The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.

The vacuum Regge Trajectory in conventional field theory

The effect on the scattering amplitude of the existence of a pole in the angular momentum plane near J = 1 in the channel with the quantum numbers of the vacuum is calculated. This is then compared with a fourth order calculation of the scattering of neutral vector mesons from a fermion pair field in the limit of large momentum transfer. The presence of the third double spectral function in the perturbation amplitude complicates the identification of pole trajectory parameters, and the limitations of previous methods of treating this are discussed. A gauge invariant scheme for extracting the contribution of the vacuum trajectory is presented which gives agreement with unitarity predictions, but further calculations must be done to determine the position and slope of the trajectory at s = 0. The residual portion of the amplitude is compared with the Gribov singularity.

Determination of electronic energy levels of molecules by 90° low energy electron scattering

A review of the theory of electron scattering indicates that low incident beam energies and large scattering angles are the favorable conditions for the observation of optically forbidden transitions in atoms and molecules.

An apparatus capable of yielding electron impact spectra at 90° with incident electron beam energies between 30 and 50 electron volts is described. The resolution of the instrument is about 1 electron volt.

Impact spectra of thirteen molecules have been obtained. Known forbidden transitions to the helium 2³S, the hydrogen b³Ʃ⁺_u, the nitrogen A³Ʃ⁺_u, B³π_g, a’π_g, and C³π_u, the carbon monoxide a³π, the ethylene ᾶ³B_1u, and the benzene ᾶ³B_1u states from the corresponding ground states have been observed.

In addition, singlet-triplet vertical transitions in acetylene, propyne, propadiene, norbornadiene and quadricyclene, peaking at 5.9, 5.9, 4.5, 3.8, and 4.0 ev (±0.2 ev), respectively, have been observed and assigned for the first time.

I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Anomalous scattering factor determined by semicircle fitting near the K-absorption edge of Ge

It is shown that the locus of the f' + if '' plot in the complex plane, f' being determined from measured f '' by using the dispersion relation, looks like a semicircle very near the absorption edge of Ge. The semicircular locus is derived from a quantum theory of X-ray resonant scattering when there is a sharp isolated peak in f '' just above the K-absorption edge. Using the semicircular behavior, an approach is proposed to determine the anomalous scattering factors in a crystal by fitting known calculated values based on an isolated-atom model to a semicircular focus. The determined anomalous scattering factors f' show excellent agreement with the measured values just below the absorption edge. In addition, the phase determination of a crystal structure factor has been considered by using the semicircular behavior.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Fluid-structure interaction with mean flow: Over-scattering and unstable resonance growth

It is known theoretically [1-3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the 'long time' limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a "wave scattering" [2,4] - as opposed to a "modal superposition" [5] - view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions. Copyright © 2010 by ASME.

Effect of flow-geometry on turbulence-scalar interaction in premixed flames

Turbulent combustion of stoichiometric hydrogen-air mixture is simulated using direct numerical simulation methodology, employing complex chemical kinetics. Two flame configurations, freely propagating and V-flames stabilized behind a hot rod, are simulated. The results are analyzed to study the influence of flame configuration on the turbulence-scalar interaction, which is critical for the scalar gradient generation processes. The result suggests that this interaction process is not influenced by the flame configuration and the flame normal is found to align with the most extensive strain in the region of intense heat release. The combustion in the rod stabilized flame is found to be flamelet like in an average sense and the growth of flame-brush thickness with the downstream distance is represented well by Taylor theory of turbulent diffusion, when the flame-brushes are non-interacting. The thickness is observed to saturate when the flame-brushes interact, which is found to occur in the simulated rod stabilized flame with Taylor micro-scale Reynolds number of 97. © 2011 American Institute of Physics.

Ultrafast collinear scattering and carrier multiplication in graphene.

Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic and nanophotonic materials. The interaction of light with charge carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools emitting phonons. Although the slower relaxation mechanisms have been extensively investigated, the initial stages still pose a challenge. Experimentally, they defy the resolution of most pump-probe setups, due to the extremely fast sub-100 fs carrier dynamics. Theoretically, massless Dirac fermions represent a novel many-body problem, fundamentally different from Schrödinger fermions. Here we combine pump-probe spectroscopy with a microscopic theory to investigate electron-electron interactions during the early stages of relaxation. We identify the mechanisms controlling the ultrafast dynamics, in particular the role of collinear scattering. This gives rise to Auger processes, including charge multiplication, which is key in photovoltage generation and photodetectors.

Effects of electron-electron interactions on the electronic Raman scattering of graphite in high magnetic fields

We report the observation of strongly temperature (T)-dependent spectral lines in electronic Raman-scattering spectra of graphite in a high magnetic field up to 45 T applied along the c axis. The magnetic field quantizes the in-plane motion, while the out-of-plane motion remains free, effectively reducing the system dimension from 3 to 1. Optically created electron-hole pairs interact with, or shake up, the one-dimensional Fermi sea in the lowest Landau subbands. Based on the Tomonaga-Luttinger liquid theory, we show that interaction effects modify the spectral line shape from (ω-Δ)-1/2 to (ω-Δ)2α-1/2 at T = 0. At finite T, we predict a thermal broadening factor that increases linearly with T. Our model reproduces the observed T-dependent line shape, determining the electron-electron interaction parameter α to be ∼0.05 at 40 T. © 2014 American Physical Society.

Dislocation core effect scattering in a quasitriangle potential well

A theory of scattering by charged dislocation lines in a quasitriangle potential well of AlxGa1-xN/GaN heterostructures is developed. The dependence of mobility on carrier sheet density and dislocation density is obtained. The results are compared with those obtained from a perfect two-dimensional electron gas and the reason for discrepancy is given.

Raman scattering study of vibrational modes and hole concentration in GaxMn1-xSb

The Raman scattering study of vibrational modes and hole concentration in a ferromagnetic semiconductor Ga1-xMnxSb grown by Mn ion implantation, deposition and post-annealing has been presented. The experiments are performed both in implanted and unimplanted regions before and after etching the samples. The Raman spectra measured from the unimplanted region show only GaSb-like phonon modes. On the other hand, the spectra measured from the implanted region show additional phonon modes approximately at 115, 152, 269, 437 and 659 cm(-1). The experimental results demonstrate that the extra modes are associated with surface defects, crystal disorder and blackish layer that is formed due to Mn ion implantation, deposition and annealing processes. Furthermore, we have determined the hole concentration as a function of laser probing position by modeling the Raman spectra using coupled mode theory. The contributions of GaSb-like phonon modes and coupled LO-phonon plasmon mode are taken into consideration in the model. The hole-concentration-dependent CLOPM is resolved in the spectra measured from the implanted and nearby implanted regions. The hole concentrations determined by Raman scattering are found to be in good agreement with those measured by the electrochemical capacitance-voltage technique.