Large q expansions for q-state gauge-matter Potts models in lagrangian form

We consider the lagrangian form of a q-state generalization of Ising gauge theories with matter fields in d = 3 and 4 dimensions. The theory is exactly soluble in the limit q → ∞ and corrections are easily calculable in power series in $\text{1}\text{q}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$. Extrapolating the series for the free energies and latent heats by the method of Padé approximants, we have constructed the phase diagrams for all values of q. Our results agree well with known results for pure spin systems and, for the case q = 2, with Ising Monte Carlo data.     

Non-string two-magnon configurations in the isotropic Heisenberg magnet

By means of the $\text{1}\text{N}$ expansion we study the Bethe-ansatz equations for two-magnon states in the one-dimensional isotropic Heisenberg spin chain of N spins $\text{1}\text{2}$. A qualitative picture of complex solutions for N → ∞ is obtained which substantially disagrees with the string hypothesis. For example, the solutions $\text{λ}{}_{\mathrm{<mtext>1,2</mtext>}}\text{= x ±}\text{i}\text{y, x ～ N,y ～}\text{N}$ are found, whereas according to the string hypothesis $\text{y →}\text{1}\text{2}$ if N → ∞.     

Radiative transitions and the P wave levels in charmonium

A value of $\text{1}\text{2}$ or less for the ratio $\text{[E(2}{}^{\mathrm{++}}\text{) ? E(1}{}^{\mathrm{++}}\text{)]}\text{[E(1}{}^{\mathrm{++}}\text{) ? E(0}{}^{\mathrm{++}}\text{)]}$ of the P level splittings in approximate agreement with the assignment of the states at 3.41, 3.50 and 3.55 to the 0⁺⁺,and 2⁺⁺ P-wave levels, is obtained with a short-range Coulomb (Lorentz vector) potential together with a long-range linear (Lorentz scalar) confining potential. The radiative transition widths Γ(ψ′ → 3.41 + γ), Γ(ψ′ → 3.50 + γ), Γ(χ′ → 3.55 + γ) are significantly smaller than those obtained in previous (one-channel) charmonium calculations. The best results were obtained by allowing the Coulomb coupling constant α_s to have a momentum dependence suggested by asymptotic freedom formulae.     

Non-gauge spin-32 fields from supercovariantly constant spinors

We point out a limiting procedure which enables one to construct in supergravity theories non-gauge, linearized spin-$\text{3}\text{2}$ fields with the aid of the supercovariantly constant spinors. We give an explicit application of the procedure for N = 2 supergravity.     

Spin-dependence and glueball mixing with θ(1640) in ordinary meson spectroscopy

It is shown from a fairly general point of view that meson spectroscopy implies that the spin-spin and tensor forces are due to very short-ranged interactions. The (Q₁, Q₂) ? (Q_A, Q_B) mixing of axial vector $\text{I =}\text{1}\text{2}$ mesons implies the presence of a substantial repulsive Thomas term as well as an attractive short-ranged spin-orbit force of comparable magnitude. This analysis makes no reference to detailed potentials or wave functions. Inverted multiplets are predicted as a consequence of the large repulsive Thomas term. The spin-dependent potentials can be interpreted as effective exchanges dominated by short-ranged vector exchange and a confining potential transforming as a Lorentz scalar, although small amounts of other exchanges are also possible. A model-dependent analysis of the gluon annihilation contribution to the mass matrix and two-body decays of the I = 0 2⁺⁺ mesons indicates significant gluon mixing in these states. The presence of a $\text{non-q}\text{q}$ state (glueball?) which mixes with f'(1514) and another I = 0 2⁺⁺ state is required by the mixing model. The possibility that this additional state is θ(1640) is considered. The mass of such a state satisfies f'(1514)<M(G₀)<θ(1640). The model predicts $\text{0.01 < Λ(θ → ηη)/Λ(θ →}\text{K}\text{K}\text{)<0.18}$, with the actual widths sensitive to the details of singlet-octet mixing in the η wave function.     

Effect of single-ion anisotropy on the critical-point properties of the exchange interaction model of ferromagnetism

For the spin S exchange interaction model it is shown that both magnetic field and single-ion anisotropy (D) can be exactly treated. When D → ± ∞ the critical-point parameters of this model are exactly the same as those of the $\text{S}\text{=}\text{1}\text{2}$ Heisenberg model.     

On Milne's quantum number function

The quantum number function N(E) introduced by Milne is studied in detail. It is shown that N(E) is not uniquely defined for energies different from the bound state values. The density of states $\text{d}\text{N}\text{d}\text{E}$ is nowhere unique and not necessarily positive.     

The correct extension of the Fortuin-Kasteleyn result to plaquette percolation

The standard s-state Potts model is generalized to a model defined of laquettes of $\text{Zz}{}^{\mathrm{d}}$, and the s → 1, 0 limits are shown to correspond to plaquette percolation and percolation of plaquette trees, respectively. The model is further extended to r-cells (cubes, hypercubes, etc.) on $\text{Z}{}^{\mathrm{d}}$ and the s → 1, 0 limits are exhibited.     

Exact saturation and degeneracy of isospin bounds and zeros trajectories in pion-nucleon scattering: D. B. Ion. Joint Institute for Nuclear Research,Dubna, Moscow,P. O. Box 79, U.S.S.R.

By exploiting the analogy between the classical equation of heat conduction and the Bloch equation, the canonical density matrix is calculated exactly for noninteracting electrons in a finite step model of a metal surface. This result is then used to calculate the spatial variation of the electron density ?(z) as a function of distance z from the planar metal surface. In particular an expansion in inverse powers of $\text{V}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and V, V being the step height, is derived. The low-order terms are used to compute the electron density at the surface of Al metal: There is good agreement with a full numerical evaluation. Finally, in the limit $\text{V}\text{E}{}_{\mathrm{f}}\text{→ ∞}$, E_f being the Fermi energy, the change in the shape and size of the exchange (Fermi) hole surrounding an electron is studied as the electron moves into the vicinity of a metal surface. The anisotropy of the Fermi hole is large and the implications for one-body potential theory are briefly discussed.     

The Klein-Gordon equation as a limiting case of a suitably hyperbolized schrödinger equation

We obtain a hyperbolic equation whose discontinuity waves are all exceptional and propagate with velocity λ. When λ → ∞ or λ=c, this equation becomes identical to the Schrödinger equation and to the Klein-Gordon equation respectively. We also show that λ is related to the dispersion relationE(p).     

Surface relaxation of Pt(111) investigated by ion scattering

The energy levels of some specific forms of screened Coulomb potential, as a function of the perturbation parameter λ, are shown to have a branch cut along the negative real axis, and singularities on the second sheet along $\text{|λ| e}{}^{\mathrm{<mtext>\pm (</mtext><mtext>3</mtext><mtext>2</mtext><mtext>)i\pi </mtext>}}$ for |λ| → 0. As a consequence, the energy levels have an asymptotic series in λ, which cannot be used to describe the energy levels to an arbitrary accuracy.     

Elastic backscattering of electrons from surfaces

A Monte Carlo algorithm is proposed for calculating the elastic reflection coefficient, η_E, for elements. The algorithm accounts for the multiple elastic scattering of electrons in solids. The calculated values of η_E compare well with the literature data for elements with atomic number up to 47 and at primary energies above 2 keV. The proposed Monte Carlo method makes it possible to determine the functional relation between η_E and the inelastic mean free path, λ. This relation turned out to be non-linear, arid it deviates from a similar relation based on published earlier single elastic scattering model. The deviation is especially pronounced for elements with medium atomic numbers. The calculated function $\text{η}{}_{\mathrm{<mtext>E</mtext>}}\text{=}\text{f}\text{(λ)}$ offers a convenient method for determining the inelastic mean free path. The values of λ derived in the present work from published experimental values of η_E compare very well with the literature data.     

Analysis of a six-quark model with right-handed currents

A model for the weak interactions using the six-quark model of Harari, right-handed currents, and heavy leptons which was proposed previously by some of us is analyzed in considerable detail. The model is one of a class of “vector-like” theories that are free of gauge theory anomalies. The neutral current is pure vector, which leads to predictions for diffractive production of vector mesons by neutrinos that are different from the predictions of the standard Weinberg-Salam model; the A₁ uncouples and the fractions of ? and ω are enhanced. It is also predicted that relative production of $\text{I =}\text{1}\text{2}$ final states is larger than $\text{I =}\text{3}\text{2}$ final states in vN → vNπ in contrast to the Weinberg-Salam model. The non-leptonic decays of hyperons and mesons and the restrictions imposed by chiral symmetry are discussed. The decays of the charmed mesons are shown to be very rich due to the presence of both V ? A and V + A interactions. The y-anomalies in neutrino interactions are discussed and calculations of $\text{d}\text{σ}\text{d}\text{x}\text{and}\text{d}\text{σ}\text{d}\text{y}$ for both neutrinos and antineutrinos using modified Kuti-Weisskopf distributions are presented. Cross sections and ratios of neutrino and a neutrino cross sections are shown along with available experimental data. The v-distribution of dimuon events is also presented and compared with experiment. It is concluded that the model is not inconsistent with the currently available data.     

Spotting glueballs in collinear gluon jets

We suggest looking for pure gluon hadronic states (glueballs) in ?→ 3g → low spherically final state (collinear gluon jets). In these events one gluon has the maximum energy, $\text{M?}\text{2}$, favouring fragmentation into a glueball. The signature for a true C = G + glueball is its prominence at the ? resonance in e⁺e^? →? → (glueball → four charged pions) + … and its absence in q$\text{q}$ jets off (we do not expect significant quark fragmentation into glueballs).     

Scaling laws for inelastic partial-wave amplitudes and the high-energy behaviour of multiparticle production

t-channel unitarity equations are derived for n-particle overlap functions. Together with s-channel unitarity they lead to scaling laws for the inelastic s-channel partial-wave amplitudes $\text{?}{}_{\mathrm{l}}{}^{\mathrm{(n)}}\text{(s)}$ in the limits $\text{s → ∞, l → ∞ x = l (}\text{μ}\text{√s}\text{)}{}^3\text{=}\text{fixed}$. Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for $\text{l > L (s) = (α(4μ}{}^2\text{) ? 1) (}\text{s}\text{4μ}\text{)}\text{log}\text{(}\text{s}\text{s}{}_1\text{)}$ we obtain constant production cross sections σ⁽ⁿ⁾(s) at high energies s → ∞ up to s factors.     

Nucleon-antinucleon bound states in a quark rearrangement model

The possibility of deeply-bound $\text{N}\text{N}$ states is studied in a quark rearrangement annihilation plus a meson-exchange potential model. It is shown that very narrow (Γ ～- 1–10 MeV) bound states may be possible even forL = 0 with binding energies varying up to $\text{E}{}_{\mathrm{<mtext>B</mtext>}}\text{?- 800–900}\text{MeV}$ in the proposed scheme. E_B is, however, very dependent on the details of the short-range treatment of the meson-exchange part. A reasonable agreement with the present controversial data can be obtained.     

Microwave spectrum of the C4v molecule IF5 in the excited vibrational states v5(B1) = 1 and v9(E) = 1: Analysis of the ν5-ν9 Coriolis resonance

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₅(B₁) = 1 and v₉(E) = 1 are reported for the transitions J4 → 5, 5 → 6, 6 → 7, 8 → 9, and 9 → 10 (27–55 GHz). The Coriolis resonance interaction between these two states is analyzed by diagonalization of Hamiltonian matrices of dimension 3 × (2J + 1) in which all (Δl,Δk) = (±2, ±2)(q⁺), (±2, ±2)(q^?), and (0, ±4)(R₆) interactions are included as off-diagonal terms in addition to the v₅ = 1 ? v₉ = 1, l₉ = ±1(R₅₉) Coriolis interaction. In the v₉ = 1 state spectra, the $\text{B}{}_1\text{B}{}_2$l-doubling of the kl = ?1 transitions and $\text{A}{}_1\text{A}{}_2$ splittings of the kl = ?3 transitions and $\text{B}{}_1\text{B}{}_2$ splittings of the kl = +3 transitions, all enhanced by the Coriolis resonance, have been observed and measured. Least-squares refined rovibrational parameters for the v₅ = 1 and v₉ = 1 states are reported and a preliminary value for the rotational constant C₉ has been obtained.     

Quark dynamics and the weak non-leptonic decays of K and D mesons

Quark model predictions for K → 2π and D → Kπ decays were investigated in dynamical frameworks based on the separable approximation (SA), current algebra (CA), current algebra modified for the meson moment dependence (CAC) and current algebra with final-state interactions (CAF). Relativistic and non-relativistic quark model predictions were compared. The effective weak hamiltonian was modified by changing the relative strengths of its flavour $\text{20}\text{and}\text{84}$ parts. All these approaches were also applied to hyperon and $\text{Ω}{}^{\mathrm{?}}$ non-leptonic decays. When using standard QCD enhancement, the best approximation for K → 2π (CAC) works poorly with D → Kπ. The best approximatiob for D→Kπ (CAF) fails in the case of K → 2π. Only CAC with the $\text{84}$ piece of the hamiltonian quenched might be in agreement with studied weak decays.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.