Showing papers on "Momentum published in 1970"
TL;DR: In this paper, the authors derived transport equations for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs.
Abstract: Transport equations are derived for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs. Care is taken to state and discuss the assumptions which are made in the derivation. The collision processes are expressed in terms of relaxation times. The accuracy is improved by considering these to depend on the average kinetic energy rather than the electron temperature. Other transport equations used in the literature are discussed, and shown to be incomplete and inaccurate in many cases. In particular, the usual assumption that the mobility and diffusion constant depend locally on the electric field strength is shown to be incorrect. Rather, these quantities should be taken as functions of the local average velocity of electrons in the lower valley.
765 citations
TL;DR: In this paper, the theory of high-energy hadron-nucleus collisions is discussed by means of the multiple-diffraction theory, and the predicted sums of the angular distributions of elastic and inelastic scattering reproduce the experimental angular distributions fairly closely.
547 citations
TL;DR: In this article, the impulse approximation (IA) was used to analyze Compton scattering measurements, and its accuracy was compared with the exact calculations for Compton scattering from a hydrogenic system.
Abstract: Exact and approximate methods for determining the momentum distribution of electronic systems from Compton scattering measurements are presented. The method used previously to analyze Compton scattering measurements, the impulse approximation (IA), is derived from first principles, and its accuracy is compared with the exact calculations for Compton scattering from a hydrogenic system. It is shown that the IA gives very accurate results for weakly bound electrons and that exact calculation may only be necessary to substract out the contributions to Compton scattering from deeply bound core electrons. Experimental results for Compton scattering from helium are presented as a test of the above ideas. Analyzing the results of the experiment in the IA gives a momentum distribution for the weakly bound helium electrons which is in excellent agreement with the momentum distribution obtained from Clementi Hartree-Fock wave functions.
410 citations
TL;DR: In this paper, the effect of the background on the wave and that of the wave on the background may be derived from Hamilton's principle using the averaged hydromagnetic Lagrangian density.
Abstract: Consider a system made up of a hydromagnetic wave and the slowly varying background fluid in which it propagates. It is shown that both the effect of the background on the wave and that of the wave on the background may be derived from Hamilton's principle using the averaged hydromagnetic Lagrangian density. The waves propagate adiabatically, conserving the wave action, and act on the background via a wave pressure term. Total momentum, angular momentum, and energy are conserved. When many waves are superimposed, as in weak turbulence, the wave kinetic equation replaces the adiabatic conservation equation. The accuracy of the averaging approximation is examined, and it is shown that it may be extended to all orders in the inhomogeneity. Also, Eulerian and Lagrangian averaging are discussed.
260 citations
TL;DR: In this article, it was shown that a Q-switched CO2 laser at 10.6μ can transfer sufficient momentum to produce a longitudinal emf in a rectangular rod typically 4 cm long.
Abstract: The transfer of momentum from a photon stream to free electrons and holes in germanium has been studied. It is shown that a Q‐switched CO2 laser at 10.6μ can transfer sufficient momentum to produce a longitudinal emf in a rectangular rod typically 4 cm long. This provides a useful, very high speed detector, operating at room temperature.
183 citations
TL;DR: In this article, the authors describe an experimental study of the occurrence, frequency and peak-to-peak amplitude of the wall pressure generated by a helical vortex in rotating flow moving axially through a straight tube.
Abstract: In rotating flow moving axially through a straight tube, a helical vortex will be generated if the angular momentum flux is sufficiently large relative to the flux of linear momentum. This paper describes an experimental study of the occurrence, frequency and peak-to-peak amplitude of the wall pressure generated by this vortex. The experimental results are displayed in dimensionless form in terms of a Reynolds number, a momentum parameter and tube geometry.
135 citations
122 citations
TL;DR: An improved version of the theory of Singwi et al. for the collective motions in classical liquids is described in this paper, which is based on a generalized mean-field approximation involving the polarization potential and the screened response function.
Abstract: An improved version of the theory of Singwi et al. for the collective motions in classical liquids is described. The theory is based on a generalized mean-field approximation involving the polarization potential and the screened response function. The latter, instead of having a free-particle form or that corresponding to the true self-motion of the particle in a liquid, is assumed to be a sum of Gaussian functions weighted by the momentum distribution of the particles. The zero and fourth moments of the scattering law determine the polarization potential and the width of the Gaussians. Numerical calculations have been made for the spectral function of the longitudinal current correlations, quasielastic scattering, and absolute intensities for liquid argon in the range of momentum transfer 0.5-6.3 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. The results are in excellent agreement with the molecular-dynamics calculations and recent experiments on a purely coherent sample of liquid argon.
83 citations
TL;DR: In this article, the Gaussian inner orbital wave function was shown to produce a form factor very close to the dipole formula, taking account of the Lorentz contraction effect of the extended nucleon core as a quark.
Abstract: Taking account of the Lorentz contraction effect of the extended nucleon core as a nucleon but not as a quark, it is shown that the Gaussian inner orbital wave function can produce the form factor very close to the dipole formula.
64 citations
TL;DR: In this paper, the authors derived dynamic equations for steady spatially varied flow in uniform channels based on momentum and energy principles and showed that the momentum equation is inherently different from the energy equation.
Abstract: Dynamic equations for steady spatially varied flow in uniform channels are derived separately based on momentum and energy principles. It is shown that the momentum equation is inherently different from the energy equation. In general, six different gradients are involved in steady spatially varied flow: the friction slope in the momentum equation, the dissipated energy gradient in the energy equation, the total head gradient, the gradient of the piezometric head, the free surface slope, and the channel slope. Conventional practice of using the Manning, Chezy, or Weisbach formulas to evaluate the friction slope or the dissipated energy gradient is only an approximation.
52 citations
01 Jan 1970
TL;DR: In this paper, high-energy neutrino-nucleon inelastic processes were discussed in the light of recent theoretical and experimental developments for the corresponding electroproduction processes.
Abstract: We discuss high-energy inelastic neutrino-nucleon inelastic processes in the light of recent theoretical and experimental developments for the . corresponding electroproduction processes. We review the kinematics for the process in a form especially convenient for experimental analysis. We discuss sum-rules and results related to current commutation relations. Consequences of the parton model and diffractive models are considered. Other results are (1) the vector and axial contributions to the total cross section are equal, provided the only symmetry breaking term in the energy density transforms like a quark mass term under U(6) @U(6). (2) Scaleinvariance of one of the three form factors (VP or VW,) describing the process implies a neutrino total cross section which rises linearly with laboratory energy, provided the lepton current is local and there is no W-boson. The effect of a W-boson on this result is studied. (3) The relation of existing neutrino data and electroproduction data given by the conserved vector current hypothesis is studied and found compatible with experiment. * Work supported by the U. S. Atomic Energy Commission.
TL;DR: In this article, the authors proposed a new Lagrangian for the A1ρπ system containing no more than two field derivatives in each term, which is determined by only four parameters gρ, gA, m ρ, MA and gives the smoothest momentum dependence for the contact vertices.
TL;DR: In this article, a theory for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat was developed.
Abstract: An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with height z above a turbulent boundary layer and the mean density decreases as z3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.The curvature of the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.
TL;DR: In this paper, a method for generating conservation laws associated with the propagation of ultrashort optical pulses is presented, and two pairs of conservation laws beyond those of field energy and field momentum are presented.
TL;DR: In this article, cross sections of final states produced in K − n interactions at 3 GeV/c were presented, obtained in a 7 events/ub bubble chamber exposure with deuterium, compared with results from an earlier K − p exposure at the same incident K − momentum.
TL;DR: In this paper, the 2 S ground state of the Li atom was determined using the natural orbital expansion of a highly accurate Hylleraas-type function (99.90% of the correlation energy) to obtain the correlated distribution.
TL;DR: In this article, the contribution of singular diagrams to the third virial coefficient was analyzed and sum the contribution from singular diagrams in terms of the singular diagrams' contribution to the virial coefficients.
Abstract: We have shown earlier how the virial coefficients can be expressed in terms of traces taken over products of multiparticle (on‐energy‐shell) scattering matrices. The traces are to be taken in the angular‐momentum representation instead of the momentum representation to avoid the infinite forward N‐particle scattering amplitude for N > 2 caused by certain singular diagrams. Here, we analyze and sum the contribution of the singular diagrams to the third virial coefficient. It is also shown that one can get the same result if off‐shell amplitudes in the momentum representation are utilized.
TL;DR: In this article, a transverse analogue of the Goos-Hanchen effect by total reflexion of a circularly polarized light beam has been tested, which expresses (over distances of the order of the wavelength) that the velocity and momentum of a spinning particle are noncolinear.
TL;DR: In this article, it is suggested that there is a quantum mechanical basis for the classical flat surface (cubes) models of gas surface scattering, the important characteristic of which is the assumption of conservation of tangential momentum of a scattering gas molecule.
Abstract: It is suggested that there is a quantum mechanical basis for the classical flat surface (cubes) models of gas–surface scattering, the important characteristic of which is the assumption of conservation of tangential momentum of a scattering gas molecule. The theory is applied to the diffractive system He–LiF, and it is shown that existing experimental data confirm some predictions of the theory.
TL;DR: In this paper, a finite difference scheme is constructed which has the property of simultaneously conserving total system mass, energy, and momentum throughout the interior of velocity space, thereby reducing nonconservation errors to boundary contributions only.
TL;DR: In this paper, a review of kaon-nucleon interactions below 1 GeV/c is given, with emphasis on direct analyses of KN scattering data, and the phenomenological use of dispersion relations.
Abstract: A review of kaon-nucleon interactions below 1 GeV/c is given, with emphasis on direct analyses of KN scattering data, and the phenomenological use of dispersion relations.
TL;DR: In this article, the interaction between mean flow and finite-amplitude disturbances in certain experimentally observed unstable, compressible laminar wakes is considered theoretically without explicitly assuming small amplification rates.
Abstract: The interaction between mean flow and finite‐amplitude disturbances in certain experimentally observed unstable, compressible laminar wakes is considered theoretically without explicitly assuming small amplification rates. Boundary‐layer form of the two‐dimensional mean‐flow momentum, kinetic energy and thermal energy equations and the time‐averaged kinetic energy equation of spatially growing disturbances are recast into their respective von Karman integral form which show the over‐all physical coupling. The Reynolds shear stresses couple the mean flow and disturbance kinetic energies through the conversion mechanism familiar in low‐speed flows. Both the mean flow and disturbance kinetic energies are coupled to the mean‐flow thermal energy through their respective viscous dissipation. The work done by the disturbance pressure gradients gives rise to an additional coupling between the disturbance kinetic energy and the mean‐flow thermal energy. The compressibility transformation suggested by work on turbulent shear flows is not applicable to this problem because of the accompanying ad hoc assumptions about the disturbance behavior. The disturbances of a discrete frequency which corresponds to the most unstable fundamental component, are first evaluated locally. Subsequent mean‐flow and disturbance profile‐shape assumptions are made in terms of a mean‐flow‐density Howarth variable. The compressibility transformation, which cannot convert this problem into a form identical to the low‐speed problem of Ko, Kubota, and Lees because of the compressible disturbance quantities, nevertheless, yields a much simplified description of the mean flow.
TL;DR: In this paper, it was shown that the energy-momentum spectrum lies in the forward light cone and that a momentum cutoff does not influence this result, and bounds on the vacuum expectation values of products of the φt's and ∆'s were obtained for theories with finite field strength renormalization.
Abstract: We consider nonlinear boson self‐interactions with a periodic spatial cutoff. We prove that the energy‐momentum spectrum lies in the forward light cone. A momentum cutoff does not influence this result. For theories with finite‐field strength renormalization, we obtain bounds on the vacuum expectation values of products of the φt's and ∇φ's. These bounds are uniform in the volume (and possible momentum) cutoff.
TL;DR: In this article, non-equilibrium thermodynamics is used to state the form of the diffusion equation and simplify the kinetic-theory calculations of its coefficients, and explicit expressions are obtained in terms of the masses, molecular diameters, and accommodation coefficients for tangential momentum, and the physical interpretation of the result is given.