Physics
Scattering Angle
The scattering angle refers to the angle between the incident direction of a particle or wave and the direction in which it is scattered after interacting with a target, such as an atom or nucleus. It is a crucial parameter in understanding the behavior of particles and waves in various scattering processes, providing valuable information about the nature of the interaction.
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6 Key excerpts on "Scattering Angle"
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 - PDF- Denis Rousseau(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
The fraction by which the scattering intensity is reduced at any angle Θ is usually called Ρ(θ). The extent of interference will be greater at higher Scattering Angles and negligible at low Scattering Angles; that is, Ρ(θ) — ► 1 as Θ —> 0. Thus the results of the previous sections may be applied to large particles, provided the intensities are measured as a function of Scattering Angle and extrapolated to Θ = 0. Moreover, the functional form and limiting slope οΐΡ(θ) contain new infor-mation about the size and shape of the scattering particles, which may constitute the strongest motivation for the light-scattering experiment. The various forms of radiation scattering have provided the most powerful techniques for determination of molecular structure. The fundamental information is always contained in the intensity variations that result from interference of the radiation as a consequence of preferential phase shifts induced by the structure of the irradiated matter. We shall present here the simplest theoretical formalism appropriate for determining the size and shape of macromolecules in solution. It is important for this and future purposes to appreciate the relationship between position in the scattering medium and phase of the scattered light. Consider the scattering diagram represented in Fig. 2. If the incident beam has a planar wave front, the phase distance may be calculated from a reference plane (plane I) perpendicular to the incident beam. To travel from plane I to the detector by a scattering event at pointy, a photon must travel a distance given by d x + r — d 2 , where d x is the distance from reference plane II (perpendicular to the scattered beam) to the detector, and d 2 the distance from point j to plane II.
eBook - PDF- Vishnu S. Mathur, Surendra Singh(Authors)
- 2008(Publication Date)
- Chapman and Hall/CRC(Publisher)
9 QUANTUM THEORY OF SCATTERING 9.1 Introduction Most of our knowledge about the structure of matter and interaction between particles is derived from scattering experiments. From a theoretical point of view, scattering problems are concerned with the continuous (and positive) energy eigenvalues and unbound eigenfunctions of the Schr¨ odinger equation. We have already encountered one-dimensional examples of scattering in Chapter 4, in the discussion of reflection and transmission of an incident particle with definite momentum from a potential step or barrier. In this chapter we consider scattering from a more formal point of view. We will confine our discussion to elastic scattering (scattering without loss or gain of energy by the projectile) from central potentials although many of the concepts and results are applicable to inelastic scattering. In a typical scattering experiment, a target particle of mass m 2 is bombarded with another particle (projectile) of mass m 1 and carrying a momentum p 1 . After interaction with the target particle the projectile is scattered at some angle θ 0 with respect to the incident direction ( z -direction). Since we will be dealing with elastic scattering from central potentials, we can infer from the symmetry of the problem that the scattering will be axially symmetric. This means the probability of the projectile being scattered in a direction θ 0 , ϕ 0 will not depend on the azimuth angle ϕ 0 . According to quantum mechanics, the angle θ 0 at which a projectile is scattered in a particular case cannot be predicted. However, if a beam consisting of a large number of identical particles, each carrying the same momentum p 1 , is incident on a target consisting of a large number of scatterers, we can use quantum mechanics to predict the angular distribution of scattered particles provided the interaction between the incident and target particles is known.
eBook - PDF- Charles G. Wohl(Author)
- 2022(Publication Date)
- CRC Press(Publisher)
16. SCATTERING 16.1. Solid Angle 16.2. Classical Particle Scattering. Rutherford 16.3. The Scattering Amplitude 16.4. The Born Approximation 16.5. Kinematics 16.6. Partial-Wave Theory 16.7. Partial-Wave Examples 16.8. Scattering of Identical Particles Problems The early studies of scattering of particles by targets used collimated beams of de- cay products from radioactive sources and low-energy beams of electrons from accelerators. Beams of electrons run into matter also produced beams of x rays. But for about 100 years now, larger and larger accelerators have produced beams of atoms, nuclei, and particles of ever greater energy and intensity. The scattering angular distributions of collisions can tell us about the forces between beam and target. However, much more than simple a + b → a + b (elastic) scattering can occur. Experiments at the higher energies have led to the discovery of scores of unexpected massive particles (E = mc 2 at work), out of range at low energies. At the energies available at large accelerators, and especially at the vastly higher energies that cosmic-ray protons can have, there are sometimes showers of hundreds of particles. But to analyze even simple two- body in elastic reactions is more than we can do here. And even for purely elastic scattering, the energies will be nonrelativistic and, except in the last section, the particles spinless. With these severe limitations, the questions we can tackle here are these: (1) Given a spherically symmetric potential energy V (r) for the interaction between beam and target, what is the scattering angular distribution as a function of energy? (2) Given an experimental angular distribution, what are the separate scattering amplitudes for the angular momentum states with ℓ = 0, 1, 2, ... , between beam and target? Sections 3 and 4 address the first of these questions, sections 6 and 7 the second. The last section is about the scattering of identical particles.
- Sydney Leach(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
The experimental quantities which must be measured are the difference between the scatter-ing intensities (Rayleigh ratios or turbidities) at a given angle θ (usually 90°) of the solution and solvent and the refractive index increment of the solution, due to the introduction of the macromolecular solute (dn/dC 2 ). C. PARTICLE GEOMETRY 1. General Equations When the dimensions of the particle are of a magnitude comparable to the wavelength of the radiation (in light scattering, a situation true for large molecules such as collagen or myosin), interference occurs between 154 S. N. TIMASHEFF AND R. TOWNEND Incident Incident Ρ (b) FIG. 3. (a) Geometry of interference between the scattering from various elements in a particle; (b) scattering envelope. For details see text. the radiation scattered from individual elements within a particle. As a result, the scattering envelope (i.e., the angular dependence of the scat-tered radiation) is asymmetric. The reason for this is shown in Fig. 3a. The particle is large with respect to the wavelength of the radiation. Let us consider scattering from elements η and m observed at points Ρ and Q. We find that when radiation scattered from elements η and m reaches point Ρ (in the forward direction), there is no great difference between the path lengths of the two rays, so that they are not greatly out of phase with each other and interference is small. However, when the radiation scattered from η and m reaches point Q (in the backward direction) the total distance traveled by the ray from m is much greater than that from η (greater by nm -f-mQ — nQ) . As a result, the two rays can become completely out of phase, leading to serious interference. In the forward direction, i.e., along the incident beam, scattered radiation from η and m is fully in phase, there is no interference, and the observed scattering is the sum of the scatterings from all elements within the particle.
- David Hysell(Author)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
6 Scattering The objective of radar is to derive meaningful information from radio signals scattered by distant targets. What is the nature of the scattering, and how do we quantify it? The scat- tering cross-section is a parameter that describes the power scattered by an object exposed to electromagnetic radiation. For some objects, it can be calculated from first principles (electrons, raindrops). For others (aircraft, ships), it usually must be measured. Sometimes it is simply related to the physical size of the object. Sometimes it is not. The scattering cross-section also generally depends on the radar frequency, polarization and orientation with respect to the target. Some definitions help clarify the distinctions. Broadly defined, scattering is the redirection of radiation away from the original direction of propagation. Reflection, refraction and diffraction all accomplish this, but often involve environmental effects and are sufficiently distinct and important in their own right to deserve independent treatments. In this text, these phenomena are grouped together under the heading “propagation.” “Scattering” is reserved for wave interaction with lumped materials. Scattering is elastic (inelastic) if the incident and scattered wave- lengths are the same (different). When a Doppler shift is imparted to the scattered wave, the scattering is termed “quasi-elastic.” This chapter is concerned with elastic and quasi- elastic scatter only. Inelastic scattering is mainly associated with optical phenomena, the phenomenon of stimulated electromagnetic emission (SEE) of radio signals being one important counterexample. Referring to the schematic diagram in Figure 6.1, we can express the power density incident on the target in terms of the transmitted power P tx , the range to the target r, and the antenna gain G as P inc = P t G 4πr 2 ( W /m). Define the total scattering cross-section σ t as the total power scattered per incident power density, or P sc = P inc σ t .
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