Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Molecular bond formation in Na*+N2 energy transfer: Crossed beam study of atomic alignment and orientation

We report the first full analysis of collisionally induced atomic alignment and orientation for a molecular collision process. In an experiment with crossed supersonic beams of N₀ and laser excited Na(3² P _3/2) we have studied the dependence of angular and energy resolved differential quenching cross sections as a function of the linear and circular polarization of the exciting laser light. The anisotropies observed in the linear polarization data range up to 2∶1 when corrected for electron and nuclear spin relaxation. The maximum effect is found at small scattering angles and intermediate energy transfer where the cross section is also largest. The atomic alignment angle most favourable for quenching relates to the scattering angle and can be understood in a model picture in such a way that the (NaN₂)^* molecular system is formed at internuclear distances as low asR=10a ₀. The circular asymmetry is small but with significant structure and is attributed to interaction on different potential surfaces atR>10a ₀. Full analysis of the four measurable parameter is given in terms of the density matrix in a frame withz-axis perpendicular to collision plane which allows a clear understanding of the properties of atomic reflection symmetry and coherence of the scattering process.     

Variational calculations of resonant states in 4He

We present a modified R-matrix method which allows microscopic calculations of nucleon-nucleus scattering at low energies. This method may be applied in conjunction with any of the commonly used methods for the ground states of few-body systems, i.e. the Green function Monte Carlo, Faddeev and variational techniques. We then report results of variational calculations of low-energy tp scattering in the region of 0⁺, 0^? and 2^? resonances in ⁴He. The energies and widths of these resonances are calculated using realistic two- and three-nucleon interactions; but, the Coulomb interaction is neglected. The three-nucleon interaction is found to have a much smaller effect on the energies of the resonances than on the ground-state energy.     

Evolution of parton densities beyond leading order: The non-singlet case

We develop a technique, based explicitly on the factorization properties of mass singularities, which allows one to calculate the evolution of parton densities beyond leading order. We present the results for the evolution of hadronic structure functions as well as for parton fragmentation functions into hadrons. Within our scheme the predictions for a particular process are obtained by convoluting a universal parton density with a “short-distance” cross section specific to the process. As an application, we calculate the QCD predictions for the Q² dependence of deep inelastic lepton-hadron scattering and of one-particle iclusive e⁺ e^? annihilation cross sections. Our results for electroproduction agree with those obtained with the operator product expansion technique. Physical quantities in scattering are related to the corresponding ones in annihilation by analytic continuation, whereas the Gribov-Lipatov relation is strongly violated.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Quasi-1 structure on q-Poincaré algebras

We use braided groups to introduce a theory of 1-structures on general inhomogeneous quantum groups, which we formulate as quasi-1 Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix from appropriate to the previous q-Euclidean and q-Minkowski space-time algebras R₂₁x₁x₂ = x₂x₁R and R₂₁u₁Ru₂ = u₂R₂₁u₁R. We obtain unitarity of the fundamental differential representations. We further show that the Euclidean and Minkowski-Poincaré quantum groups are twisting equivalent by another quantum cocycle.     

Color screening,absorption, and σ tot pp at LHC

We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances R _c ? 0.3 fm allows extending the BFKL technique from deep inelastic to hadron-hadron scattering. With the inclusion of the absorption corrections our results are in agreement with the LHC data on σ _tot ^pp .     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.     

Phase transitions in RbCaF3. II: Neutron scattering

The 196 K phase transition of RbCaF₃ has been identified as a phonon condensation at the R point (cubic [111] zone boundary). Above the transition temperature, a ridge of scattering extending from the [110] zone boundary (M point) to the R point was observed, corresponding to a line of soft phonons from M₃ to R₂₅. Below the transition the scattering at M decreases rapidly with temperature, indicating a lattice stabilization which causes the ridge of scattering to disappear.     

Wooden windows: Sound insulation evaluation by means of artificial neural networks

Windows are the weakest part of a façade in terms of acoustic performance: the weighted sound insulation index (R_w), measured according to ISO 140-3, is the fundamental parameter to evaluate the façade acoustic insulation.The paper aims at developing an artificial neural network (ANN) model to estimate the R_w value of wooden windows based on a limited number of windows parameters; this is a new approach because acoustic phenomena are non-linear and affected by a plurality of factors and, therefore, usually investigated through experimentation.Data set is taken from experimental campaigns carried out at the Laboratory of Acoustics, University of Perugia. A multilayer feed-forward approach was chosen and the model was implemented in MATLAB. On the basis of the results obtained by means of a preliminary training and test campaign of several ANN architectures, five main parameters were selected as network inputs: window typology, frame and shutters thickness, number of gaskets, R_w of glazing; R_w value of the window is the network output. Different ANN configurations were trained and a root mean-square error less than 3% was obtained, comparable to measurement uncertainty.This approach allows to develop a model which, with input parameters varying within appropriate ranges, can easily estimate the acoustic performance of wooden windows without experimental campaign on prototypes, saving both money and time. If the training data set is large enough, the presented approach could be very useful for design and optimization of acoustic performance of new products.     

R-parity violation and unification

The reported anomaly in deep-inelastic scattering at HERA has revived interest in the phenomenology of R-parity violation. From the theoretical point of view, the existence of R-violating interactions poses two considerable problems. The first one concerns the flavour structure of the interactions and the origin of an appropriate suppression of flavour-changing neutral-current processes and lepton-family transitions. The second one concerns the way of embedding R-violating interactions in a grand unified theory (GUT) without introducing unacceptable nucleon decay rates. We show that the second problem can be solved by mechanism which is purely group theoretical and does not rely on details of the flavour theory. We construct explicit GUT models in which our mechanism can be realized.     

Quantum dynamics of strings in black hole space times

We quantize a bosonic string in the D-dimensional Schwarzschild geometry following the method recently proposed by the present authors. This allows us to take into account strong-curvature effects of the black hole. We start from the exact motion of the center of mass of the string, and compute the quantum fluctuations around it to first and second order. This provides the dominant term for physical magnitudes in an expansion in powers of √α' / R_S (√α' = l_pl = Planck length, R_S = Schwarzschild's radius). The mass spectrum and critical dimension are the same as in flat space-time but there is non-trivial elastic and inelastic scattering by the black hole. Ingoing and outgoing modes are introduced in a light-cone-gauge formalism. A linear transformation relating these modes desribes two main effects: (i) polarization changes and (ii) mixing of the particle and antiparticle modes reversing, at the same time, their right or left character.     

Coupled-channel R-matrix method on a Lagrange mesh

The coupled-channel R-matrix method on a Lagrange mesh is a very simple approximation of the R-matrix method with a basis. The mesh points are zeros of shifted Legendre polynomials. Bound-state energies and scattering matrices are easily calculated with small numbers of potential values at mesh points. A test with an exactly solvable two-channel potential provides an excellent accuracy over a broad energy range with only 30 mesh points. The efficiency of the method is illustrated for a single channel on α + α scattering and for two channels on the deuteron ground-state energy and on nucleon-nucleon scattering.     

The XXZ Heisenberg model on random surfaces

We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.     

The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as \({x\to\pm\infty}\). The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.     

π-N scattering in the operator droplet model

π-N scattering is treated within the framework of the operator droplet model. We have incorporated spin dependent effects, and we calculate the differential cross section, polarization and spin rotation parameters, R and A, at infinite energy. Considerable structures in R and A have been found in contrast with the prediction of the present favourite idea of S-channel helicity conservation for high-energy scattering. The original parametrization of the fit of Byers and Yang for π⁻p → π^On is used to calculate energy dependent amplitudes in elastic πN scattering. Without any new parameters, we have obtained a good fit for total cross sections, polarization and a consistent fit for the R- and A-parameters. Further possible developments are indicated.     

A generalization of Wigner's R-matrix method

A generalization of the Wigner's non-relativistic R-matrix theory of scattering by a central potential field is proposed. The idea is to use an R-matrix expansion basis generated by a Sturm-Liouville problem with an eigenparameter included both in a differential equation and in a boundary condition (in the standard theory an R-matrix basis is obtained by solving an eigenvalue problem with fixed boundary conditions). A partial fraction expansion of an R^(η)-matrix introduced is derived and shown to converge faster than a partial fraction expansion of Wigner's R-matrix used in the standard theory.     

Comments on worldsheet description of the Omega background

Nekrasov?s partition function is defined on a flat bundle of R⁴ over S¹ called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes scattering amplitudes of self-dual gravitons and graviphotons in type II superstring compactified on a Calabi-Yau manifold. We propose a generalization of this correspondence when the fibration is not necessarily self-dual.     

Determination of nuclear parameters by inelastic electron scattering at low-momentum transfer

The second-order Born-approximation treatment of Cutler and Schucan was applied to inelastic electron scattering data on ⁶Li, ⁶⁰Ni, and ¹¹⁴Cd acquired at low momentum transfers. The form factors as a function of momentum transfer q in the range of 0.25–0.57 fm^?1 were obtained by angular distribution measurements performed at incident energies of 30 to 60 MeV. The correlation between two parameters deduced from the measurements, the reduced transition probability B(E2↑) and the transition radius R⁽²⁾_tr, is discussed. It is suggested that inelastic electron scattering data at low-q is best used either in conjunction with an accurate value of B(EL↑) (available from the model-independent analysis of “photon” experiments at zero momentum transfer) to allow accurate determination of R⁽²⁾_tr, or in conjunction with high-q inelastic electron scattering data to allow accurate determination of B(EL↑) as well as R⁽²⁾_tr.