comparable in magnitude or larger than the triple-dipole dispersion energy.

One neutron pickup reactions in the 32S+144Sm and 32S+166Er systems at energies close to the Coulomb barrier.

One neutron transfer cross sections in the systems $^{32}\mathrm{S}$${+}^{144}$Sm and $^{32}\mathrm{S}$+ $^{166}\mathrm{Er}$ have been measured at energies close to the Coulomb barrier. Mass and charge identification was achieved using characteristic x rays. Transfer probabilities were analyzed by considering barrier penetration mechanisms. Possible enhancement effects due to permanent quadrupole deformations are investigated and compared with the experimental results.

Molecular theory of order electricity

The concept of order electricity has been employed by Durand, Barbero and colleagues to explain, in particular, the existence of equilibrium conical anchoring at liquid crystal interfaces. In this paper we examine this concept from a molecular point of view, using the density functional theory of liquid crystals. We show that the long range nature of the electrostatic force between molecules with permanent quadrupoles creates formal problems with rather profound consequences on the link between microscopic and macroscopic formulations of liquid crystal theory. One result is that the Landau-de Gennes gradient expansion must be employed with extreme caution in an inhomogeneous nematic. These formal problems have analogues in the theory of dielectrics and were explored by Ewald long ago. In addition we derive from a statistical mechanical viewpoint the phenomenological relations used to describe order electricity, and explore in detail the consequences of order electricity at an isotropic-nematic interface and at a nematic-substrate interface.

Total (elastic and inelastic) scattering cross sections for several positron-molecule systems at 10-5000 eV: H2, H2O, NH3, CH4, N2, CO, C2H2, O2, SiH4, CO2, N2O, and CF4.

We report calculations on the total (elastic plus inelastic) positron-scattering cross sections from several diatomic and polyatomic molecules (${\mathrm{H}}_{2}$, ${\mathrm{H}}_{2}$O, ${\mathrm{NH}}_{3}$, ${\mathrm{CH}}_{4}$, ${\mathrm{N}}_{2}$, CO, ${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$, ${\mathrm{O}}_{2}$, ${\mathrm{SiH}}_{4}$, ${\mathrm{CO}}_{2}$, ${\mathrm{N}}_{2}$O, and ${\mathrm{CF}}_{4}$) where experimental data are available. The impact energy (E) range is 10--5000 eV. A local spherical complex optical potential (SCOP) is calculated for each positron-molecule system from the target charge density [\ensuremath{\rho}(r)], which in turn is determined from the corresponding molecular wave function at the Hartree-Fock level. The real part of the SCOP is composed of the repulsive static and attractive positron-correlation-polarization potential of Jain [Phys. Rev. A 39, 2437 (1990)]. The imaginary component of the SCOP, the so-called absorption potential, is derived semiempirically as a function of \ensuremath{\rho}(r), E, and the mean excitation energy. The resulting complex optical potential is treated exactly in a variable-phase approach to yield complex phase shift and the total-cross-section quantities. In this intermediate- and high-energy region, the small contribution due to the nonspherical nature of the target is neglected. In addition, we fit the total-cross-section values to a simple analytic formula. For molecules possessing a permanent dipole or quadrupole moment, the present results are reliable only roughly above 50 eV.

Collision-induced absorption in cyclopropane (C3H6)

We have measured the far-infrared absorption spectrum of cylopropane (C3H6) at frequencies up to 400 cm−1, at densities up to 5 amagat at 295 K and up to 16 amagat at 360 K, using a combination of Fourier-transform and laser techniques. (An amagat is defined as the density of a gas at N.T.P.). By studying the density-dependence of absorption, we have isolated the collisional component of the spectrum. This arises from pair dipole moments induced by the permanent quadrupole, octopole, and hexadecapole moments of the C3H6 molecule. To the extent that the intermolecular potential is isotropic, the induced spectrum can be expressed as the convolution of symmetric top free rotation spectra with translational spectra representing the relative motion of an interacting molecular pair. The former are calculated using expressions recently derived. For the latter we use information theory to provide a "least-biased" estimate based only on available information concerning the zeroth and second moments of the translational frequency spectrum, which can be calculated without approximation within the framework of equilibrium statistical mechanics. The result of these computations is a simple analytic expression for the absorption coefficient [Formula: see text], which is entirely free of adjustable parameters, and yet yields a good representation of the experimental results over most of the frequency range. Our results lend strong support to the theoretical values of the multipole moments calculated by other workers.

Performance of an expanding telescope used to obtain a low divergence H − beam

An expanding telescope constructed by Los Alamos National Laboratory was installed at Argonne National Laboratory to produce a low divergence, 50 MeV H − beam. The telescope with a twenty times magnification consisted of a singlet eyepiece and triplet objective lens constructed from permanent quadrupole magnets. The output beam divergence was measured with a rms resolution near 1 μ rad using a pinhole membrane and an optical imaging system. This system also provided a measure of the third order geometric aberrations of the telescope by the displacement of the centroids in the projected image of a rectilinear array of pinholes placed across the beam diameter. The geometric aberrations were found to be in agreement with computer calculations, having magnitudes on the order of a few μ rad/cm 3. Chromatic aberrations in the telescope were also found to be in agreement with theory. These measurements showed that the telescope achieved a nearly parallel beam with a divergence of less than 25 μ rad.

Accurate nonrelativistic expectation values for H +2

Two separate approaches (a perturbation theory which extends the Born—Oppenheimer approximation of molecular physics and finite element analysis of the three body Coulomb problem) are used to solve the nonrelativistic Schrödinger equation for the hydrogen molecular ion ground state. For both approaches, expectation values are calculated for the bond length, the rotational constant, the permanent quadrupole moment, the Fermi contact parameter, and other operators. These results are compared with “nonadiabatic” variational results, where available.

Total (elastic plus inelastic) cross sections for electron scattering from diatomic and polyatomic molecules at 10-5000 eV: H2, Li2, HF, CH4, N2, CO, C2H2, HCN, O2, HCl, H2S, PH3, SiH4, and CO2.

By employing a previously proposed model [A. Jain, Phys. Rev. A 34, 3703 (1986); J. Phys. B 22, 905 (1988)], we report calculations on the total (elastic plus inelastic) electron-scattering cross sections in a wide energy range (10--5000 eV) from several diatomic and polyatomic molecular targets (${\mathrm{H}}_{2}$ ${\mathrm{Li}}_{2}$, HF, ${\mathrm{CH}}_{4}$, ${\mathrm{N}}_{2}$, CO, ${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$, HCN, ${\mathrm{O}}_{2}$, HCl, ${\mathrm{H}}_{2}$S, ${\mathrm{PH}}_{3}$, ${\mathrm{SiH}}_{4}$, and ${\mathrm{CO}}_{2}$). A model complex optical potential (composed of static, exchange, polarization, and absorption terms) is calculated for each collision system from the corresponding molecular wave function at the Hartree-Fock level. The resulting complex optical potential, free from any adjustable parameter, is treated exactly in a variable-phase approach to yield scattering complex phase shifts and the total cross sections. In the intermediate- and high-energy region, the small contribution due to the nonspherical nature of the target is treated perturbatively in the first-order Born approximation. The present method is quite simple in nature and is able to reproduce fairly well the experimental total cross sections in the present energy region. Results are also given for individual elastic and absorption (accounting for all energetically possible inelastic processes in an approximate way) cross sections. In addition, we provide Born-Bethe parameters for all the above molecules including those of ${\mathrm{H}}_{2}$O and ${\mathrm{NH}}_{3}$. We have also examined the correlation between molecular properties and the total-cross-section parameter. For molecules possessing a permanent dipole or quadrupole moment, the present results are only roughly reliable above 100 eV.

The UCLA Phi Factory detector, the integration of superconducting compensation solenoids and the final focus interaction region quadrupoles

The proposed Phi Factory for the University of California at Los Angeles (UCLA) is a small 510 MeV electron-positron colliding beam storage ring with high luminosity (greater than 10 32 cm −2 s −1). In order to do high quality Phi physics, a particle detector system with a large solid angle (preferably greater than 98 percent) is required. Particle detection and analysis will be done within a 0.5 tesla solenoidal magnetic field. The solenoidal field within the detector causes coupling between beam oscillations in the horizontal and vertical directions. Therefore, compensation solenoids are required to keep the circulating particle beams from seeing the effects of the field from the main detector solenoid. Since high luminosity and a large solid angle are required, the detectors and a pair of compensation solenoids must be integrated with the final focus quadrupoles within the detector straight section. This report describes the design of two tapered, 0.5 tesla, superconducting compensation solenoids which must go around six rare earth permanent final focus quadrupoles or six superconducting quadrupoles on either side of the beam collision point. A cryogenic cooling system for these two solenoids, which will be coupled with the cooling system for the primary detector solenoid, is also described.