Investigation of the ηη system in π − p interactions at a momentum of 32.5 GeV/c at the GAMS-4π spectrometer

The ηη system produced in charge-exchange π ^? p interaction at a momentum of 32.5 GeV/c is studied in an experiment performed with the GAMS-4π spectrometer at the 70-GeV accelerator of the Institute for High-Energy Physics (IHEP, Protvino). A partial-wave analysis is performed in the mass range between 1.1 and 3.9 GeV for ?t <0.2 (GeV/c)², S, D, G, and J waves being taken into account in this analysis. The S wave has a complicated structure, displaying peaks at about 1.5 and 1.7 GeV. These peaks are associated with the f ₀(1500) and f ₀(1710) mesons. One of the solutions (preferable one) involves the f ₀(2200) and f ₂(1950) resonances. The mass region above 2.4 GeV is dominated by the G wave. A broad state of mass about 3 GeV and width 0.7 GeV is found in the J wave. The parameters of the resonances in question and their production cross sections are measured.     

The spectrum of protons produced in pp collisions at 31 GeV total energy

Data are reported on the distributions in longitudinal and transverse momentum of protons produced in the range 0.5 < x < 1.0 (x = Feynman variable) and 0.2 < p_T² < 1.8 (GeV/c)² in proton-proton collisions at 31 GeV c.m. energy at the CERN ISR. The invariant inelastic cross section shows a peak at high longitudinal momenta. The shape of this peak suggests substantial production of states with masses up to at least 7 GeV.     

Unitarily invariant convex functions on the state space of type I and type III von Neumann algebras

Properties of unitarily invariant convex functions, defined on subsets of positive linear forms of type I and type III IV¹-algebras have been investigated. We especially characterize those pairs of positive linear forms f, g for which Ψ(f) ? Ψ(g) holds for every unitarily invariant convex function Ψ and in which case we call f “more chaotic” than g.     

Associated average charged particle multiplicities in K+p interactions at 32 GeV/c

The average charged particle multiplicities, 〈n_R(M_X²)〉, in the reactions K⁺p → π^?X and K⁺p → K⁰X at 32 GeV/c are studied as functions of the mass squared M_X² of the “associated” system X. A comparison with the corresponding results obtained at lower incident momenta is presented.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

Absolute γ-decay rates of the fc(3.55) from tensor meson dominance and QCD-potentials

We compute the coupling gf_c of the 2⁺⁺ cc? meson f_c(3.55) to the energy-2-momentum tensor, 〈0|T_μν|f_c〉·√ = gf_c?μν, from the QCD-potential of Barbieri, Gatto, Kögerler and Kunszt. Vector meson and tensor dominance then imply, including color, Γ(Ψ' → γf_c) = 20 keV in good agreement with experiment. Other potentials available in the literature yield widths which are larger by up to a factor 2. A naive formulation of vector meson dominance for both γ's in f_c → γγ yields A width which is an order of magnitude above the experimental limit.     

Charged particle multiplicity distributions for 32 GeV/c K±p and pp interactions and for 50 GeV/c π±p interactions

Topological cross sections are presented for K⁺p, K^?p and $\text{p}\text{p}$ interations at 32 GeV/c and for π⁺p and π^?p interactions at 50 GeV/c observed in the 4.5 m Mirabelle hydrogen bubble chamber at Serpukhov. Parameters characterizing the behaviour of the multiplicity distributions, namely 〈n_c〉, D and f₂ and the normalized moments are given. The dependence of these parameters on the energy and the nature of the beam particle is discussed. The multiplicity distributions obtained cannot be described by a single function in the KNO variables.     

Features of multiplicity distributions in a bootstrap model of inclusive spectra

Using a bootstrap model of inclusive spectra we derive an integral equation satisfied by the generating function for multiplicity distributions. The (semi-asymptotic) solution of this equations has the form Ψ(λ, s) = Ψ(λ, s₀)(s/s₀)^b(λ) where s is the usual energy variable and b(λ) satisfies an eigenvalue equation and is completely determined by the leading particle distribution. Closed formulae for the binomial moments and for correlation coefficients are also given, and in addition we discuss some general features of the bootstrap model. As a phenomenological application we discuss the rate of variation with energy of multiplicity moments. Our results are expected to be representative for multiperipheral-like models.     

Measurement of the surface density of states by field ionization

It is shown that recent measurements of field ion energy distributions from clean tungsten surfaces probe the density of metal states in the vicinity of the surface. We find j(ω) = (2π/kh)Σ_m| ∫ d³rψ_m(r)γ_z|²δ(ω??_m), where j(ω) is the ion current a ω, ψ_mand ?_m are electronic metal eigenfunctions and eigenvalues in the presence of the external electric field used in field ionization and γ(z) is a function which is large near the noble gas atom. An explicit expression for γ(z) is given in the text. It is estimated that tungsten metal states with values of k₆ at least as large as 0.5 Å^?1 make an appreciable contribution to j(ω) where k₆ is the electron momentum parallel to the surface.     

Energy dependence of transverse momentum invariant distribution of pions and neutral kaons in K−p interactions between 14.3 and 70 GeV/c

The energy dependence of the transverse momentum invariant distribution of pions and neutral kaons is studied in K^?p interactions between 14.3 and 70 GeV/c. The large P_T part of the distributions violates the Feynman scaling and, above P_T ? 1.5 GeV/c, appears to be reasonably described by hard scattering models. The variation of the average transverse momentum is also studied as a function of the c.m. reduced longitudinal momentum, and its behaviour is compared to the data obtained via the hadronic shower produced in lepton-hadron interactions.     

Leading role pseudovector and vector mesons in quasielastic pion electroproduction on a nucleon by longitudinal photons at comparatively high virtual momenta in the range 0.4 ≤ |k| ≤ 1 GeV/c

It is shown that, under kinematical conditions of quasielastic knockout, the differential cross section for the exclusive process p(e, e′π ⁺)n induced by longitudinal virtual photons γ* _L changes its physical nature as the recoil momentum |k| of the spectator nucleon grows from values in the range |k| ～ 0.1–0.4 GeV/c, which are typical in studying the pion cloud of the nucleon, to values around |k| ～ 1 GeV/c. Calculations within the ³ P ₀ quark microscopic model reveal that the amplitudes for the deexcitation of vector and pseudovector mesons via the processes ρ ⁺ + γ* _L → π ⁺ and b ₁ ⁺ + γ* _L → π ⁺ become dominant here. Concurrently, the effective momentum distributions develop a substantial angular anisotropy of about 50% with respect to the angle between the momentum of the photon γ* _L and the recoil momentum of the spectator nucleon, the longitudinal differential cross sections undergoing respective changes. In this region, the energy of knock-on pions is expected to be about 5 GeV under conditions of quasilastic kinematics.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Resonances in the ωω system

Results of a partial-wave analysis for the reaction π ^? → ωωn studied at the VES spectrometer (Institute for High Emergy Physics, Protvino) are presented. The behavior of the J ^PC = 2⁺⁺ amplitudes in the ωω system is described by the f ₂(1565) and f ₂(1910) resonances, whose parameters were fixed at M = 1.590 ± 0.010 GeV and Γ = 0.140 ± 0.011 GeV for the former and at M = 1.890 ± 0.010 GeV and Γ = 0.165 ± 0.019 GeV for the latter. The decay f ₄(2050) → ωω was observed at parameters values of M = 1.960 ± 0.015 GeV, Γ = 0.290 ± 0.020 GeV.     

Inclusive neutral kaon production in 70 GeV/c K+p interactions

The inclusive production of neutral kaons in 70 GeV/c K⁺p interactions is studied with the CERN BEBC bubble chamber. The (semi-)inclusive cross sections are interpreted in terms of the various strangeness channels leading to neutral kaon production. The invariant inclusive cross section for kaon production is studied as a function of p_t² and the Feynman variable x. The latter distributions are considered both “raw” and corrected for the presence of K⁰'s resulting from K¹ decay. They are compared with the predictions expected from the Regge-Mueller formalism, the recombination model and fragmentation models.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

The 2‐matrix of the spin‐polarized electron gas: contraction sum rules and spectral resolutions

The spin‐polarized homogeneous electron gas with densities ρ_↑ and ρ_↓ for electrons with spin ‘up’ (↑) and spin ‘down’ (↓), respectively, is systematically analyzed with respect to its lowest‐order reduced densities and density matrices and their mutual relations. The three 2‐body reduced density matrices γ_↑↑, γ_↓↓, γ_a are 4‐point functions for electron pairs with spins ↑↑, ↓↓, and antiparallel, respectively. From them, three functions G_↑↑(x,y), G_↓↓(x,y), G_a(x,y), depending on only two variables, are derived. These functions contain not only the pair densities according to g_↑↑(r) = G_↑uarr;(0,r), g_↓↓(r) = G_↓↓(0,r), g_a(r) = G_a(0,r) with r = | r ₁ ‐ r ₂|, but also the 1‐body reduced density matrices γ_↑ and γ_↓ being 2‐point functions according to γ_s = ρ_sf_s and f_s(r) = G_ss(r, ∞) with s = ↑,↓ and r = | r ₁ ‐ r ^′₁|. The contraction properties of the 2‐body reduced density matrices lead to three sum rules to be obeyed by the three key functions G_ss, G_a. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions n_↑(k) and n_↓(k), following from f_↑(r) and f_↓(r) by Fourier transform, are correctly normalized through f_s(0) = 1. In addition to the non‐negativity conditions n_s(k),g_ss(r),g_a(r) ≥ 0 [these quantities are probabilities], it holds n_s(k) ≤ 1 and g_ss(0) = 0 due to the Pauli principle and g_a(0) ≤ 1 due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin‐unpolarized homogeneous electron gas in terms of 2‐body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin‐polarized case and (ii) to the 2‐body reduced density matrix giving thus its spectral resolutions.     

Measure permutation formulas in Feynman’s operational calculi

In Jefferies-Johnson’s theory of Feynman’s operational calculi for noncommuting operators, the two operators T _{µ 1,µ 2} f(Ã, \(\tilde B\)) and T _{µ 2},µ₁ f(Ã, \(\tilde B\)) are not equal. Relationships between these two operators are given, i.e., “measure permutation formulas” in Feynman’s operational calculi are developed; they correspond to the “index permutation formula” in Maslov’s discretized version of Feynman’s operational calculus.