Theory of reactive scattering. 6: Volterra equation formalism for coupled channel amplitude densities and modified wavefunctions
Volterra equation for coupled channel amplitude densities and modified wave functions
Kouri, D. J.↗
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New techniques for diffusing-wave spectroscopy
We present two new types of measurements that can be made with diffusing-wave spectroscopy (DWS), a form of dynamic light scattering that applies in limit of strong multiple scattering. The first application is to measure the frequency-dependent linear viscoelastic moduli of complex fluids using light scattering. This is accomplished by measuring the mean square displacement of probe particles using DWS. Their response to thermal fluctuations is determined by the fluctuation-dissipation relation, and is controlled by the response of the surrounding complex fluid. This response can be described in terms of a memory function, which is directly related to the complex elastic modulus of the system. Thus by measuring the mean square displacement, we are able to determine the frequency dependent modulus. The second application is the measurement of shape fluctuations of scattering particles. This is achieved by generalizing the theory for DWS to incorporate the effects if amplitude fluctuations in the scattering intensity of the particles. We apply this new method to study the thermally induced fluctuations in the shape of spherical emulsion droplets whose geometry is controlled by surface tension.
Mason, T. G.↗
A multiphoton treatment of near resonant light scattering in intense fields
The scattering by a two-state atom of monochromatic light of arbitrary intensity and detuning, is treated by solving Schroedinger's equation directly for the state of the scattered field. The calculation is performed in a basis of dressed atom states, which include to all orders the coupling of the incident field to the atom. Amplitudes describing sequences of scattering events are found by a nonperturbative method. A scattered intensity spectrum, directly related to the rate of change of energy in any given scattered field mode, is constructed in terms of bilinear products of the amplitudes representing all possible sequences of photon emission, and in the steady state limit the spectrum is found to be identical to the widely quoted results of Mollow. A discussion is devoted to understanding in physical terms the various quantities appearing in the expression for the intensity spectrum.
Ballagh, R. J.↗
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Sun, Yan↗
Bootstrap Principle for the Spectrum and Scattering of Strings
We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude—including the mass spectrum—is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.
Field & string theory models & techniques↗
Optimization of fringe-type laser anemometers for turbine engine component testing
The fringe type laser anemometer is analyzed using the Cramer-Rao bound for the variance of the estimate of the Doppler frequency as a figure of merit. Mie scattering theory is used to calculate the Doppler signal wherein both the amplitude and phase of the scattered light are taken into account. The noise from wall scatter is calculated using the wall bidirectional reflectivity and the irradiance of the incident beams. A procedure is described to determine the optimum aperture mask for the probe volume located a given distance from a wall. The expected performance of counter type processors is also discussed in relation to the Cramer-Rao bound. Numerical examples are presented for a coaxial backscatter anemometer.
Seasholtz, R. G.↗
Optimization of fringe-type laser anemometers for turbine engine component testing
The fringe type laser anemometer is analyzed using the Cramer-Rao bound for the variance of the estimate of the Doppler frequency as a figure of merit. Mie scattering theory is used to calculate the Doppler signal wherein both the amplitude and phase of the scattered light are taken into account. The noise from wall scatter is calculated using the wall bidirectional reflectivity and the irradiance of the incident beams. A procedure is described to determine the optimum aperture mask for the probe volume located a given distance from a wall. The expected performance of counter type processors is also discussed in relation to the Cramer-Rao bound. Numerical examples are presented for a coaxial backscatter anemometer. Previously announced in STAR as N84-25019
Seasholtz, R. G.↗
Spectral characteristics of the return
Doppler spectra of VHF radar returns typically indicate a Gaussian back-ground shape with superimposed spikes. An average of 10 Doppler spectra are shown which are calculated from a time series of seven min of complex data. A proper Gaussian fit to the background distribution is possible by neglecting the strong amplitude spikes. If this background distribution is due to beam width broadening, either diffuse reflection or rather isotropic scattering is required. If beam width broadening is neglected, the width of the distribution is given by turbulent velocity fluctuations. The reflected component is about 1/3 of the scattered component. It is assumed that the amplitude spikes due to diffuse reflection indicate a Gaussian frequency distribution such as for the amplitudes due to scattering.
Rottger, J.↗
Glauber exchange amplitudes
The extrapolation method of Ochkur, valid for intermediate energies (about 50 eV), is applied to the exchange form of the Glauber amplitudes. In the case of elastic scattering of electrons from hydrogen atoms at 54.4 Ev the 'post' and 'prior' forms of the exchange amplitude are equivalent, whereas for the case of inelastic scattering there is a minute discrepancy between the two forms of the amplitude. The results are compared with the close-coupling calculation. The investigation is expected to be useful for optically forbidden exchange-allowed transitions due to electron impact at intermediate energies.
Madan, R. N.↗
Generation and Radiation of Acoustic Waves from a 2-D Shear Layer
A parallel numerical simulation of the radiation of sound from an acoustic source inside a 2-D jet is presented in this paper. This basic benchmark problem is used as a test case for scattering problems that are presently being solved by using the Impedance Mismatch Method (IMM). In this technique, a solid body in the domain is represented by setting the acoustic impedance of each medium, encountered by a wave, to a different value. This impedance discrepancy results in reflected and scattered waves with appropriate amplitudes. The great advantage of the use of this method is that no modifications to a simple Cartesian grid need to be made for complicated geometry bodies. Thus, high order finite difference schemes may be applied simply to all parts of the domain. In the IMM, the total perturbation field is split into incident and scattered fields. The incident pressure is assumed to be known and the equivalent sources for the scattered field are associated with the presence of the scattering body (through the impedance mismatch) and the propagation of the incident field through a non-uniform flow. An earlier version of the technique could only handle uniform flow in the vicinity of the source and at the outflow boundary. Scattering problems in non-uniform mean flow are of great practical importance (for example, scattering from a high lift device in a non-uniform mean flow or the effects of a fuselage boundary layer). The solution to this benchmark problem, which has an acoustic wave propagating through a non-uniform mean flow, serves as a test case for the extensions of the IMM technique.
Agarwal, Anurag↗
Amplitude Scintillation due to Atmospheric Turbulence for the Deep Space Network Ka-Band Downlink
Fast amplitude variations due to atmospheric scintillation are the main concerns for the Deep Space Network (DSN) Ka-band downlink under clear weather conditions. A theoretical study of the amplitude scintillation variances for a finite aperture antenna is presented. Amplitude variances for weak scattering scenarios are examined using turbulence theory to describe atmospheric irregularities. We first apply the Kolmogorov turbulent spectrum to a point receiver for three different turbulent profile models, especially for an exponential model varying with altitude. These analytic solutions then are extended to a receiver with a finite aperture antenna for the three profile models. Smoothing effects of antenna aperture are expressed by gain factors. A group of scaling factor relations is derived to show the dependences of amplitude variances on signal wavelength, antenna size, and elevation angle. Finally, we use these analytic solutions to estimate the scintillation intensity for a DSN Goldstone 34-m receiving station. We find that the (rms) amplitude fluctuation is 0.13 dB at 20-deg elevation angle for an exponential model, while the fluctuation is 0.05 dB at 90 deg. These results will aid us in telecommunication system design and signal-fading prediction. They also provide a theoretical basis for further comparison with other measurements at Ka-band.
Ho, C.↗
On time-dependent backgrounds in 1 + 1 dimensional string theory
In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1 + 1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The equatorial electrojet satellite and surface comparison
The OGO 4 and 6 (POGO) magnetic field results for the equatorial electrojet indicate that while the present models are approximately correct, the possibility of a westward component must be incorporated. The scatter diagrams of POGO amplitudes and surface data show a correlation. The ratios between the amplitudes estimated from surface data and those at 400 km altitude are as follows: India 5 to 8, East Africa (Addis Ababa) 4, Central Africa 3, West Africa (Nigeria) 3, South America (Huancayo) 5, and Philippines 5. The variation in the ratio is due to the conductivity structure of the earth in various zones.
Cain, J. C.↗
Differential cross section for positronium formation in positron-atomic-hydrogen collisions
The differential cross section for positronium formation in its ground state due to collision of a positron and a hydrogen atom is obtained on the basis of the combination of the L = 0 and 1 (L is the angular momentum quantum number) partial wave amplitudes with the L not less than 2 Born amplitudes. Minima at the scattering angles of 57 and 51 degrees were found for positron energies of 0.64 and 0.75 Ry. Total cross sections for positronium formation at low and intermediate impact energies are presented.
Drachman, R. J.↗
Aerocapture Guidance Performance for the Neptune Orbiter
A performance evaluation of the Hybrid Predictor corrector Aerocapture Scheme (HYPAS) guidance algorithm for aerocapture at Neptune is presented in this paper for a Mission to Neptune and the Neptune moon Triton'. This mission has several challenges not experienced in previous aerocapture guidance assessments. These challengers are a very high Neptune arrival speed, atmospheric exit into a high energy orbit about Neptune, and a very high ballistic coefficient that results in a low altitude acceleration capability when combined with the aeroshell LD. The evaluation includes a definition of the entry corridor, a comparison to the theoretical optimum performance, and guidance responses to variations in atmospheric density, aerodynamic coefficients and flight path angle for various vehicle configurations (ballistic numbers). The benefits of utilizing angle-of-attack modulation in addition to bank angle modulation to improve flight performance is also discussed. The results show that despite large sensitivities in apoapsis targeting, the algorithm performs within the allocated AV budget for the Neptune mission bank angle only modulation. The addition of angle-of-attack modulation with as little as 5 degrees of amplitude significantly improves the scatter in final orbit apoapsis. Although the angle-of-attack modulation complicates the vehicle design, the performance enhancement reduces aerocapture risk and reduces the propellant consumption needed to reach the high energy target orbit for a conventional propulsion system.
Masciarelli, James P.↗
Split-helicity tree amplitudes and flag cluster algebras
Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Steepening of parallel propagating hydromagnetic waves into magnetic pulsations - A simulation study
The steepening mechanism of parallel propagating low-frequency MHD-like waves observed upstream of the earth's quasi-parallel bow shock has been investigated by means of electromagnetic hybrid simulations. It is shown that an ion beam through the resonant electromagnetic ion/ion instability excites large-amplitude waves, which consequently pitch angle scatter, decelerate, and eventually magnetically trap beam ions in regions where the wave amplitudes are largest. As a result, the beam ions become bunched in both space and gyrophase. As these higher-density, nongyrotropic beam segments are formed, the hydromagnetic waves rapidly steepen, resulting in magnetic pulsations, with properties generally in agreement with observations. This steepening process operates on the scale of the linear growth time of the resonant ion/ion instability. Many of the pulsations generated by this mechanism are left-hand polarized in the spacecraft frame.
Akimoto, K.↗
An optical model for composite nuclear scattering
The optical model of composite particle scattering is considered and compared to the accuracies of other models. A nonrelativistic Schroedinger equation with two-body potentials is used for the scattering of a single particle by an energy-dependent local potential. The potential for the elastic channel is composed of matrix elements of a single scattering operator taken between the ground states of the projectile and the target; the coherent amplitude is considered as dominating the scattering in the forward direction. A multiple scattering series is analytically explored and formally summed by the solution of an equivalent Schroedinger equation. Cross sections of nuclear scattering are then determined for He-4 and C-12 nuclei at 3.6 GeV/nucleus and O-16 projectiles at 2.1 GeV/nucleus, and the optical model approximations are found to be consistently lower and more accurate than approximations made by use of Glauber's theory.
Wilson, J. W.↗