Elliptic solutions of ℂP n-1 models and their properties

A new family of elliptic solutions in the general charge sector of ?P ^n-1 model is proposed. Forn=2 these solutions interpolate between merons and arbitrary instantons; forn≧3 the situation is less clear. Various properties are investigated, both in Euclidean and Minkowski space. The solutions are found to interact through a potential rising more slowly than logarithmic.     

The rotation-vibration spectrum and double-minimum ν12 potential function of propadienone: A semirigid bender analysis

Propadienone is an interconverting molecule having a pair of equivalent symmetry related conformers separated by an energy barrier rising well above the vibrational ground state. Microwave spectra of molecules in excited states of the large-amplitude in-plane bending mode ν₁₂, including intersystem lines, have been successfully represented using the semirigid bender model. The model reveals a double-minimum bending potential with a barrier rising 359 cm⁻¹ above the minima at C₁C₂C₃ = 142°. In the ground state the interconversion frequency is 3.7 GHz and the ν₁₂ fundamental frequency is predicted to be 160 cm⁻¹. Analysis of other vibrational satellites involving the lowest-frequency out-of-plane mode ν₈ indicates a vibrational frequency of 240 cm⁻¹. The inplane vibrational satellite and also the ground state substitution spectra are quite accurately reproduced by the model. Our generalized semirigid bender method offers a variety of approaches to fitting molecular parameters to the experimental data.     

Conductivity of lithium gallium silicates

Lithium gallium silicates, Li_1−xGa_1−xSi_2+xO₆: 0.03 < x < 0.37, with a beta-spodumene structure, have a low Li⁺ ion conductivity, ca. 10⁻⁹ ω⁻¹ cm⁻¹ at 400 K rising to ca. 10⁻³ ω⁻¹ cm⁻¹ by 1000 K, that changes little with composition. The phase, LiGaSiO₄, with an alpha-eucryptite structure, exhibits mainly electronic conductivity, but at a low level, ca. 10⁻⁸ ω⁻¹ cm⁻¹ at 600 K, rising to ca. 10⁻⁵ ω⁻¹ cm⁻¹ at 1000 K.     

Twist-4 gluon recombination corrections for deep inelastic structure functions

We calculate twist-4 coefficient functions for the deep inelastic structure function F₂(x,Q²) associated to 4-gluon operator matrix elements for general values of the Bjorken variable x and study the numerical effect on the slope ∂F₂(x,Q²)/∂logQ². It is shown that these contributions diminish the strongly rising twist-2 terms towards small values of x.     

Sur l'evolution des proprietes physiques de la perovskite GdCoO3 entre 77 et 1200 K

GdCoO₃, which has the GdFeO₃ structure, has been studied between 77 and 1200 K by D.T.A., X-ray diffraction, magnetic susceptibility, electric conductivity and thermoelectric power. All properties observed, although different from those of LaCoO₃, fit with the corresponding Goodenough localized electron model. With rising temperature cobalt ions pass progressively from a low-spin Co^III(t⁶_2ge_g⁰) state to a Co³⁺(t⁴_2ge_g²) high-spin state.     

On the effective quark potential in baryons

We analyse the splitting of the non-strange memebers of the first excited level [70,1^?]₁ of baryon resonances. The spin-dependent forces (spin-spin, spin-orbit, tensor) are supposed to arise from the Coulomb term due to one-gluon exchange, from the long-range linearly rising part of the potential, and from additional “hard-core” spin-spin terms which may be generated by higher-order graphs contributing to the qq kernel. For the long range part we either assume that it comes from a superposition of a vector and a scalar kernel of the form ?(γ^μ ? γ_μ ? 1 + (1 ? ?)(1 ? 1 ? 1) (+ permutations), or, alternatively, that it arises from a vector exchange with an anomalous moment κ in the quark-gluon vertex. Values of ? ≈ 0 orκ ≈ ?1 turn out to be favoured. The strong coupling constant and the slope of the linear potential come out in the correct order of magnitude. Very large hard-core spin-spin terms are needed. This fact makes the determination of the effective potential from the underlying theory of quantum chromodynamics as well as the phenomenological analysis of the observed spectra rather problematic.     

Analysis of cosmic ray data on nucleon-nucleus collisions and its implication on high energy behaviour of nucleon-nucleon total cross section

From existing cosmic ray measurements of theinelastic collision cross sections of nucleons on nuclei of carbon, iron and lead in the range of energies 10² to 10⁴ GeV as well as the measurements of cross sections on air nuclei in the extensive air shower (EAS) regions (10⁵ to 10⁸ GeV), we conclude that the Glauber multiple scattering theory is adequate to account for the data. Recent suggestion of Maor and Nussinov to parametrize the nucleon-nucleon total cross section with a component growing proportional to ln² E (E is the incident energy) is at variance with the EAS data. However the data are consistent with a nucleon-nucleon total cross section rising no faster than lnE in these energy regions.     

Quark confinement and vortices in massive gauge-invariant QCD

Massive gauge-invariant QCD can support vortices (analogous to Nielsen-Olesen strings) of nearly finite classical action per unit area (there is a logarithmic short-distance singularity which is of little consequence). These vortices lead, in analogy to Abelian lattice-gauge theories, to confinement of fractionally charged quarks and color screening for gluons. In this paper, we make some qualitative remarks about the (Minkowski-space) dynamics which follows from this sort of confinement, studying not only $\text{q}\text{q}$ processes but also qqq processes. For the latter, the effective long-range vortex-induced interaction is approximately described as a sum of two-body potentials each of half the strength of the $\text{q}\text{q}$ potential (just as for the asymptotically free short-distance potentials), and linearly rising non-relativistically. There is an essential two-dimensionality about the confinement process which suppresses what would be the transverse degrees of freedom of strings joining quarks. A fully relativistic dynamics is given which is amenable to a simple phenomenological joining of long- and short-distance effects, with a running coupling constant such that g²(k) ～ k^?2 for small k. Spin-dependent potentials have no linearly-rising parts, and there are no strong Van der Waals forces. Little is said about gluon dynamics, except to point out the existence of rather massive hadronic glueballs and of (classically singular) instanton-like solutions which are screened at large distances.     

What is the relativistic generalization of a linearly rising potential?

Recent progress in summing graphs of non-Abelian gauge theories focuses attention on certain manifestly Lorentz-invariant classical action-at-a-distance theories, whose solution allows for the construction of field-theoretic Green functions in the WKB approximation. The sum of graphs is of QED type, except that the gluon propagator is modified to incorporate the renormalization-group-invariant charge $\text{g}\text{(k)}$. The purely phenomenological choice $\text{g}{}^2\text{～ k}{}^{\mathrm{?2}}$ is equivalent non-relativistically to a linearly rising potential and yields a fully relativistic classical action-at-a-distance theory with exactly soluble circular orbits, whose Bohr quantization yields an asymptotic approximation to the poles of the Green function. One finds asymptotically linear Regge trajectories, but other phenomenological aspects are not as promising when only a linearly rising potential is used (in common with other phenomenological studies). As a redeeming feature, there do not appear to be any obvious pathologies of the sort familiar from string theories and ad hoc generalizations of linearly rising potentials.     

Hysteresis effects at a cooperative high-spin (5T2) ⇌ low-spin (1A1) transition in dithiocyanatobis (4, 7-dimethyl-1, 10-phenanthroline) iron (II)

Hysteresis has been observed at the cooperative high-spin (⁵T₂) ? low-spin (¹A₁) transition in Fe (4, 7-(CH₃)₂-phen)₂(NCS)₂ where phen = 1, 10-phenanthroline. The transition is centered on T_c> = 121.7 K for rising and on T_c< = 118.6 K for lowering of temperature. The observations are in only qualitative agreement with the thermodynamic theory of Slichter and Drickamer.     

High energy pp data and the reggeon theory of diffraction scattering

Recent proton-proton scattering experiments from the CERN ISR show several striking features. There is strong evidence that the total cross section is rising. The elastic differential cross section shows a break in the forward slope, as well as a pronounced dip-bump structure, with the dip located at t ? ? 1.3 (GeV/c)². We demonstrate that all these features and their energy dependence can be simultaneously and quantitatively very well described within the framework of Gribov reggeon calculus.     

3H(p,n)3He reaction with polarized protons from threshold to 2.9 MeV

A polarized beam was used to measure angular distributions of the analyzing power of the ³H($\text{p}$, n)³He reaction at 9 energies from 1.30 to 2.90 MeV. The data were measured typically to an accuracy of 0.02 with a target 25 keV thick at 2 MeV bombarding energy. The analyzing power can be fitted with associated Legendre polynomials. The coefficient of P₁¹ is small, near zero at the upper and lower energies and negative in between; the coefficient of P₂¹ is much larger and positive, rising to a maximum at 2.2 MeV. Comparison of the analyzing power A with earlier data for the neutron polarization P induced with unpolarized protons shows the coefficients of P₁¹ to be equal and those of P₂¹ to have a similar energy dependence but with larger values for A than for P. Theoretical treatment elsewhere of the inequality of P and A infers that transitions between ³P₂ and ³F₂ are responsible. Polarization contour maps are given.     

Alpha-transfer processes in heavy-ion scattering

In the differential cross sections for the elastic scattering between an α-conjugate target and projectile, a rising oscillatory structure is often observed in the backward-angle region. An α-transfer mechanism is proposed to explain this anomalous phenomenon. A nuclear molecularorbit approximation theory for both 1α- and 2α-transfer processes has been formulated and applied to ¹⁶O + ²⁰Ne and ¹²C + ²⁰Ne scattering systems with different projectile energies. The experimental rising structures shown in these scatterings are well reproduced with parameters fairly consistent with spectroscopic data. An independent-α-particle model wave function has been used for the evaluation of the exchange potential, which gives better agreement with experiment than the Buttle-Goldfarb approximation can usually provide.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

The pomeron in elastic meson-baryon scattering

We show that a pomeron (P) trajectory with α_P(t) ≈ 1.07 + 0.22t provides a simple and satisfactory fit to π^±p and K^±p elastic scattering data (as well as pp and $\text{p}$p considered in an earlier publication) for |t| < 1.2 GeV², including the rising total cross sections. The destructive term needed to explain the diffraction minimum in pp may be explained as a weak P ? P cut effect provided that the Gribov vertices are given suitable structure, and the prediction is then made that similar minima should be observed in meson-baryon scattering at FNAL somewhere in the region 1.5 < |t| < 2.5 GeV². The P ? P cut does not seem to be related (at least directly) to the unitarization effects which must eventually make σ_tot ～ log²s (but not until s > 10⁸GeV²). Thus the “effective” J-plane singularity structure, at currently available energies seems to be much simpler than it can be asymptotically.     

A relativistic model of the composite π meson

The pion is treated as a fermion-antifermion composite state, described by the Euclidean Bethe-Salpeter equation. The kernel of the equation is a local potential having an exponentially infinite spectral function, connected with the empirical mass spectrum of resonances. For the simplest potential U(r) = f²(r²?a²)^?1 the equation for the massless pion is solved by using WKBJ method, and the parameters f, a and the fermion mass M are estimated.     

Quantum transport in a time-dependent random potential with a finite correlation time

Using an earlier density matrix formalism in momentum space we study the motion of a particle in a time-dependent random potential with a finite correlation time τ, for 0 < t ? τ. Within this domain we consider two subdomains bounded by kinetic time scales (t _c ² = 2m? ^-1 c ², c ² = σ ², ξ ², σξ, with 2σ the width of an initial wavepacket and the correlation length of the gaussian potential fluctuations), where we obtain power law scaling laws for the effect of the random potential in the mean squared displacement 〈x ²〉 and in the mean kinetic energy 〈E _kin〉. At short times, ? min (t _σ ², 1/2t _ξ ²), 〈x ²〉 and 〈E _kin〉 scale classically as t ⁴ and t ², respectively. At intermediate times, t _σξ ? t ? 2t _σ ² and 1/2t _ξ ² ? t ? t _σξ, these quantities scale quantum mechanically as t ^3/2 and as √t, respectively. These results lie in the perspective of recent studies of the existence of (fractional) power law behavior of 〈x ²〉 and 〈E _kin〉 at intermediate times. We also briefly discuss the scaling laws for 〈x ²〉 and 〈E _kin〉 at short times in the case of spatially uncorrelated potential.     

On a field-theoretic non-polynomial interaction

We consider the field-theoretic potential ω²x² + gx⁴/(1 + αgx²), α > 0, g > 0, and show that there exists a class of exact eigenvalues and eigenfunctions when certain algebraic relations between g and α hold. Comparison with large-order perturbation theory is made and, contrary to recent results, an important difference between the above potential and the field-theoretic ω²x² + gx⁴ interaction is discovered.     

Quantum Tunneling and Caustics under Inverse Square Potential

We examine the quantization of a harmonic oscillator with inverse square potential V(x)=(mω²/2) x²+g/x² on the line −∞<x<∞. We find that, for 0<g<3?²/(8m), the system admits a U(2) family of inequivalent quantizations allowing for quantum tunneling through the infinite potential barrier at x=0. These are a generalization of the conventional quantization applied to the Calogero model in which no quantum tunneling is allowed. The tunneling renders the classical caustics which arise under the potential anomalous at the quantum level, leading to the possibility of copying the profile of an arbitrary state from one side x>0, say, to the other x<0.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.