s-channel unitarity and inclusive distributions in cut reggeon field theory

Unitarity constraints on generalized eikonal diagrams with pomeron interactions are shown to hold in cut reggeon field theory. A non-perturbative proof of the AGK cancellation in this class of diagrams is given for the single-particle inclusive distribution. However, the two-particle distribution turns out to be modified by pomeron interactions in a non-trivial way. An approximate calculation shows that these modifications are crucial for consistency with momentum sum rules.     

s-channel discontinuities of the torus insertion in the dual unitarisation scheme

The refined analysis of the s-channel discontinuities of the torus insertion in the topological expansion is performed. Assuming the dependence on reggeon masses of the fixed-pole residue similar to that given by the Veneziano model we obtain almost exact cancellations of the discontinuities which in the one-dimensional approximation were argued to be responsible for the exchange degeneracy breaking between ? and A₂ trajectories. Implications on different f-IP schemes are discussed.     

The s-channel dual absorptive model as a consequence also of t-channel absorption

The dual absorptive model applied to t-channel predicts that Regge residues above threshold are I_n-functions which for t ? 0, for the leading trajectory, are simply J_n(R_o√−t). Thus s-channel absorptive models can be expressed entirely in terms of t-channel quantities. Implications to complex Regge poles is discussed.     

Finite-element analysis of planar dielectric waveguide discontinuities

The finite element method is combined with the mode-matching method and the multi-mode network method to analyze the scattering and radiation characteristics of a class of planar dielectric waveguide discontinuities. Unlike the conventional method to treat the radiation as a source-field problem, in the present approach, the dispersion characteristics of dielectric guided-wave structures are calculated first, and then the radiation problem is transferred to the propagation problem of a series of surface-waves and space waves from the viewpoint of scattering, thus the analysis is tremendously simplified.     

Light propagation in a planar dielectric slab waveguide with step discontinuities

The common matrix formalism for multi-layer systems is generalized to describe the optical field propagation along an arbitrary cascade of step discontinuities in a planar dielectric waveguide. The reflection and transmission properties of the step cascade are modelled by rigorous operator relations in a Hilbert-space calculus. In this way the complete propagation problem is reduced to two basic transformations. TE- and TM-polarized fields are treated simultaneously.     

A duality property of planar Feynman diagrams

It is found that the Fourier-transform of the amplitude of a planar Feynman diagram G can be written as the amplitude of the Feynman diagram G?, where G? is the dual of G in the sense of graph theory of graph theory, the propagators of G? being the Fourier-transformed of the ordinary ones.     

Some t-channel aspects of a geometrical Pomeron

We discuss the geometrical scaling in the case of total cross-sections behaving at high energies like (lns)^η and show that i) the case ?1?η?0 is inconsistent with t-channel unitarity; ii) the structure of the t-channel partial wave amplitudes is $\text{A(t,j)∝}\text{1}\text{(?t)}{}^{\mathrm{1+r}}\text{H(k≡}\text{(j?1)}\text{(?t)}{}^{\mathrm{r}}\text{)}$ with r=η^? and iii) the t-dependence of the j-plane singularities is given for η > 0 by $\text{α(t)=1+a(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>\eta </mtext>}}$ with a being const.     

Vertex counting: Statistical distribution of vertices in large sets of tree diagrams

We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and we compute the mean and variance of this distribution for several theories. We show that the distribution's ”fine structure”, arising from topological sum rules, can be obtained. Received: 12 September 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: petros@sci.kun.nl RID="b" ID="b" e-mail: kleiss@sci.kun.nl     

General features of the reggeon calculus with α > 1

We discuss some general properties of the reggeon calculus with input intercept greater than one, in an attempt to formulate a model yielding indefinitely rising cross sections which is consistent with t-channel unitarity. In general the leading behaviour of the amplitude always factorises. If interactions between reggeons are ignored the scattering is equivalent to that from a grey absorbing disk of radius O (ln s). Diagrams involving such interactions are subject to large-scale cancellations. These enable the model to give sensible results for inclusive cross sections. In quantum number exchange reactions, factorisation of the Regge pole residues is weakly broken in the model.     

The structure of t-channel exchanges in KN scattering

Recent phase-shift solutions are used to evaluate KN FESR integrals in order to examine zeros and phases of the t-channel exchange amplitudes in the most model-independent way. The results suggest that the line reversal breaking in KN CEX observed for pL ? 5.5 GeV/c is due to a large EXD breaking component in the A₂ exchange flip amplitude. The ? exchange flip amplitude is well described by a Regge pole amplitude with NWSZ at ?t ≈ 0.5 (GeV/c)². The imaginary parts of ? and ω exchange non-flip amplitudes are both peripheral.     

An s-channel amplitude analysis of the reaction π+p→Δ++π0 using the dual absorptive model

The dual absorptive model proposed by Harari and extended by Loos and Matthews is shown to give a reasonable parameterisation of the available data on π⁺p→Δ⁺⁺π⁰ over the momentum range 4 – 13 GeV/c. The differential cross sections are well fitted using only the Δλ = 0 and Δλ = 1 amplitudes. Density matrix elements are compared with the model at 5.5 GeV/c.     

Energy levels of n-channel accumulation layer on InP surface

Electronic structure of the low lying quantized subbands is calculated for the electron accumulation layer on InP (100) system in a metal-insulator-semiconductor (MIS) structure. Hartree self-consistent technique at an arbitrary temperature has been used, neglecting many-body effects. In contrast to Si MIS system, a second subband is found to be populated even at low temperatures and moderate densities. Excitation energy, E₁₀, is found to be about 30–40 meV in the temperature range 0–300 K at an electron density of 10¹² cm^?2.     

Assignments of visible absorption of s-tetrazine vapor

A detailed vibrational analysis of the 5515 Å absorption of s-tetrazine (tetra-azabenzene) vapor is attempted. More than 80% of the total intensity of the system can be accounted for by band assignments to a single allowed electronic transition, ¹B_3u-¹A_g. The only progression-forming vibration in absorption in ν_6a. Three progressions in ν′_6a account for all intense cold bands. Isotopic shifts of bands lead to convincing assignments of the two excited-state vibrations upon which ν_6a progressions are based, namely ν_6b and ν_8a. It is shown that in all probability the antisymmetric mode ν_6b is prominent because of vibrational (Fermi) resonance rather than because of vibronic interactions.     

Oscillator strengths for the 2s2, 2p2, 2s3s(1S)-2s2p(1P) transitions of B(II)

Accurate configuration interaction wavefunctions for the 2s²(¹S), 2p²(¹S), 2s3s(¹S) and 2s2p (¹P) states of B(II) are calculated in a single optimized orbital basis of 7s, 6p and 4d Slater-type orbitals. 95, 84, 57 and 90% of the correlation energies, respectively, are realized by these wavefunctions. Oscillator strengths for the three ¹S-¹P transitions are calculated from these and from less accurate wavefunctions in the same orbital basis. The length values obtained from our most accurate wavefunctions, in order of increasing ¹S energy, are 0.9885, 0.202 and 0.007. The degree of accuracy of these oscillator strengths is estimated by noting the convergence to final values as increasing percentages of correlation energies are included in the wavefunctions together with the increasing agreement between length and velocity formulas. The exact theoretical oscillator strength for the resonant line is projected to be 0.985 with an error almost certainly not greater than ±0.015. The theoretical oscillator strengths for the other lines are considered to be 0.21±0.02 and less than 0.007, respectively.     

Electron energy loss spectra of the silicon 2p, 2s, carbon 1s and valence shells of tetramethylsilane

Inner shell excitation spectra of tetramethylsilane, (CH₃)₄Si, have been measured in the silicon 2s, 2p (L_I,II,III-shell) and carbon is (K-shell) regions using electron energy-loss spectroscopy at an impact energy of 2.5 keV and a scattering angle of ~1°. The high-resolution valence shell spectrum has also been observed at an impact energy of 3 keV and a zero degree scattering angle. The silicon 2p spectra are compared and contrasted with published photoabsorption spectra of SiF₄, SiH₄, and other related Si-containing molecules with varying ligands.     

Oscillator strengths and transition probabilities of the Be(I) isoelectronic sequence for 2p2-2s2p and 2s2p-2s2 transitions

Oscillator strengths and transition probabilities are obtained from an intermediate coupling scheme. The initial basis of the eigenstates is formed inLS-coupling. To obtain the resulting energy matrix,Z^-1 perturbation theory is applied. The values of oscillator strengths and transition probabilities for 1s²2p²?1s²2s2p and 1s²2s2p?1s²2s² transitions are calculated and the comparison is made with some recent results. The nuclear charges (Z) involved varied fromZ=4(Be(I)) toZ=35(Br(XXXII)).     

The calculation of planar one-loop diagrams in string theory using the BRS formalism

The fact is exploited that the operator counting the number of non-transverse modes for the bosonic string in 26 dimensions can be written as the anticommutator of the BRS charge Q with another operator to calculate planar one-loop diagrams. This results in a significant simplification over the earlier calculation of Brink and Olive.     

CPA treatment of the s-d model at high temperatures

The coherent potential approximation (CPA) is applied to spin-disorder scattering in systems described by the s-d model such as moderately doped magnetic semiconductors. The possibility of a split conduction band at zero temperature is shown to persist also at high temperatures. Band-narrowing is described and conclusions are drawn regarding optical ‘red-shifts’, the Born-approximation, and the paramagnetic spin polaron in narrow energy bands.     

Three-dimensional step discontinuities in planar waveguides: Angular-spectrum representation of guided wavefields and generalized matrix-operator formalism

For obliquely incident guided modes the light propagation in slab waveguides with step discontinuities can be described by means of an angular-spectrum representation of the electromagnetic fields together with a generalized matrix-operator formalism. By means of a discretization of the radiation and evanescent modes, the computation of the reflection and transmission coefficients can be reduced to the numerical solution of algebraic equations. The TE-TM coupling, which takes place for oblique incidence, and the different evanescent field effects are discussed in detail.