Physics
Scattering
Scattering refers to the process in which particles or waves are deflected or redirected as they interact with other particles or obstacles. This phenomenon is fundamental in understanding the behavior of light, sound, and subatomic particles. In physics, scattering is used to study the properties of materials, the structure of atoms, and the behavior of electromagnetic waves.
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8 Key excerpts on "Scattering"
eBook - PDFFundamentals of Condensed Matter and Crystalline Physics
An Introduction for Students of Physics and Materials Science
- David L. Sidebottom(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
PART II Scattering Most of the light that enters our eyes has been scattered and when we see objects we see them because of the diffuse Scattering of light they produce. Even the sky is blue because of how it scatters sunlight. But Scattering is also an important mechanism for observing very small objects. As a classic example, recall how Lord Rutherford unveiled the internal structure of the atom by studying the Scattering pattern of alpha particles directed at gold atoms. The abnormally large number of particles backscattered by these gold atoms pointed to the existence of a small, but very dense, center which we now refer to as the nucleus. In the next chapter, we develop the basic framework for the Scattering of waves by condensed matter by looking at how electromagnetic waves scatter from the electrons contained in the particles. Although this is strictly relevant only for the Scattering of X-rays and visible light, much of the formalism that develops will apply equally to other waves, including particle waves (electrons or neutrons) that interact with things other than electrons. In the following chapter ( Chapter 6 ), we look at how X-rays scatter from crystals. There we will fi nd Scattering that is reminiscent of how visible light is scattered by a diffrac-tion grating in that the scattered radiation exits as a set of discrete beams. This discrete (Bragg) diffraction is contrasted in Chapter 7 by the continuous pattern of Scattering produced by glasses or liquids. In the fi nal chapter on Scattering ( Chapter 8 ), we examine how waves of a longer wavelength can be used to study structures of a larger extent. These include liquid crystals, whose symmetry is intermediate between those of crystals and liquids, and notable self-similar (i.e. fractal) objects such as polymers and aggregates.
eBook - PDF- Ashok Das(Author)
- 2012(Publication Date)
- WSPC(Publisher)
Chapter 15 Scattering theory Scattering is a valuable probe to study the structure of particles when we cannot directly see them. For example, it is through Scattering experiments that we have learned that the hydrogen atom consists of a nucleus and an electron going around it. We know that electrons are point particles also from the results of Scattering experiments. Furthermore, the Scattering experiments have told us that protons consist of yet other constituents – the quarks. Therefore, we see that Scattering is an essential tool in our understanding of the quantum nature of particles. We will, therefore, spend some time studying this topic. However, let me begin by recapitulating some of the features of Scattering theory in classical physics. Classically, the simplest Scattering that we can consider is that of a beam of particles from a fixed center of force as shown in Fig. 15.1. We can think of the fixed center of force to be a charged particle of infinite mass, if the particles that are being scattered are thought of as electrons or protons. Let us assume that a beam of particles is incident on the fixed source of force along the z -axis. The trajectories of the particles change due to the force experienced and the deflection of the trajectory, from the initial direction, is known as the Scattering angle. θ z → Figure 15.1: Classical Scattering of a beam of particles from a scat-tering source. 409 410 15 Scattering theory Classically, of course, we are not interested in measuring the exact trajectory of each of the particles. In fact, it is impossible if the number of particles involved is very large. We can only measure the initial velocity of the particles (which are assumed to be of the same energy) and their final velocities. Furthermore, this is done statistically. Namely, we measure how many particles scatter into a solid angle d Ω at θ .
eBook - PDFTheory of Stellar Atmospheres
An Introduction to Astrophysical Non-equilibrium Quantitative Spectroscopic Analysis
- Ivan Hubeny, Dimitri Mihalas(Authors)
- 2014(Publication Date)
- Princeton University Press(Publisher)
Chapter Six Continuum Scattering A photon is scattered when it interacts with a Scattering center and moves away in a different direction and perhaps with a different frequency. Unlike absorption and emission processes, which create and destroy photons in first-order transitions between well-defined quantum states, photon Scattering is the result of higher-order quantum interactions with free charged particles and resonances with bound elec-trons in molecules and atoms. If the energy of an incoming photon is much less than the rest energy of the Scattering center, so little energy is delivered to the particle that the internal (excitation, ionization, kinetic) energy of the particles in the gas is essentially unaltered. In this case, the rate at which the radiation field is changed by its interaction with the material is set primarily by the local value of the radiation field itself, and only secondarily by the thermodynamic properties of the gas. An important point is that in all Scattering processes photon numbers are conserved ; i.e., they are neither created nor destroyed, as in absorption and emission processes. Scattering processes can also polarize radiation. We will not address these phenomena; see, e.g., [225, 573, 574, 789, 1085]. In hot stellar atmospheres, hydrogen and helium are strongly ionized; hence the main continuum Scattering process affecting the radiation field is Thomson Scattering by the abundant free electrons. 1 Although we describe other continuum Scattering processes in this chapter, we consider mainly Scattering by free electrons in the remainder of this book. In § 6.1 we use electromagnetic theory to compute the energy scattered by an electron having a hypothetical “natural oscillation frequency” ω 0 (e.g., because it is bound in an atom or molecule) that is driven into motion by radiation having frequency ω .
eBook - PDF- Gerald Oster, Arthur W. Pollister, Gerald Oster, Arthur W. Pollister(Authors)
- 2013(Publication Date)
- Academic Press(Publisher)
The cloud of electrons in the matter which had been set into oscillation by the incident light now behaves in a similar manner to a radio antenna and will send off an amount of electromagnetic energy, the intensity, determined by the size of the oscillators and their number and by the frequency of their oscillations (i.e., by the wave length of the incident light). Subsequent developments in the theory were concerned primarily with the interactions between the scattered wavelets from non-independent Scattering particles, as in non-ideal solutions, or from the same particles where the particles are not small compared with the wave length of the incident light. Comprehensive reviews of the theory of light Scattering have appeared in recent years (Oster, 1948, 1949, 1950a; Doty and Steiner, 1950; Tonnelat, 1950; Doty and Edsall, 1951; Riley and Oster, 1951). A complete under-standing of the derivation of light Scattering formulae requires an elemen-tary knowledge of electromagnetic theory and of the thermodynamics of solution. Lack of such knowledge, however, does not preclude one from carrying out significant experiments in light Scattering as long as the limita-tions of the formulae to be applied to the data are sufficiently appreciated. 2. S M A L L I N D E P E N D E N T P A R T I C L E S When a beam of light traverses a light-Scattering system its intensity is decreased by virtue of the energy withdrawn from the beam in the form of scattered radiation. For colorless particles the logarithm of the fractional decrease in the transmitted intensity I is given by the turbidity τ where I = IQ exp ( — rZ), JO being the initial intensity and Ζ the path length of the L I G H T S C A T T E R I N G 53 Scattering system. In terms of logarithms and τ is in reciprocal centimeters if I is given in centimeters.
- Thomas G. Kyle(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
Absorption is found to be proportional to particle volume, not volume squared as Scattering is. This means the ratio of absorption to Scattering goes as 1/fl 3 . As particles become smaller and smaller, Scattering becomes less in relation to absorption. At some size absorption will become the dominant process. Raleigh Scattering theory seems to give satisfactory results even when the particles are closer together than a wavelength of light. In the Scattering of light in the atmosphere, there are many particles in a sphere 1 wavelength in diameter. It must be that the random spacing of particles permits the difficulties to be avoided. This still Scattering 121 leaves the question of how closely packed the particles can be and still scatter according to Rayleigh theory instead of as a solid. RAMAN Scattering Raman scattered light is shifted either upward or downward in frequency. The proper description of the Raman effect requires quantum mechanics, but a classical or semiclassical overview can provide an introduction. Raman Scattering is unimportant in the atmosphere except when used as an experimental tool. For example, Raman Scattering of laser illumination can provide range resolved measurements of water vapor. Raman Scattering is somewhat related to Rayleigh Scattering. That explains the placement of Raman Scattering here instead of in the chapter dealing with quantum effects. The classical view of Rayleigh Scattering given above explains the Scattering as being due to charge redistribution when molecules are subjected to an electromagnetic field. In particular, the incident radiation causes a continuously varying charge redistribution or electric polarization. The Raman effect also comes about through variation in polarization. As a molecule vibrates, or as the electrons rotate in their orbits, it is reasonable to expect the polarizability of the molecule to vary.
- Knut Stamnes, Gary E. Thomas, Jakob J. Stamnes(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
In both gaseous and aqueous media of interest to us, the squares of the electric fields of the scattered waves are added as if all the particles were independent scatterers. In both cases, the direct beam experiences the collective effects of refraction and reflection. In the classical picture, the Scattering process occurs as a result of the incident electric field inducing temporary electric dipoles, which then act as sources of sec- ondary radiation. The radiation emanating from these sources is called first-order Scattering. Radiation produced by further interactions of the first-order radiation with the medium is called multiple Scattering. Scattering processes, in which there is no net energy exchange between the gas and the photons, are classified as con- servative. If some absorption occurs, the process is called non-conservative. The frequency dependence of the absorption line profile was illustrated by solution of the forced classical damped harmonic oscillator. The concepts of resonance and Rayleigh Scattering follow from various limiting forms of the classical oscillator solution. The Lorentz line-broadening profile as well as the Rayleigh Scattering phase function also follow from this formulation. The classical picture of an induced dipole was extended to describe Scattering as an excitation of a quantized state. The concept of pressure broadening is understood as the extension of the harmonic oscillator damping to include perturbations of the excited state by elastic collisions. Doppler and mixed (Voigt) line broadening were shown to result from the spectral line shifts from a gaseous ensemble in which there is a dispersion 24 See chapter 5 of Bohren and Huffman (1998); chapter 9 of Zdunkovski et al. (2007); chapter 2 and appendix A of Stamnes and Stamnes (2015) for detailed discussions of Mie–Debye theory. Exercises 87 of velocities, described by the Maxwell–Boltzmann distribution.
eBook - PDF- Fayyazuddin, Riazuddin;;;(Authors)
- 2000(Publication Date)
- WSPC(Publisher)
Chapter 2 Scattering AND PARTICLE INTERACTION Most of the information about the properties of particles and their interactions is extracted from the experiments involving scatter-ing of particles. We, therefore, start this chapter by studying the kinematics of Scattering processes. 2.1 Kinematics of a Scattering Process Consider a typical 2-body Scattering process a + b —► c -(-d. We denote the four momenta of particles a, 6, c and d by p a , pb, p c , Pd respectively. Energy momentum conservation gives: Pa + Pb=Pc + Pd (2.1a) Pa + Pb = Pc + Pd (2.1b) E a + E b = E c + E d (2.1c) The reaction transition amplitude is a function of scalars (i.e. Lorentz invariants) formed out of the four vectors p a ,Pb,Pc and pd-We assume Lorentz invariance in any process involving particles. The invariants are s = (Pa+p b ) 2 = (Pc + Pd) 2 (2.2a) t = (Pa -Pc) 2 = (Pd ~ Pb) 2 (2.2b) U = ( Pa -Pd) 2 = (Pc-Pb) 2 . (2.2C) 27 28 Scattering and Particle Interaction Figure 1 Two-body Scattering: a + b — ► c + d. But only two of the three scalars are independent: s + t + u = 3pl + pl+p 2 c +pl + 2p a -(p b -p c -p d ) (2.3) = ml + m + m 2 c + m In an actual Scattering experiment, we have a projectile (let it be a) and a target (6), which is stationary in the laboratory frame. Thus Pa = (EL, P L) = (V L , PL ) Pb = K , 0 ) (2.4) p c = (£ c L ,p c L ), p d =(E^d)' Hence in the laboratory frame: S = (p a + p b f = ml + ml + 2m b v L , (2.5a) * = {Pa-Pcf = ml + ml-2u L E^ +2 p L p^cose L -(2.5b) Kinematics of a Scattering Process 29 Figure 2 Two-body Scattering in the laboratory frame. or m: — mi VL = Pi = IPLI 2m b Pa-Pb m b Pa + L = ~< + V l yj{s, ml, m 2 b ) 2m b where A (x, y, z) = x 2 + y 2 + z 2 - 2xy -2xz -2yz. (2.6a) (2.6b) (2.6c) (2.7) Theoretically, it is convenient to consider a Scattering pro-cess in the center of mass (cm.) frame.
eBook - PDF- A P Kazantsev, G I Surdutovich, V P Yakovlev(Authors)
- 1990(Publication Date)
- World Scientific(Publisher)
C H A P T E R 2 Scattering OF ATOMS BY LIGHT The theoretical and experimental problems associated with the study of induced light pressure are discussed here. The classical pattern of Scattering and the pulse regime of the atomic beam Scattering by a standing light wave are considered (Sec. 4), as well as various mechanisms of atom acceleration (Sec. 5). In addition, the quantum effects in Scattering are investigated, i.e., the diffraction (Sec. 6) and interference (Sec. 7) of atoms in the light field. 4. The Classical Picture of Scattering The simplest way to investigate the forces of induced light pressure is to study the Scattering of atoms by standing light waves. Figure 4.1 illustrates schematically the principle of such an experiment. The incident atomic beam propagates along the y-axis and crosses a standing light wave which is situated parallel to the z-axis. Scattered atoms are registered by a detector (heated wire) which can be moved along the z-axis. The distance t from the interaction region of a size o to the detector is large: L~> a. The Scattering pattern depends essentially on (a) the atomic beam char-acteristics (angular divergence r = v x /v u and distribution function of the particles in longitudinal velocities v y ), (b) the field parameters (intensity, 45 46 Mechanical Action of Light on Atoms Fig. 4.1 An arrangement for observing the Scattering of an atomic beam by a standing light wave. frequency and spectrum of radiation), (c) the atom-field interaction time T. Under stationary conditions r coincides with the time-of-flight of atoms and is 1 0 -5 — 1 0 -6 s for an unfocused light beam and 1 0 -7 s for a focused one. Under the pulse regime of Scattering time r is the duration of a pulse and may be approximately 10~ 7 — 1 0 -8 s. Next, we will consider some characteristic cases of atomic momentum change due to induced light pressure force action and estimate the efficiency of Scattering and acceleration of atoms by light.
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