J-matrix method of scattering in one dimension: The nonrelativistic theory

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly non-trivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.Comment: 24 pages, 9 figures (3 in color

Sub-wavelength surface IR imaging of soft-condensed matter

Outlined here is a technique for sub-wavelength infrared surface imaging performed using a phase matched optical parametric oscillator laser and an atomic force microscope as the detection mechanism. The technique uses a novel surface excitation illumination approach to perform simultaneously chemical mapping and AFM topography imaging with an image resolution of 200 nm. This method was demonstrated by imaging polystyrene micro-structures

A three dimensional model of the photosynthetic membranes of Ectothiorhodospira halochloris

The three dimensional organization of the complete photosynthetic apparatus of the extremely halophilic, bacteriochlorophyll b containing Ectothiorhodospira halochloris has been elaborated by several techniques of electron microscopy. Essentially all thylakoidal sacs are disc shaped and connected to the cytoplasmic membrane by small membraneous ldquobridgesrdquo. In sum, the lumina of all thylakoids (intrathylakoidal space) form one common periplasmic space. Thin sections confirm a paracrystalline arrangement of the photosynthetic complexes in situ. The ontogenic development of the photosynthetic apparatus is discussed based on a structural model derived from serial thin sections

Exact solutions for the electromagnetic fields of a flying focus

The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwell's equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. The approach combines the complex source-point method, which transforms multipole solutions into beam-like solutions, with the Lorentz invariance of Maxwell's equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus

Differential (2+1) Jet Event Rates and Determination of alpha_s in Deep Inelastic Scattering at HERA

Events with a (2+1) jet topology in deep-inelastic scattering at HERA are studied in the kinematic range 200 < Q^2< 10,000 GeV^2. The rate of (2+1) jet events has been determined with the modified JADE jet algorithm as a function of the jet resolution parameter and is compared with the predictions of Monte Carlo models. In addition, the event rate is corrected for both hadronization and detector effects and is compared with next-to-leading order QCD calculations. A value of the strong coupling constant of alpha_s(M_Z^2)= 0.118+- 0.002 (stat.)^(+0.007)_(-0.008) (syst.)^(+0.007)_(-0.006) (theory) is extracted. The systematic error includes uncertainties in the calorimeter energy calibration, in the description of the data by current Monte Carlo models, and in the knowledge of the parton densities. The theoretical error is dominated by the renormalization scale ambiguity.Comment: 25 pages, 6 figures, 3 tables, submitted to Eur. Phys.

Multi-Jet Event Rates in Deep Inelastic Scattering and Determination of the Strong Coupling Constant

Jet event rates in deep inelastic ep scattering at HERA are investigated applying the modified JADE jet algorithm. The analysis uses data taken with the H1 detector in 1994 and 1995. The data are corrected for detector and hadronization effects and then compared with perturbative QCD predictions using next-to-leading order calculations. The strong coupling constant alpha_S(M_Z^2) is determined evaluating the jet event rates. Values of alpha_S(Q^2) are extracted in four different bins of the negative squared momentum transfer~\qq in the range from 40 GeV2 to 4000 GeV2. A combined fit of the renormalization group equation to these several alpha_S(Q^2) values results in alpha_S(M_Z^2) = 0.117+-0.003(stat)+0.009-0.013(syst)+0.006(jet algorithm).Comment: 17 pages, 4 figures, 3 tables, this version to appear in Eur. Phys. J.; it replaces first posted hep-ex/9807019 which had incorrect figure 4

Multiplicity Structure of the Hadronic Final State in Diffractive Deep-Inelastic Scattering at HERA

The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep -> eXY, where Y is a hadronic system with mass M_Y< 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t|<1 GeV^2, is studied as a function of the invariant mass M_X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-of-mass system of X. The data are compared to results in e+e- annihilation, fixed-target lepton-nucleon collisions, hadro-produced diffractive final states and to non-diffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q^2. A model with soft colour interactions is also successful.Comment: 22 pages, 4 figures, submitted to Eur. Phys. J., error in first submission - omitted bibliograph

Measurements of Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Measurements of transverse energy flow are presented for neutral current deep-inelastic scattering events produced in positron-proton collisions at HERA. The kinematic range covers squared momentum transfers Q^2 from 3.2 to 2,200 GeV^2, the Bjorken scaling variable x from 8.10^{-5} to 0.11 and the hadronic mass W from 66 to 233 GeV. The transverse energy flow is measured in the hadronic centre of mass frame and is studied as a function of Q^2, x, W and pseudorapidity. A comparison is made with QCD based models. The behaviour of the mean transverse energy in the central pseudorapidity region and an interval corresponding to the photon fragmentation region are analysed as a function of Q^2 and W.Comment: 26 pages, 8 figures, submitted to Eur. Phys.