Showing papers on "Scattering published in 1969"
TL;DR: In this article, an integrodifferential equation for the sputtering yield is developed from the general Boltzmann transport equation, and solutions of the integral equation are given that are asymptotically exact in the limit of high ion energy as compared to atomic binding energies.
Abstract: Sputtering of a target by energetic ions or recoil atoms is assumed to result from cascades of atomic collisions. The sputtering yield is calculated under the assumption of random slowing down in an infinite medium. An integrodifferential equation for the yield is developed from the general Boltzmann transport equation. Input quantities are the cross sections for ion-target and target-target collisions, and atomic binding energies. Solutions of the integral equation are given that are asymptotically exact in the limit of high ion energy as compared to atomic binding energies. Two main stages of the collision cascade have to be distinguished: first, the slowing down of the primary ion and all recoiling atoms that have comparable energies---these particles determine the spatial extent of the cascade; second, the creation and slowing down of low-energy recoils that constitute the major part of all atoms set in motion. The separation between the two stages is essentially complete in the limit of high ion energy, as far as the calculation of the sputtering yield is concerned. High-energy collisions are characterized by Thomas-Fermi-type cross sections, while a Born-Mayer-type cross section is applied in the low-energy region. Electronic stopping is included when necessary. The separation of the cascade into two distinct stages has the consequence that two characteristic depths are important for the qualitative understanding of the sputtering process. First, the scattering events that eventually lead to sputtering take place within a certain layer near the surface, the thickness of which depends on ion mass and energy and on ion-target geometry. In the elastic collision region, this thickness is a sizable fraction of the ion range. Second, the majority of sputtered particles originate from a very thin surface layer (\ensuremath{\sim}5 \AA{}), because small energies dominate. The general sputtering-yield formula is applied to specific situations that are of interest for comparison with experiment. These include backsputtering of thick targets by ion beams at perpendicular and oblique incidence and ion energies above \ensuremath{\sim}100 eV, transmission sputtering of thin foils, sputtering by recoil atoms from $\ensuremath{\alpha}$-active atoms distributed homogeneously or inhomogeneously in a thick target, sputtering of fissionable specimens by fission fragments, and sputtering of specimens that are irradiated in the core of a reactor or bombarded with a neutron beam. There is good agreement with experimental results on polycrystalline targets within the estimated accuracy of the data and the input parameters entering the theory. There is no need for adjustable parameters in the usual sense, but specific experimental setups are discussed that allow independent checks or accurate determination of some input quantities.
2,552 citations
TL;DR: In this article, a solution to an inverse scattering problem that arises in the application of holography to the determination of the three-dimensional structure of weakly scattering semi-transparent objects is presented.
1,285 citations
TL;DR: In this article, the singularities of x-ray absorption or emission in metals are studied by a new "one-body" method, which describes the scattering of conduction electrons by the transient potential due to the deep hole.
Abstract: The singularities of x-ray absorption or emission in metals are studied by a new "one-body" method, which describes the scattering of conduction electrons by the transient potential due to the deep hole. Using the linked-cluster theorem, the net transition rate in the time representation is expressed as the product of two factors: a one-electron transient Green's function $L$, and the deep-level Green's function $\mathcal{G}$. These factors obey simple Dyson equations, which can be solved asymptotically by using Muskhelishvili's method. The x-ray transition rate is found to behave as $\frac{1}{{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}}$, where $\ensuremath{\epsilon}$ is the frequency measured from the threshold, and $\ensuremath{\alpha}$ an exponent involving the various phase shifts ${\ensuremath{\delta}}_{l}$ which describe scattering by the deep hole. $\ensuremath{\alpha}$ may be g0 (infinite threshold) or 0 (zero threshold). The experimental implications of these results and their relation to the Friedel sum rule are briefly discussed.
903 citations
TL;DR: In this article, a model for highly inelastic electron-nucleon scattering at high energies is studied and compared with existing data, where the proton is composed of pointlike constituents (partons) from which the electron scatters incoherently.
Abstract: A model for highly inelastic electron-nucleon scattering at high energies is studied and compared with existing data. This model envisages the proton to be composed of pointlike constituents (“partons”) from which the electron scatters incoherently. We propose that the model be tested by observing ϒ rays scattered inelastically in a similar way from the nucleon. The magnitude of this inelastic Compton-scattering cross section can be predicted from existing electron-scattering data, indicating that the experiment is feasible, but difficult, at presently available energies.
746 citations
TL;DR: In this article, a new method was developed for integrating coupled differential equations arising in bound state and scattering problems in quantum mechanics, and wavefunctions were easily constructed in piecewise analytic form, to any prescribed accuracy.
Abstract: A new method is developed for integrating coupled differential equations arising in bound state and scattering problems in quantum mechanics. The wavefunctions are easily constructed in piecewise analytic form, to any prescribed accuracy.
531 citations
TL;DR: In this paper, the reliability of many formulas used in the radiative corrections to elastic and inelastic electron scatterings when only the scattered electrons are detected was investigated and a practical and reliable recipe for unfolding the entire electron spectra including effects due to virtual photons, internal and external bremsstrahlungs, was given.
Abstract: We have investigated and improved the reliability of many formulas used in the radiative corrections to elastic and inelastic electron scatterings when only the scattered electrons are detected. The radiative corrections to muon scattering are also investigated. A practical and reliable recipe for unfolding the entire inelastic spectra, including effects due to virtual photons, internal and external bremsstrahlungs, is given. Examples of actually unfolding the inelastic electron spectra are given using the experimental data obtained by the electron-scattering group at the Stanford Linear Accelerator Center.
521 citations
TL;DR: In this paper, a triple-axis neutron spectrometer with polarization sensitive crystals on both the first and third axes is described, and the calculation of polarized-neutron scattering cross sections is presented in a form particularly suited to apply to this instrument.
Abstract: A triple-axis neutron spectrometer with polarization-sensitive crystals on both the first and third axes is described. The calculation of polarized-neutron scattering cross sections is presented in a form particularly suited to apply to this instrument. Experimental results on nuclear incoherent scattering, paramagnetic scattering, Bragg scattering, and spin-wave scattering are presented to illustrate the possible applications of neutron-polarization analysis.
494 citations
TL;DR: In this article, the inelastic scattering of electrons from hydrogen was measured for incident energies from 7 to 17 GeV at scattering angles of 6\ifmmode^\circ\else\textdegree\fi{} to 10\ifmode^''circ\circ/else \textdegree'' fi{} covering a range of squared four-momentum transfers up to 7.4
Abstract: Cross sections for inelastic scattering of electrons from hydrogen were measured for incident energies from 7 to 17 GeV at scattering angles of 6\ifmmode^\circ\else\textdegree\fi{} to 10\ifmmode^\circ\else\textdegree\fi{} covering a range of squared four-momentum transfers up to 7.4 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. For low center-of-mass energies of the final hadronic system the cross section shows prominent resonances at low momentum transfer and diminishes markedly at higher momentum transfer. For high excitations the cross section shows only a weak momentum-transfer dependence.
428 citations
TL;DR: In this article, a model for estimating effects due to electron scattering from grain boundaries, occurring simultaneously with background scattering, was developed for polycrystalline metal films in which a very fine-grained structure is often found.
Abstract: A model is developed for estimating effects due to electron scattering from grain boundaries, occurring simultaneously with background scattering. Since grain‐boundary effects are negligible in bulk materials, the model is particularly relevant to polycrystalline metal films in which a very fine‐grained structure is often found. It is shown by solution of the appropriate Boltzmann equation, that the total resistivity can be strongly dominated by grain‐boundary scattering. If grain size increases with film thickness, a marked dependence of resistivity on thickness exists, even when scattering from external surfaces is negligible or is completely specular.
393 citations
TL;DR: In this article, a crossed-beam detector for thermal energy neutral-neutral reactions is described, which consists of a high efficiency electron bombardment ionizer, quadrupole mass filter, scintillation ion counter, and gated scalers synchronized with the beam modulation.
Abstract: A crossed beams apparatus for study of thermal energy neutral-neutral reactions is described. The detector comprises a high efficiency (∼0.1%) electron bombardment ionizer, quadrupole mass filter, scintillation ion counter, and gated scalers synchronized with the beam modulation. The ionizer is nested within three chambers, each pumped by a separate ion pump and the innermost attached to a liquid nitrogen trap. The design is such that molecules which pass through the ionizer without being ionized fly on into another differentially pumped region before hitting a surface. The entire detector unit, including pumps and trap, is mounted on a rotatable platform (angular range ∼140°) which forms the lid of the scattering chamber. The beam sources also comprise modular units, mounted in differentially pumped side chambers which insert into ports in the scattering chamber. Angular distributions of reaction products have been measured for several reactions of Cl, Br, or D atoms with halogen molecules or hydrogen halides. Product velocity distributions have also been measured by time of flight for some of these reactions. In most cases, the partial pressure of interfering background species in the ionization region was ⪝ 10−15 Torr, and satisfactory data could be obtained with reactive scattering signals of a few counts per second.
TL;DR: In this paper, the theory of light scattering from a collection of free electrons is reviewed, and it is shown that the frequency spectrum observed at a detector is precisely that of the density fluctuations of a particular scale length in the scattering medium, the scale length being determined by the wavelength of the incident light and the geometry of the experimental arrangement.
Abstract: The theory of light scattering from a collection of free electrons is reviewed, and it is shown that the frequency spectrum observed at a detector is precisely that of the density fluctuations of a particular scale length in the scattering medium, the scale length being determined by the wavelength of the incident light and the geometry of the experimental arrangement. The electron density fluctuation in a plasma is calculated, and it is shown that the plasma Debye shielding distance λD is a critical length in the theory, the electrons behaving independently on a scale shorter than λD and collectively on a scale longer than λD. The collective behaviour is characterized by the presence of waves that can give rise to well-defined resonances in the scattered-light spectrum. The effects of differing ion and electron temperatures, current flowing in the plasma, magnetic field, and Coulomb collisions are considered briefly. Technical considerations in planning experiments to test the theory and to apply it to the diagnosis of real laboratory plasmas are discussed, with attention being given to signal-to-noise ratio, stray light, and the dispersing instrument to be used at the detector. Some representative experiments that have been carried out are reviewed.
TL;DR: In this paper, the complete Waller-Hartree theory with all exchange terms has been used and incoherent scattering factors for all aspherical free atoms have been computed from numerical SCF Hartree-Fock wavefunctions.
Abstract: Incoherent scattering factors for all aspherical free atoms have been computed from numerical SCF Hartree–Fock wavefunctions. The complete Waller–Hartree theory with all exchange terms has been used.
TL;DR: In this article, a cloudy atmosphere model for radiative transfer in a condensed powder is developed in which the scatter is considered to be both nonconservative and linearly anisotropic.
Abstract: Infrared emissivities of powered silicates are shown by experiment to contain new maximums and minimums that are representative of both composition and particle size. A cloudy atmosphere model for radiative transfer in a condensed powder is developed in which the scatter is considered to be both nonconservative and linearly anisotropic. The scattering parameters are computed as functions of frequency from the Mie diffraction theory. Detailed calculations of the spectral emissivity of quartz are presented. The model is shown to account for many features observed experimentally in the spectrums of quartz powders and sand. Changes in the spectrum with particle size can be understood in terms of changes in the albedo for single scattering and the degree of forward scatter with particle size. The principal Christiansen frequencies of silicate powder films obtained from transmission measurements are shown to be diagnostic of mineralogy and to be frequencies of maximum emissivity for powders. The relationship is discussed in detail for quartz.
TL;DR: In this paper, the problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered, and the mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body.
Abstract: The problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered The mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body A solution is effected by the method of moments, and the results are expressed in terms of generalized network parameters The expansion functions chosen for the solution are harmonic in o (azimuth angle) and subsectional in t (contour length variable) Because of rotational symmetry, the solution becomes a Fourier series in o, each term of which is uncoupled to every other term Illustrative computations are given for radiation from apertures and plane wave scattering from bodies of revolution The impedance elements, currents, radiation patterns, and scattering patterns for a conducting sphere are computed both from the general solution and from the classical eigenfunction solution The agreement obtained serves to check the general solution Similar computations for a cone-sphere illustrate the application of the general solution to problems not solvable by classical methods
TL;DR: In this paper, the scattering of infinitesimal surface waves normally incident on a rectangular obstacle in a channel of finite depth is considered and a variational formulation is used as the basis of numerical computations.
Abstract: The scattering of infinitesimal surface waves normally incident on a rectangular obstacle in a channel of finite depth is considered. A variational formulation is used as the basis of numerical computations. Scattering properties for bottom and surface obstacles of various proportions, including thin barriers and surface docks, are presented. Comparison with experimental and theoretical results by other investigators is also made.
TL;DR: In this paper, the authors derived the semiclassical theory of potential scattering from Feynman's path-integral formulation of quantum mechanics and applied it to scattering by a noncentral field.
Abstract: The semiclassical theory of potential scattering is derived from Feynman's path-integral formulation of quantum mechanics. Since the partial-wave expansion is avoided, the results are applicable to scattering by a noncentral field. Special attention is given to the conditions for validity of the semiclassical approximation.
TL;DR: In this article, a series of papers on high-frequency scattering of a scalar plane wave by a transparent sphere (square potential well or barrier) is presented, where the amplitude of the wave is characterized in terms of multiple internal reflections.
Abstract: This is Paper I of a series on high‐frequency scattering of a scalar plane wave by a transparent sphere (square potential well or barrier). It is assumed that (ka)⅓≫1,|N−1|½(ka)⅓≫1, where k is the wave‐number, a is the radius of the sphere, and N is the refractive index. By applying the modified Watson transformation, previously employed for an impenetrable sphere, the asymptotic behavior of the exact scattering amplitude in any direction is obtained, including several angular regions not treated before. The distribution of Regge poles is determined and their physical interpretation is given. The results are helpful in explaining the reason for the difference in the analytic properties of scattering amplitudes for cutoff potentials and potentials with tails. Following Debye, the scattering amplitude is expanded in a series, corresponding to a description in terms of multiple internal reflections. In Paper I, the first term of the Debye expansion, associated with direct reflection from the surface, and the second term, associated with direct transmission (without any internal reflection), are treated, both for N > 1 and for N 1, the behavior of the first term is similar to that found for an impenetrable sphere, with a forward diffraction peak, a lit (geometrical reflection) region, and a transition region where the amplitude is reduced to generalized Fock functions. For N 1 and for N < 1. In the former case, surface waves make shortcuts across the sphere, by critical refraction. In the latter one, they excite new surface waves by internal diffraction.
TL;DR: In this paper, the problem of electromagnetic scattering from a randomly rough surface is analyzed in the high-frequency limit with the use of the Kirchhoff approximation in conjunction with the vector Kirchoff equation.
Abstract: The problem of electromagnetic scattering from a randomly rough surface is analyzed in the high-frequency limit with the use of the Kirchhoff approximation in conjunction with the vector Kirchhoff equation. The surface is allowed to have a finite conductivity but is assumed to be homogeneous. The analysis does not require that the surface be described as a Gaussian process; however, explicit formulas are presented for this case. A major new consideration is the effect of shadowing by the surface on its ability to scatter energy.
TL;DR: In this article, a simple-minded formulation of the Glauber model of the high energy multiple scattering of strongly interacting composite particles is derived for the elastic scattering amplitudes at small scattering angles.
TL;DR: In this paper, a detailed study of the first and second-order Raman effect in cubic ZnS using both 4880 and 5145 \AA{} excitation was presented.
Abstract: We present a detailed study of the first- and second-order Raman effect in cubic ZnS using both 4880 and 5145 \AA{} excitation. Our primary interest is to determine to what extent information on lattice dynamics can be extracted from Raman studies in a case where the crystal structure is relatively simple. Aside from interpreting the observed spectra and determining the energies of the phonon branches at the Brillouin-zone center and boundary, the study emphasizes two things. First, we examine experimentally the relation between first-order Raman intensities and the linear electro-optic effect. We find that the linear electro-optic constant derived from the absolute Raman intensities of the longitudinal- (LO) and transverse- (TO) optic modes agrees quite well with the constant obtained from direct measurement. This close agreement is particularly significant in the zinc-blende structure, since only one electro-optic constant and two optical modes are involved in the comparison. Also, it provides experimental evidence that the macroscopic, and not the local, electric field caused by the polar phonons should be used in calculations involving semiconducting crystals. Second, emphasis was also placed on comparing the observed selection rules or polarization properties of the second-order Raman effect with that predicted at the two most important or highest-symmetry critical points ($X$ and $L$) on the Brillouin-zone boundary. The agreement between observed and calculated selection rules is quite good, although in some cases, certain polarization characteristics which are allowed by symmetry are not detected. Also, some evidence of two-phonon scattering from other points in the Brillouin zone is found. The polarization properties of single-crystal Raman spectra are more conveniently discussed in terms of the irreducible representations of the polarizability, rather than depolarized spectra or depolarization ratios which apply more directly to liquid or polycrystalline samples. The observed and calculated selection rules for second-order Raman scattering are compared in detail, using these polarizability representations. The LO and TO phonon energies are 271 and 352 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the zone center and 306 and 333 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the zone boundary, and the TA and LA energies are 88 and 110 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the boundary.
TL;DR: In this paper, the dominant role of large longitudinal distances linearly increasing with the energy was investigated in the process of virtual photon and neutrino scattering on nucleons, and the conclusion that large longitudinal distance dominates the process was made.
TL;DR: In this paper, a model for highly inelastic electron-nucleon scattering at high energies is studied and compared with existing data, where the proton is composed of point-like constituents from which the electron scatters incoherently.
Abstract: A model for highly inelastic electron-nucleon scattering at high energies is studied and compared with existing data. This model envisages the proton to be composed of pointlike constituents ("partons") from which the electron scatters incoherently. We propose that the model be tested by observing $\ensuremath{\gamma}$ rays scattered inelastically in a similar way from the nucleon. The magnitude of this inelastic Compton-scattering cross section can be predicted from existing electron-scattering data, indicating that the experiment is feasible, but difficult, at presently available energies.
TL;DR: In this paper, the Thomson scattering on T3 has been used to obtain temperatures of 100 eV up to 1 keV and densities in the range 1 −3 × 1013 cm−3.
Abstract: Electron temperatures of 100 eV up to 1 keV and densities in the range 1–3 × 1013 cm−3 have been measured by Thomson scattering on Tokamak T3. These results agree with those obtained by other techniques where direct comparison has been possible.
TL;DR: Volume distributions of mammalian cells and plastic microspheres agree with other independent determinations on small angle light scattering by spherical particles.
Abstract: Theory predicts that small angle light scattering by spherical particles of 5 to 20 μ diam is nearly proportional to volume and insensitive to particle refractive index. A flow system photometer with helium‐neon laser light source measures the scattering between 0.5 and 2.0° from individual particles at 104 to 105/min. Volume distributions of mammalian cells and plastic microspheres agree with other independent determinations.
TL;DR: In this paper, Raman radiant intensities and depolarization ratios measured for gases with mercury arc irradiation and photoelectric detection have been collected, and the observed intensities have been reduced to values of the scattering activity, gj (45αj12+7γj12).
Abstract: Raman radiant intensities and depolarization ratios measured for gases with mercury arc irradiation and photoelectric detection have been collected. The observed intensities have been reduced to values of the scattering activity, gj (45αj12+7γj12). The scattering activity and Raman scattering cross sections are explicitly related. Data for strong sharp bands are accurate to about ± 5% – 10%, while data for weak and broad bands are less accurate.
01 May 1969
TL;DR: In this article, the authors re-examined the Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic plane-wave excitation.
Abstract: The Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic plane-wave excitation, is re-examined. The analysis employs a technique developed to locate singularities of solutions to the Helmholtz equation. When applied to the surface profile v = b cos κu (-∞ 0·448; this is more precise than an earlier result. It is shown how these findings may be reconciled with the work of others who have suggested, or concluded, that the Rayleigh assumption is never valid.