Elastic scattering slope and total cross section relations

The empirical equality of $\text{B}{}^2\text{σ}{}_{\mathrm{<mtext>t</mtext>}}$ is noted, for the pomeron terms in NN, πN, KN, ?N, ωN, and φN scattering, where B is the elastic slope parameter and σ_t is the total cross section. This ratio increases slowly with energy, but remains the same in all channels. This is equivalent to a relation between the diffractive interaction radii and opacities; the opacity scales with the square of the radius. We conjecture that this systematics extends to ψN scattering. We contrast $\text{B}{}^2\text{σ}{}_{\mathrm{<mtext>t</mtext>}}$ universaility with the slope predictions of an f-coupled pomeron model. Some other predictions of the f-dominance hypothesis are tested against data.     

Resonant motion of a spherical pendulum

The weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω₀) to the planar displacement εl cos ωt (ε ? 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion. The loci of equilibrium points and the corresponding bifurcation points in this space are determined. The control parameters are $\text{α= 2δ/ε}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and . If α < 0.441 there is a finite interval of v within which no stable equilibrium points exist. As v decreases through the upper bound (a Hopf-bifurcation point) of this interval the motion in the phase space becomes periodic and then, following a period-doubling cascade, chaotic. There may be alternating sub-intervals of chaotic and periodic motion. The chaotic trajectories in the phase space appear to lie on fractal attractors.     

On some recent results concerning the superconducting transition temperature

The Eliashberg gap equations relate the transition temperature T_c of an isotropic superconductor to its electron-phonon spectral function α²F(ω) and Coulomb pseudopotential parameter $\text{μ}{}^1$. Recently the Eliashberg theory has been used to derive some supposedly rigorous results bearing on the problem of attaining higher superconducting transition temperatures: Bergmann and Rainer derived an expression for the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{F(ω)}$; Allen and Dynes showed that in the asymptotic limit of very large $\text{λ(λ?10)k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{=f(μ}{}^1\text{)(λ〈ω}{}^2\text{〉)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and Leavens proved that for any isotropic superconductor k_BT_c ?0.2309A, where A is the area under its electron-phonon spectral function. In this letter we show that the result of Allen and Dynes is not compatible with the other results and is, in fact, incorrect.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

On a least upper bound Tc of superconductors with paramagnetic impurities

We have obtained a least upper bound, $\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{? c(μ}{}^1\text{, t)A}$, on the critical temperature T_c of an isotropic superconductor with paramagnetic impurities described by the scattering matrix t for fixed values of μ¹. We have also obtained the corresponding optimal spectrum $\text{α}{}^2\text{F(m) = Aδ[ω?d(μ}{}^1\text{, A]}$. The numerical results for the functions $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ are presented for $\text{α}{}^1\text{= 0.1}$ and 0.16 in the form of universal curves representing $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ as functions of the reduced impurity concentration $\text{t}\text{= t/A}$. We have also established an upper limit to the reduced critical concentration $\text{t}{}_{\mathrm{crit}}$ for an arbitrary shape of α²F(ω)1.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

Upper bounds on the fine structure constant and on nucleon magnetic moments in terms of Compton scattering cross sections

We derive and compare with experimental data the bound

$\text{α??λm}{}_{\mathrm{<mtext>p</mtext>}}\text{?m}{}_{\mathrm{<mtext>p</mtext>}}\text{ν}{}^2{}_1\text{2π}{}^2\text{∫}\text{ν}{}_0\text{∞}\text{d}\text{ν′σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(ν′)}\text{(ν′}{}^2\text{+ν}{}^2{}_1\text{)}\text{+2πm}{}_{\mathrm{<mtext>p</mtext>}}\text{∫}\text{ν}{}_0\text{∞}\text{ν′}{}^2\text{d}\text{ν′σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(ν′)}\text{(ν′}{}^2\text{+ν}{}^2{}_1\text{){ν′}{}^2\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_0\text{+πλ}{}^2\text{+2ν′|λ|}\text{π}\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_0\text{?}\text{σ}{}^2{}_{\mathrm{<mtext>tot</mtext>}}\text{16π}\text{}}{}^{\mathrm{?1}}$

, where α is the fine-structure constant, m_p the proton mass, ν₀ the photo-pion production threshold, σ_tot and $\text{(}\text{d}\text{σ}\text{d}\text{t}\text{)}{}_0$ are the unpolarized total hadronic photo-absorption cross section on protons and the unpolarized forward differential cross section for proton Compton scattering at photon-lab energy ν′, and λ and ν₁ are any real numbers. We derive similar bounds on proton and neutron magnetic moments.     

Bi-solitons for a class of non-linear equations with quadratic non-linearity. I

We consider the class of non-integrable, non-linear equations,

$\text{L}{}_{\mathrm{q}}\text{K=K}{}^2\text{, L}{}_{\mathrm{q}}\text{=? +}\text{∑}\text{1?i+j?q}\text{aij?}{}^{\mathrm{i}}{}_{\mathrm{x}}{}^{\mathrm{i}}\text{?}{}^{\mathrm{j}}{}_{\mathrm{t}}{}^{\mathrm{j}}\text{, ?≠0,}$

in 1+1 dimensions. We seek rational solutions K(ω₁,ω₂), which we call bi-solitons, with exponential type variables ω_i = exp(γ_ix + ρ_it). In this paper, we restrict to q = 2 and 3, and investigate the general q case in the following paper. We find that these bi-solitons exist when the operator L_q (with ± ?) can be factorized as the product of smaller order differential operators. Besides the trivial factorized bi-solitons, we show that there exist non-trivial ones whenever K may be written as Σ^lmaxx ω^l₂F_l(Z = ω₁ + ω₂). In order to understand the origin of the factorization property, to any polynomial K = Σω^l₂F_l(Z) we associate a linear transformation such that L_qK has only the power ω^l₂ of K². For q = 2 and 3, we find that there exist particular polynomials of this type restraining L_q to be a product of smallr order operators. For the full non-linear equations we verify that all the bi-solitons can be obtained from these particular polynomials.     

Production of A20and ω1 (1675) in the reaction π−p → π+π−π0n at 12 and 15 GeV/c

Data on the reaction π^?p → π⁺π^?π⁰ have been taken at 12 and 15 GeV/c with the CERN Omega multiparticle spectrometer. In a 3-pion partial-wave analysis strong production of $\text{A}{}_2{}^0\text{(1310)}\text{and}\text{ω}{}^1\text{(1675)}$ is observed. Total and differential cross sections are determined and density matrix elements presented as a function of t in the t- and s-channel frames. The energy dependence of A₂⁰ production is studied, and a comparison of $\text{ω(780),}\text{A}{}_2{}^0\text{(1310)}\text{and}\text{ω}{}^1\text{(1675)}$ production is made.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

A test of factorisation predictions for the fragmentation processes pp→π± at p momenta of 9.1 and 4.6 GeV/c

Relations have been derived between the invariant cross sections for various inclusive processes by assuming factorisation of the leading (pomeron) and non-leading (meson) trajectories. In this paper predictions for the invariant cross sections $\text{f(}\text{p}\text{p}\text{→π}{}^{\mathrm{\pm }}\text{)(2E}{}^1\text{/π√s)}\text{d}{}^2\text{σ/}\text{d}\text{x}\text{d}\text{p}{}^2{}_{\mathrm{\perp }}{}^2$ have been tested using data from $\text{p}\text{p}$interactions at 4.6 and 9.1 GeV/c.A large discrepancy between experiment and theory is apparent for the π^? data: in the π⁺ case the discrepancy is less marked but still present.     

Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

The breakdown of the Born-Oppenheimer approximation for a diatomic molecule: The dipole moment and nuclear quadrupole coupling constants

In the Born-Oppenheimer approximation the dipole moment of the vibrational levels of a ¹Σ electronic state of a heteronuclear diatomic molecule can be expressed as a power series in [$\text{(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v +}\text{1}\text{2}\text{)}$], where v is the vibrational quantum number, and to order $\text{(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)}{}^2$ this expression is

$\text{μ}{}_{\mathrm{v}}\text{=[μ}{}_{\mathrm{e}}\text{+(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)}{}^2\text{μ}{}_{\mathrm{c}}\text{]+μ}{}_1\text{[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]+μ}{}_2\text{(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]}{}^2$

Similarly the nuclear quadrupole coupling constant eQq of each nucleus in the molecule can be expressed as

$\text{eQq=[eQq}{}_{\mathrm{e}}\text{+(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)}{}^2\text{eQq}{}_{\mathrm{c}}\text{]+eQq}{}_1\text{[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]+eQq}{}_2\text{(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]}{}^2$

In this paper the effect of the breakdown of the Born-Oppenheimer approximation on the expressions for μ_v and eQq for an isolated ¹Σ ground electronic state of a heteronuclear diatomic molecule is determined. The effect is to change only μ_c and eQq_c and, therefore, to alter the relationship between the μ_v or eQq values of two isotopes of a molecule. The intensities of the lines in the rotation and rotation-vibration spectrum are also slightly modified by this effect.For the HCl molecule we find that

$\text{μ}{}_{\mathrm{v}}\text{=[1.0908+(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(164)]+8.6[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]?9.5[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]}{}^2\text{D}$

where the second term (+164 D) would have the value ?4 D in the Born-Oppenheimer approximation. Similarly for the ³⁵Cl nucleus of the HCl molecule we have

$\text{eQq=[?66.806+(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(2460)]?472.23[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]+750[(}\text{B}{}_{\mathrm{e}}\text{ω}{}_{\mathrm{e}}\text{)(v+}\text{1}\text{2}\text{)]}{}^2\text{MHz}$

where the second term (+2460 MHz) would be ?110 MHz in the Born-Oppenheimer approximation.     

Long time expansion of two-dimensional correlation functions

We show that the long time behaviour of the velocity correlation function in a two-dimensional classical system with pairwise repulsive potentials can be represented by a series expansion of the form

$\text{〈υ}{}_{\mathrm{1x}}\text{υ}{}_{\mathrm{1x}}\text{(t)〉 = d}{}_0\text{t}{}^{\mathrm{?1}}\text{+ d}{}_1\text{t}{}^{\mathrm{?1}}\text{log}\text{t/t}{}_0\text{+ d}{}_2\text{t}{}^{\mathrm{?1}}\text{(}\text{log}\text{t/t}{}_0\text{)}{}^2\text{+ …}$

, where t₀ is mean free time between collisions. To lowest order in the density an exact expression has been obtained for d₁ employing the kinetic theory ofsystems with hard-core interactions. The significance of the series is discussed at low and intermediate densities.     

Information on the dynamics of the reaction KN → K1N from KLN interactions

If $\text{K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{is a K}{}^1$ resonance decaying into K_S,L (the short- and long-lived kaon) and a neutral system S^o of pions, one can isolate the C-even and C-odd, crossed-channel contributions to $\text{KN → K}{}^1\text{N}$ by using the reactions $\text{K}{}_{\mathrm{L}}\text{N → K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{N}$ whether S^o is a C-eigenstate, or a mixture of C-even and C-odd states. Applications to the production of K¹(890) and the Q-meson are discussed, and simple numerical predictions made for Q_S,L production. Q-production data indicate approximate t-channel helicity conservation for the ω and P' exchanges at vertices involving a spin change, in similarity to the belief for the pomeron. Q_S,L production data can give information also on Q-decays.     

Prediction of strong magnetic quantum oscillations of the nuclear spin relaxation in a quasi-two-dimensional metal

The nuclear spin lattice relaxation rate in a quasi-two-dimensional (2-D) metal under strong magnetic fields is studied in a special case where the electronic cyclotron mass is small compared with the free electron mass. In the pure limit (ω_cτ ? 1) and for sufficiently low temperatures ($\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{> 2π}{}^2\text{k}{}_{\mathrm{B}}\text{T}$) we find remarkable quantum oscillations of the relaxation rate as a function of the magnetic field. The period of these oscillations is identical to that of the de Haas-van Alphen oscillations and their amplitude grows linearly with the magnetic field. The possibility of observing such oscillations experimentally in the quasi-2-D mercury chain compound Hg_3?δAsF₆ is discussed.     

The A-dependence of J/ψ-particle inclusive distributions

The differential cross sections $\text{d}\text{σ}\text{d}\text{x}$ and $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2$ of inclusive J/ψ production by 43 GeV/c π^? off Be, Cu and W nuclei have been measured. Fitting $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2\text{～ A}{}^{\mathrm{\alpha }}\text{(p}{}_{\mathrm{t}}{}^2\text{)}$ we observed the increase of α with p_t².     

High-pt hadrons in the pionization region in QCD

We show that in QCD the production of high-p_t hadrons in the pionization region $\text{ln}\text{(}\text{p}{}_{\mathrm{<mtext>t</mtext>}}{}^2\text{μ}{}^2\text{) < [(}\text{8N}\text{D0.21 β}{}_2\text{)}\text{ln}\text{x}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is not a rare process, but a usual “soft” one. Its inclusive cross section ? behaves as $\text{? =}\text{d}\text{σ}\text{d}\text{y}\text{d}\text{p}{}_{\mathrm{<mtext>t</mtext>}}{}^2\text{∝}\text{σ}{}_{\mathrm{<mtext>t</mtext>}}\text{p}{}_{\mathrm{t0}}{}^2$. At ISABELLE energies and p_t = 10 GeV we estimate this cross section to be at least an order larger than the value obtained by commonly used parametrizations.     

Moments of two-time spin-pair correlation functions for a one-dimensional anisotropic Heisenberg model at infinite temperature

The first ten moments of the infinite-temperature space and frequency dependent two-spin correlation functions, $\text{?}{}^{\mathrm{x}}{}_{\mathrm{r}}\text{(ω)}$ and $\text{?}{}^{\mathrm{z}}{}_{\mathrm{r}}\text{(ω)}$ are obtained for the one-dimensional anisotropic Heisenberg model for r = 0 and r = 1. These are compared with those previously known.