Triple Contributions Research Articles

Probing anomalous triple boson vertices at future e+e- colliders.

We explore the detection potential of the four lepton production processes $e^{+}e^{-} \rightarrow l^{+} \nu l^{\prime -}\overline{\nu}$ for anomalous contributions to the triple boson vertices at proposed future high energy colliders with center-of-mass energies of 500 GeV and 1 TeV. The predicted bounds are of the order of a few percent for the $CP$-even couplings $\kappa_{V}$ (V=$\gamma$,Z) at the higher energy; we show that these limits can be improved by as much as a factor of two through suitable phase space cuts. A polarized beam facility, with its ability to access helicity information, could provide constraints on the vertices significantly tighter than those achievable from an analysis of total cross-section alone. The asymmetries in experimental observables produced by an explicitly $CP$ violating triple vertex contribution are seen to be below the expected level of statistical precision of approximately $1.5 \%$; asymmetries in the individual contributing helicity amplitudes might however be detectable.

An ab initio molecular orbital study of the unimolecular dissociation reactions of di- and trichloroethylene

The potential energy surfaces for the unimolecular ground state elimination reactions of dichloroethylene (DCE) and trichloroethylene (TCE) are studied with ab initio molecular orbital calculations. By the gradient optimization with the second-order Mo/ller–Plesset perturbation (MP2) method and single point calculations with the fourth-order Mo/ller–Plesset perturbation (MP4) and the quadratic single and double configuration interaction including a triple contribution [QCISD(T)], many molecular elimination channels including three- and four-center HCl, H2, and Cl2 elimination and H and Cl migration reactions are systematically examined. For cis- and trans-DCE, the three-center HCl elimination with subsequent chlorovinylidene rearrangement has the lowest overall barrier, whereas for 1,1-DCE for which the three-center path is not available, the four-center elimination has a rather low barrier. Another path starting with the rearrangement of DCE isomers to 1,2-dichloroethylidene followed by HCl elimination is not far in energy from these paths, complicating the overall mechanism of HCl elimination. The H2 elimination from DCE isomers also can take either the three-center path or the 1,2-dichloroethylidene path. For TCE, though the overall barrier to produce HCl+dichloroacetylene is the lowest for the four-center HCl elimination pathway, the production of HCl itself is most easily accomplished by the three-center HCl elimination, and the easiest path for disappearance of TCE is its rearrangement via H or Cl migration to give the 1,2,2-trichloroethylidene intermediate. Thus the overall mechanism of HCl elimination reactions from TCE can also be complicated.

An ab initio molecular orbital study of the unimolecular dissociation reactions of vinylchloride

The potential energy surface for the unimolecular ground state elimination/detachment reactions of vinylchloride (VCl) is studied with ab initio molecular orbital calculations. Using second order Mo/ller–Plesset perturbation (MP2) gradient optimizations and quadratic single and double configuration interaction including a triple contribution [QCISD(T)] single point calculations, many possible channels—three- and four-center elimination reactions of HCl and H2, H, and Cl migrations, single atom detachments—are systematically examined. The overall barrier for the HCl three-center elimination, 69.1 kcal/mol, and subsequent vinylidene rearrangement is lower than that for the four-center elimination, 77.4 kcal/mol, the result being consistent with the most recent experiments. The H2 elimination, with a barrier of 97.2 kcal/mol and more difficult than the HCl elimination, also proceeds via a three-center transition state, followed by an easy H migration from chlorovinylidene intermediate. The lowest energy path from VCl is the α-H migration with a barrier of 68.8 kcal/mol, which gives a stable intermediate, α-chloroethylidene, with an energy of 55 kcal/mol relative to VCl. This path cannot however proceed further because of a very high barrier for subsequent H2 and HCl elimination, but the return to VCl provides the easiest mechanism for H scrambling in VCl. The β-chloroethylidene species is only a marginally stable intermediate and would not contribute to the reaction.

Unitarization of structure functions at large 1/ x

We discuss the effects of the s-channel unitarization on the x and Q 2 dependence of structure functions. The unitarization is implemented at the level of photoabsorption cross sections by resorting to the light-cone wave functions of virtual photons and to the diagonalization property of the scattering matrix in a basis of Fock states of the photon with fixed transverse size. The triple pomeron contribution is explicitly calculated. We find large unitarity corrections to the structure functions at x<10 −2. The results are in very good agreement with the existing NMC and the preliminary HERA data.

Adding the linked contributions of Triples and Quadruples to a size-consistent Singles and Doubles CI

A convenient procedure has been proposed recently to insure the size-consistence of Singles and Doubles CI; the method goes through a self-consistent dressing of the energies of the excited determinants which incorporates the unlinked effects of the Triples and Quadruples. Two strategies are proposed here to add thelinked contributions of the Triples and Quadruples, either by an perturbative MP-type calculation of these effects, or by a redefinition of the dressing of the SD-CI matrix. Test calculations on Be2, FH, NH3 and F2 molecules show that both methods efficiently approach the Full CI results (error ∼ 1 kcal mol−1). The second one satisfactorily treats the single-bonds breaking. It is finally shown that the effect of the T-Q linked effects may be efficiently approximated by truncating the MO basis set to the most occupied virtual quasi-natural MOs.

Stability ladder of various HC2N conformers and their excitation energies

The molecular structure of various stationary points of HC2N has been studied using the quadratic configuration interaction including single and double substitutions with triples contributions (QCISD(T)). A Huzinaga–Dunning double-zeta plus polarization (D95**) basis set was used. A stability ladder of these species is calculated using the configuration interaction including single and double substitutions (SDCI) with the Davidson correction (SDCI+Q). The general contraction scheme of the [5s3p2d1f(C and N)/3s2p1d(H)] atomic natural orbital basis set was chosen. The natural orbitals obtained in the preceding complete active space self-consistent field (CASSCF) calculations were applied to the open-shell SDCI. The triplet cyanomethylene is bent, and the barrier to linearity is 1.4 kcal/mol at the single-reference SDCI+Q level of theory in accord with the Schaefer and Roos’ values (0.8–1.0 kcal/mol). The nine-reference SDCI+Q calculation increases the energy separation by 0.7 kcal/mol. The thermal energy change between the two (1 and 2) including the calculated zero-point vibrational energies is 1.4 kcal/mol. The enthalpy barrier (ΔH≠) to linearize 1 to transition state 2 in a (hypothetical) reaction is predicted to be 0.0 kcal/mol using the single-reference SDCI+Q bent-linear energy separation. As a result, experiments might find no barrier to inversion of bent triplet 1. The most stable singlet species 6 (ring form of HC2N) lies 7.7 kcal/mol above the triplet bent cyanomethylene. Vertical excitation energies from the ground-state (3A″) of triplet bent cyanomethylene to 1A′ and 1A″ are studied using the CASSCF and SDCI methods; the SDCI+Q energies are 0.93 and 1.11 eV, respectively. These excitation energies are compared with those in the methylene and oxygen molecules having a qualitatively similar electronic structure to the present HCCN species, where two electrons occupy near-degenerate π-like (or degenerate π) highest occupied molecular orbitals (HOMO) forming a triplet ground-state. The excitation energies of 0.93 and 1.11 eV are close to the relative energies of the 3, 8, and 9 to the most stable triplet bent cyanomethylene.

End reflections and triple transit contribution to the band shape of magnetostatic volume wave delay lines

An analysis of the signal reflections originating at the garnet film ends and of the triple transit between the microstrip transducers in magnetostatic volume wave delay lines has been performed. The influence of those effects on the band shape and on the insertion loss of magnetostatic wave devices has been inferred and compared with experimental results. In this framework, the possible utilization of the reflections for filterbank applications is also proposed.

The analytic gradient of the perturbative triplet excitations correction to the Brueckner doubles method

To determine correlated properties accurately, it is necessary to go beyond the level of single and double excitations from a single determinant and include the effects of the connected triple excitations. A formula for the analytic gradient of the closed-shell perturbative triple excitations correction is presented for the Brueckner doubles varinat of coupled cluster theory. Optimised geometries and harmonic frequencies are presented for H 2O and the multiple bonded systems HCN, NNO and O 3. For these molecules, the use of Brueckner orbitals and the triples contribution show significant effects.

Triple and quadruple excitation contributions to the binding in Be clusters: Calibration calculations on Be3

We have investigated the contribution of connected triple and quadruple excitations to the binding in Be3 by comparing various coupled-cluster (CC) and truncated configuration-interaction (CI) treatments with multireference CI (MRCI) and full CI (FCI) calculations. The CC method with single and double excitations (CCSD) produces results that differ substantially from more elaborate treatments, but most extensions to CCSD that account approximately for connected triple excitations perform very well. In contrast, good agreement with FCI for Be2 can be achieved only with the highest level CC and MRCI methods.

Hyperpolarizabilities and polarizabilities of neon: Discrepancy between theory and experiment

The coupled-cluster doubles (CCD) model, supplemented by fourth-order singles and triples contributions computed with CCD amplitudes, is used to calculate the dipole-dipole-quadrupole ( B) and second dipole (γ) hyperpolarizabilities, and the dipole (α 1) and quadrupole (α 2) polarizabilities of the neon atom using a large basis set. The results, α 1 =2.698 e 2 a 0 2 E h −1, α 2= 7.525 e 2 a 0 4 E h −1, B = − 18.08 e 3 a 0 4 E h −2, and γ = 113.9 e 4 a 0 4 E h −'3, are likely to be the best currently available theoretical estimates. The calculated γ hyperpolarizability does not agree with a recent estimate based upon an experimentally determined hyperpolarizability dispersion curve. Further experimental work may be needed to resolve this discrepancy.

Thermodynamic analysis of thermal measurements in thermoelastic martensitic transformations

The thermodynamics of thermoelastic martensitic transformations are reformulated from the point of view of calorimetric experiments. It is shown that the heat released or absorbed by the specimen is due to a triple contribution: the latent heat of transformation, the reversibly stored elastic enthalpy and the irreversible work mainly spent in moving the interfaces. The main assumption is that a thermoelastic growth behaviour is equivalent to a null production of irreversible heat. Then the three energy terms can be separated by application of the first and second thermodynamic principles to a complete cycle, and evaluated quantitatively from heat-flow DSC data. The relative importance of the three energy terms determines the shape of the hysteresis loop in entropy vs temperature coordinates. Four examples on three shape-memory alloy systems (Fe-Pt, Cu-Al-Ni, Cu-Zn-Al) are studied.

Effect of three-body interactions on the early stages of atomic cluster growth

The sequence of conformations a cluster assumes as it grows from a trimer into a thirteen-atom aggregrate under a given model potential has been studied. The model potential proposed is a construction composed of a van der Waals pairwise term and a three-body term composed of the triple dipole contribution and the exchange overlap contribution. A parametric study of the thermodynamically preferred structures is given. After reaching a boundary between regions in the parameter space, equilibrium mixtures of isomers with different packings are obtained. The normal frequency spectrum is given for clusters up to thirteen atoms.

Towards a full CCSDT model for electron correlation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT-1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth-order MBPT. In this approximation, an MBPT(4)-like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT-1 results.

A coupled cluster approach with triple excitations

The coupled-cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions. The detailed equations for triple excitation amplitudes are presented, and a simplified version implemented that retains the dominant terms. The model presented, CCSDT-1, provides the energy correct through fourth order and the wave function through second order. The CCSDT-1 model is illustrated by comparing with full CI results for HF, BH, and H2O, the latter at several geometries.

Inclusive Vector Meson Production in Fragmentation Regions of Meson at Small PT

Inclusive vector meson spectra in fragmentation regions of meson at small PT are studied from a two-component model (quark fragmentation and triple Regge contributions). It is shown that our model can explain successfully various inclusive vector spectra. The analyses of this paper show that quark functions into vector mesons are nearly the same as those into pseudo-scalar mesons and the strange quark suppression factor ≃0.2, which is nearly the same as in pseudo-scalar meson production.

Prong cross-sections from a realistic two-component model

The inclusive pp → pX data, supporting a large triple Pomeron contribution, is invoked to predict the diffractive multiplicity distributions. Poisson decay is assumed for the excited cluster. The predicted diffractive prong cross-sections agree with the empirical estimates at 200 GeV c and suggest a significant broadening at 1500 GeV c (giving a rise in σ T ∼ 2.5 mb). Consequently the full prong distribution should develop no dip.

Kinetic theory of moderately dense gases-additional computations of the triple collision contributions to the transport coefficients for the rigid sphere model

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The three-Reggeon vertex: Analyticity, asymptotics and the Toller pole model

The incorporation of the local analyticity properties of the six-particle amplitude in a previous treatment of the three-Reggeon vertex is considered. A triple Regge pole contribution is shown to be singular on the boundary between two parts of the physical region where the partial-wave expansion was shown to take different forms. This sungularity can be removed by appropriate behaviour of the residue function, but the asymptotic region where the pole contribution can be expected to dominate behaves unsatisfactorily. For comparison, the connection between the singularity of a Regge pole contribution and the bad behaviour of the asymptotic region is also discussed for the zero momentum transfer problem. Analytic group variables, uniformly related to the invariants are introduced for the six-particle amplitude. A Lorentz-group expansion incorporating the vertex covariance condition is given and a triple Toller pole shown to be a possible uniform asymptotic approximation to the amplitude in the neighbourhood of the boundary considered. The treatment of the three-Reggeon vertex is used to give a full group theoretic treatment of an arbitrary multiparticle amplitude.

Divergence in the Density Expansion of the Transport Coefficients of a Two-Dimensional Gas

An analysis is presented of the first density correction to the viscosity and thermal conductivity coefficient of a two-dimensional gas of rigid disks. The existence of a divergence in the density expansion is established explicitly. For a two-dimensional gas the triple collision contribution to the transport coefficients diverges logarithmically with the time between collisions. In particular, for rigid disks the coefficient of the logarithmic singularity in the viscosity and thermal conductivity is evaluated in the first Enskog approximation. The possibility that as a consequence the transport coefficients depend logarithmically on the density is discussed.

Triple Collision Contribution to the Transport Coefficients of a Rigid Sphere Gas

An analysis is made of the triple collision integrals which appear in the expressions for the first density correction to the thermal conductivity and the viscosity of a gas of rigid spheres. It is shown that these triple collision integrals can be written as a sum of integrals associated with six triple collision events, each of which consists of a certain sequence of correlated successive binary collisions. A number of integrations are carried out, and the originally 15-fold triple collision integrals are reduced to 7-fold integrals in a form suitable for numerical analysis. The results are compared with the approximate predictions given by the Enskog theory for a dense gas of rigid spheres.