Experimental determination of the critical exponent η for nickel

The first unambiguous experimental determination of the critical exponent η, describing the critical point line shape of the spin correlation function, is presented for a three dimensional magnetic system. As a consequence of a finite value of η the critical scattering displays a maximum at T_max(q) above the Curie temperature T_c. The shift of the maximum with increasing scattering vector q was observed by a neutron small-angle experiment, yielding η=0.041±0.009 for a nickel single-crystal.     

Confined acoustic modes and spectral determination of network connectivity: Raman signatures of nanometric structure in g-GexSe1−x

Low-temperature Raman scattering results are presented on three glass compositions of Ge_xSe_1−x (15, 20, and 27 At. Ge%), and conciled with their reported structural data. The acoustic range is marked by the absence of Boson peak, and features discrete modes corresponding to nanometric dynamic aggregates. First sharp diffraction peak (FSDP) in structure factor S(k), due to Ge-Ge correlations brought about by shared Ge[Se_1/2]₄ tetrahedra medium-range structures, signifies 3D networking of Se-chains. A measure of volume-fraction of these entities determined from the FSDP area, and their number density ρ_MRS∝(k³Area)_FSDP is found to relate directly to the network connectivity, defined from optical Raman spectra in terms of the degree of cross-linking of Se-chains.     

Determination of the ππ scattering lengths from data on πN → ππN reactions by the method of Roy equations

Fitted phase-shift curves from the threshold to the dipion mass, which is equal to 1 GeV, are constructed on the basis of all available experimental values of the S-and P-wave phase shifts for five charged channels of pion-pion scattering. The resulting phase-shift curves are introduced in the Roy equations in order to obtain the subtraction constants λ _l ^I (s). By using these subtraction-constant values as functions of the dipion mass, the S ₀-and S ₂-wave pion-pion scattering lengths are found to be a ₀ ⁰ = (0.240 ± 0.023)m _π ^?1 and a ₀ ² = (?0.034 ± 0.013)m _π ^?1 . A strong correlation of the S-wave scattering lengths is demonstrated.     

Adiabatic theorem in axiomatic quantum field theory

It is shown that Møller matricesS _± and scattering matrixS in axiomatic field theory can be expressed through their adiabatic analogs. In particular, it is proved under certain conditions that \(S_ - = \mathop {s\lim }\limits_{\alpha \to 0} S_\alpha (0,\infty )W_\alpha \) whereW _α is a trivial phase factor [i.e. a unitary operator of the form exp i / α ∝r(k)a ⁺ (k)a(k)dk]. Corresponding results in Hamiltonian approach are discussed.     

The structure factor and the transport properties of dense fluids having molecules with square well potential,a possible generalization

An analytical expression of the static structure factor S(k) has been presented, treating the square well potential as a perturbation on the hard sphere system incorporating the correct equation of state given by Carnahan and Starling (CS). Reasonable values of potential parameters are obtained from a fit with the experimental peak of S(k). The present calculation of transport coefficients for liquid sodium at 373 K, is found to be in closer agreement with the experimental data. The role of back scattering correction is also discussed.     

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.     

γγ→π0 transition and asymptotics of γγ and γγ transitions of unflavored pseudoscalar mesons

For the spacelike momenta k of the virtual photon γ, the π⁰(p)γ(k)γ(k^′) transition form factor is considered in the coupled Schwinger–Dyson and Bethe-Salpeter approach in conjunction with the generalized impulse approximation using the dressed quark–photon–quark vertices of the Ball–Chiu and Curtis-Pennington type. These form factors are compared with the ones predicted by the vector meson dominance, operator product expansion, QCD sum rules, and the perturbative QCD for the large spacelike transferred momenta k. The most important qualitative feature of the asymptotic behavior, namely the 1/k² dependence, is in our approach obtained in the model-independent way. Again model-independently, our approach reproduces also the Adler–Bell–Jackiw anomaly result for the limit of both photons being real. For the case of one highly virtual photon, we find in the closed form the asymptotic expression which is then easily generalized both to the case of other unflavored pseudoscalar mesons P⁰=π⁰,η₈,η₀,η_c,η_b, and to the case of arbitrary virtuality of the other photon.     

Density correlations of hadron gas and the origin of early multiplicity scaling

We will define a sequence of functions called density correlations which measure statistical correlations between momentum space densities of particles in the ensemble of inelastic final states produced by scattering a pair of hadrons. Then we will show that early multiplicity scaling of the distribution of charged particles produced by pp collisions can primarly be explained by the assumption that fluctuations of the density of charged particles are quite random and therefore higher correlation functions are small in an appropriate sense, combined with the assumption that the first three density correlations fulfill an approximate form of Feyman scaling at small values of x. These assumptions will aslo be used to derive an expression for the scaling function Ψ(η) which is completely determined by <N²>_S/<N>_S² and <N³>_S/<N>_S³, and recursion relation to calculate <N^m>_S/<N>_S^m, m ? 4, from <N²>_S/<N>_S² and <N³>_S/<N>_S³. The prediction for Ψ(η) accurately reproduces data in the interval 0.2 ? η ? 3.1, 50 GeV/c ? p_L ? 303 GeV/c, and the predictions for <N_S>^m/<N>_S^m, 4 ? m ? 10, agree with observed values in the interval 50 GeV/c ? p_L ? 303 GeV/c.     

Dynamic structure function of liquid 3He

The dynamic structure function S(Q, ω) of liquid ³He is evaluated in the impulse approximation, based on a theoretically calculated momentum distribution n(k). The gap of n(k) at the Fermi surface gives rise to discontinuities in the slope of S(Q = const., ω) which may be detectable in neutron- or γ-ray scattering experiments.     

Two-Channel Effective Range Expansion and Bound-State Properties

The S matrix and the f matrix amplitudes are considered for the case of two coupled elastic scattering channels, which differ in values of orbital angular momenta. Matrix elements of S and f matrices are parametrized in terms of scattering phases ?? _i (i?=?1, 2) and a mixing parameter ${\epsilon}$ and are expressed in terms of matrix elements c _ij = (K ^?1) _ij where K is the reaction K matrix. Quantities ${g_{ij}(k)=k^{l_i+l_j+1}c_{ij}(k)}$ are expanded in powers of k ², k being the relative momentum of colliding particles B and C. Then functions g _ij (k) and c _ij (k) are continued analytically to the pole of amplitudes f _ij corresponding to the bound state A of colliding particles. This procedure allows to get the position of the pole as well as the residues of amplitudes f _ij at that pole which are related directly to vertex constants and asymptotic normalization coefficients corresponding to the vertex A ?? B?+?C.     

Hadronic wave functions at short distances and the operator product expansion

The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the high-Q² limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α_S(Q²)/Q² fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

Anderson localization and superconducting transition temperature in two-dimensional systems

Effects of the Anderson localization on superconducting transition temperature T_c are examined by calculating a two-electron propagator K rigorously up to 0[(?_Fτ₀)^?1ln(Tτ₀)], where τ₀ is the electron life time due to impurity scattering and ?_F the Fermi energy. The results show that in K the pair-breaking terms cancel out among themselves exactly and the remaining terms which contribute to the correction to the density of states and to the renormalization of electron-electron interaction by impurity scattering lead to the changes in T_c of 0[{ln(Tτ₀)}²] and of 0[{ln(Tτ₀)}³], respectively.     

Electron-phonon relaxation time in mercury

Electron scattering times determined by Azbel'-Kaner cyclotron resonance in mercury are discussed in terms of the electron-phonon interaction. Anisotropy in the electron-phonon relaxation time is explained in terms of an orbital α _k ² (ω)F _k (ω) function which describes the electron-phonon interaction and the phonon spectrum. AT ⁵ temperature dependence of the electron-phonon relaxation frequency is also considered.     

Critical properties of high-spin Ising models on anisotropic lattices

The coordinates of the critical points of spin-S Ising models with coupling constants J and J′ are calculated for 1/2 ≤ S ≤ 13/2. The calculations are performed for several values of S and Δ ≡ J′/J independently by using the phenomenological renormalization-group method or (approximate) self-duality. Numerical results combined with a mean-field analysis show that the critical coupling strength for Δ ～ 1 (weakly anisotropic lattice) is K _c ^(S) (Δ) = K _c ^(S) (1)[1 + a(1 ? Δ)], where a = (d ? 1)/d is independent of S (d is the space dimension). Both free energy and internal energy are determined at the critical points. An extremum of the critical internal energy is found at Δ* ∈ (0, 1). The parameter Δ* can be used as a criterion that separates quasi-isotropic and quasi-one-dimensional regimes (Δ* < Δ ≤ 1 and Δ < Δ*, respectively). The finite-size scaling amplitudes A _s and A _e of the inverse spin-spin and energy-energy correlation lengths are estimated. Calculations show that the amplitudes A _s and A _e are independent of S within the accuracy of the adopted approximations. Moreover, their ratio A _e/A _s is independent of the anisotropy parameter Δ. These results support the Ising universality hypothesis.     

Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data

Parameters of the effective-range function K(k ²) having a pole are found from the results that were obtained by calculating the S-wave phase shifts for doublet proton-deuteron scattering and the binding energies of three-nucleon nuclei on the basis of Faddeev equations and within the N/D method and which are known from the literature. The convergence of the expansion of K(k ²) in powers of the momentum is studied. The energy of the proton-deuteron resonance corresponding to the virtual triton state is calculated.     

Characterization of nonlinear optical parameters of KDP,LiNbO3 and BBO crystals

Third-order nonlinear susceptibilities (χ⁽³⁾) and nonlinear refractive indices (n₂) of KDP, BBO and LiNbO₃ crystals are measured at the wavelengths of 1064 nm and 532 nm by Z-scan technique. The measurements were carried out at different pulse energies, focusing conditions, and crystals’ lengths. It was shown that the increase of phase-matching angle leads to the decreasing of χ⁽³⁾ of KDP crystals. The parameters of multi-photon absorption in KDP, BBO and LiNbO₃ crystals are determined. The analysis and comparison of experimental and theoretical values of nonlinear susceptibilities are presented.     

The unitarity defect of the S-matrix and the underlying absorptive potential

A relation is derived which connects the unitarity defect function S⁺S − 1 with the imaginary part of the absorptive potential responsible for the nuclear scattering. The concept of angle-dependent reaction cross section is introduced for the purpose. A similar relation is also obtained for the equivalent quantity S⁺ − S⁻. Several applications to nuclear scattering are made.     

Effective-range function for doublet nd scattering from an analysis of modern data

The parameters of the generalized effective-range function K(k ²) having a pole are found by using the results that were obtained by calculating the S-wave phase shift δ(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k ²) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k ²) is also calculated within a two-body model featuring various potentials.