Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and “active” emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections. Received: 26 February 1998 / Revised: 13 March 1998 / Accepted: 15 March 1998     

Exotic Behavior of Elastic Scattering Differential Cross-Sections of Weakly Bound Nucleus 17F at Small Angles

The differential cross-sections for elastic scattering of ¹⁷F and ¹⁷O on ²⁰⁸Pb have been measured at Radioactive Ion Beam Line at Lanzhou (RIBLL). The variation of the logarithms of differential cross-sections with the square of scattering angles shows clearly that there exists a turning point in the range of small scattering angles (6°—20°) for ¹⁷F having exotic structure, while no turning point was observed in the ¹⁷O elastic scattering. The experimental results have been compared with previous data. Systematical analysis on the available data seems to conclude that there is an exotic behavior of elastic scattering differential cross-sections of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the fact that the turning point of the logarithms of differential cross-sections appears at small angle for weakly bound nuclei could be used as a new probe to investigate the halo and skin phenomenon.     

Interaction potentials and rotational scattering for H2 and MuH with He

Elastic and inelastic differential cross-sections for the rotational scattering of p-H₂ and MuH by He at a single collision energy are calculated with potential surfaces obtained by varying the parameters in a model potential. The importance of the attractive and repulsive terms in the potential, and of the available kinetic energy in the different channels is demonstrated, and it is shown that the whole potential surface determines the scattering cross-sections. Inelastic and elastic scattering are compared, and the differences between the rotational scattering of homonuclear and heteronuclear homopolar molecules are ascribed to the molecular constants rather than to the numbers of open channels.     

Differential and integral cross-sections of e-O<Subscript>2</Subscript>, O<Subscript>3</Subscript>, NO,CO scattering at energies 100–1000 eV

A modified additivity rule is formulated to calculate the differential cross-sections for elastic scattering of electrons from molecules. It improves the results at small angles and at relatively lower incident energies (<1000 eV). Integral cross-sections calculated presently are combined with the known total ionization cross-sections to obtain total (complete) cross-sections. An extension of the present approximation to larger molecules is also suggested.     

Surface plasmon polariton scattering by small ellipsoid particles

Scattering of surface plasmon polaritons (SPP’s) by small ellipsoid particles placed near a dielectric–metal interface is theoretically considered. Using the Green’s function formalism and the dipole approximation, we consider the differential and total scattering cross-sections associated with the SPP-to-SPP scattering as well as with the SPP scattering into waves propagating away from the interface, analyzing the influence of system parameters. As an example, scattering cross-sections of differently shaped gold spheroid particles placed near an air–gold interface are evaluated at the light wavelength of 800 nm. It is shown that the differential and total cross-sections depend strongly upon the particle-to-surface distance, the ratio between the major and minor axes and their orientation with respect to both the interface and the direction of SPP incidence. Implications of the obtained results to the design of SPP micro-optical components are also discussed.     

Approximate and exact photon-maxwellian electron cross-sections and a Monte Carlo sampling scheme

Fast and accurate approximate methods for computing temperature-corrected photon-Maxwellian electron cross-sections, using distribution averaged electron energies and scattering angles, are presented. Use is made of the covariant (frame independent) picture of scattering for relativistic electrons. The schemes are motivated and detailed, predictions are obtained and compared with exact values, and appropriate limiting forms that retain the Thomson and Klein-Nishina cross-section structure are also recovered. A two-parameter fit to the total cross-sections in a Klein-Nishina picture is detailed using an invariant scattering kernel. This particular fit is useful in extending existing sampling schemes which employ the static probability density. Extensions of Kahn's technique (for sampling the Klein-Nishina density) arepresented for a temperature-corrected set of probability densities obtained from the fitted cross-sections. The methods are amenable to further pointwise (Monte Carlo) or multigroup (S_n) cross-section processing. An exact numerical scheme employing adaptive quadrature techniques, as implemented in the production code module MAXWELL is also described.     

e−-H(2S) elastic scattering in the two-potential eikonal approximation

The differential scattering cross-sections fore ^??H (2S) elastic scattering are calculated at intermediate energies by using the two-potential eikonal approximation. The results are compared with the recent theoretical data and the conventional Glauber cross-sections.     

Deceleration of muonic hydrogen atoms in solid hydrogens

Results of recent calculations of cross-sections for muonic hydrogen atom scattering in solid hydrogen isotope targets are presented. The coherent parts of these cross-sections, namely, the elastic Bragg scattering and phonon coherent scattering, are calculated accurately for the first time. A fine structure of Bragg peaks is obtained in the case of Bravais fcc structure of hydrogen targets frozen rapidly at 3 K. The one-phonon coherent cross-section is estimated using the Debye approximation. The calculated differential cross-sections are used for Monte Carlo simulations of muonic atom diffusion and slowing down in solid hydrogens. Also is calculated the energy-dependent rate of resonant ddμ molecule formation in 3 K solid deuterium quantum crystal, using the Debye model and Van Hove's formalism of the response function. This rate is very different from that obtained for the 3 K gas model. The influence of dμ atom slowing down on the average ddμ formation rate is considered. It is shown that very slow dμ deceleration below 10 meV is important for explanation of experimental results. This revised version was published online in August 2006 with corrections to the Cover Date.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Direct Monte Carlo simulation of scattering processes of kV electrons in aluminum; comparison of theoretical N(E) spectra with experiment

A Monte Carlo simulation of the scattering processes of kV electrons penetrating into aluminum was performed. The simulation is based on the use of different types of differential cross-sections for individual elastic and inelastic scattering: (i) Elastic scattering; the differential cross-sections derived by partial wave expansion method. (ii) Inelastic scattering; Gryzinski's excitation function for inner-shell electron excitation, Streitwolfs excitation function for conduction electron excitation, and Quinn's mean free path for plasmon excitation. For verification the energy loss spectra obtained from the Monte Carlo calculations were then compared with experiment done with commercial type Auger microprobes, JAMP-3, for angle of incidence 45° and JAMP-10 for normal incidence at primary electron energies of 1.5 and 3.0 keV, respectively. The results show satisfactory agreement between theory and experiment.     

Raman scattering and optical susceptibilities of Nd-doped glasses

The absolute Raman scattering cross-sections of three Neodymium-doped glasses have been measured. These cross-sections have been used to determine the nonlinear optical susceptibility tensor of the three glasses. We have estimated the relative contributions of the “electronic” and “nuclear” nonlinearities to self-focusing index for linearly polarized light in these glasses. We have also performed numerical computations of the Hibert transform of our Raman scattering cross-sections, which are useful in the prediction of any other nonlinear effects. Work supported in part by the National Science Foundation, and in part by the U.S. Atomic Energy Commission under the University of California Lawrence Livermore Laboratory subcontract No. 2713005.     

Determination of the Scattering Amplitudes of Schrödinger Operators from the Cross-Sections,a New Approach

In this Letter we show how the scattering amplitudes of nonrelativistic one-particle Schrödinger operators with a scalar (not necessarily rotation invariant) potential may be obtained from the scattering cross-sections for the system where a scalar potential is added and whose scattering amplitudes are known explicitly.     

Total (complete) and ionization cross-sections of argon and krypton by positron impact from 15 to 2000 eV – Theoretical investigations

Considering interactions and scattering of positrons with argon (Ar) and krypton (Kr) atoms, we have calculated total cross-sections (Q _T?=?Q _el?+?Q _inel ) using complex spherical potentials for these systems. In positron?Catom scattering it is difficult to bifurcate the ionization and cumulative excitation contained in the total inelastic cross-section. An approximate method called CSP-ic (complex scattering potential-ionization contribution) similar to electron?Catom scattering has been applied to bifurcate ionization and cumulative excitation cross-sections at energies from the threshold to 2000?eV. Adequate comparisons of the present results are made, with available data.     

Local effective polarization and absorption potentials from cross-sections for e-atom scattering

A possibility of obtaining local, effective, energy-dependent polarization and absorption potentials from experimental cross-sections for electron scattering is investigated. Potentials have been fitted with the help of the genetic algorithm on large sets of experimental data for e-He, e-Ne and e-Ar elastic scattering at impact energies 20-3000 eV. The obtained potentials reproduce the cross-sections within experimental errors.     

Inelastic scattering of positrons by lithium-isoelectronic ions

Summary The inelastic scattering of positrons by 11 lithium-isoelectronic ions, (with nuclear chargesZ=4,5,… 14) is investigated for the first time within the framework of the coupled-static and frozen-core approximations. It is assumed that the elastic and positronium channels, in each process, are open and all excitation channels of the target are closed. The calculations of the total cross-sections are carried out by employing eight partial waves, (corresponding to 0≤l≤7, wherel is the total angular momentum of the scattering problem considered). Also, the effect of switching on the polarization potentials of the positroniums on the rearrangement cross-sections is investigated in details. Particular attention is devoted to the relation between the positronium formation cross-sections and the increase in the nuclear charge of the targets. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Alpha particle scattering in the rigid projectile approximation

We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.     

Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range

We present a joint theoretical-experimental study on electron scattering by C₂H₂ in the intermediate energy range. We report calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and absorption cross-sections at impact energies ranging from 10 to 500 eV. Also, experimental absolute elastic cross-sections are reported in the (50-500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. The iterative Schwinger variational method, combined with the distorted-wave approximation, is used to solve the scattering equations. Experimentally, the angular distributions of the scattered electrons are converted to absolute cross-sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.Received: 26 August 2004, Published online: 5 October 2004PACS: 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Elastic and inelastic scattering of positrons from hydrogenlike ions

Summary The total elastic cross-sections of the collisions of positrons with various hydrogenlike targets (with nuclear chargeZ=1, 2, 3, 4, 5 and 11) are determined at 13 values of the incident energy lying below 6.8 e V(the positronium formation threshold of e⁺-H scattering). The inelastic scattering of positrons by the same targets is investigated for the first time at energies above the positronium formation thresholds. Both scattering processes are treated using a coupled-static formalism and an iterative Green's function partial wave expansion technique. The resulting cross-sections demonstrate the stability of this technique and emphasize the importance of exploring the aspects of positron-ion collisions more fundamentally on both theoretical and experimental levels.