Scattering

Source: Wikipedia, the free encyclopedia.
For other uses, see Scattering (disambiguation).
Scattering
Electron scattering
Feynman diagram of scattering between two electrons by emission of a virtual photon
Wine glass in LCD projectors light beam makes the beam scatter.

Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as

specular (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century[1]). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800.[2] John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s.[3] Near the end of the 19th century, the scattering of cathode rays (electron beams)[4] and X-rays[5] was observed and discussed. With the discovery of subatomic particles (e.g. Ernest Rutherford in 1911[6]
) and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.

Scattering can refer to the consequences of

particle-particle collisions between molecules, atoms, electrons, photons and other particles. Examples include: cosmic ray scattering in the Earth's upper atmosphere; particle collisions inside particle accelerators; electron scattering by gas atoms in fluorescent lamps; and neutron scattering inside nuclear reactors.[7]

The types of non-uniformities which can cause scattering, sometimes known as scatterers or scattering centers, are too numerous to list, but a small sample includes

scattering theory
.

Some areas where scattering and scattering theory are significant include radar sensing,

S-Matrix, introduced and developed by John Archibald Wheeler and Werner Heisenberg.[9]

Scattering is quantified using many different concepts, including scattering cross section (σ), attenuation coefficients, the bidirectional scattering distribution function (BSDF), S-matrices, and mean free path.

Single and multiple scattering

Zodiacal light is a faint, diffuse glow visible in the night sky. The phenomenon stems from the scattering of sunlight by interplanetary dust spread throughout the plane of the Solar System.[10]

When radiation is only scattered by one localized scattering center, this is called single scattering. It is more common that scattering centers are grouped together; in such cases, radiation may scatter many times, in what is known as multiple scattering.

diffusion theory.[12]

Because the location of a single scattering center is not usually well known relative to the path of the radiation, the outcome, which tends to depend strongly on the exact incoming trajectory, appears random to an observer. This type of scattering would be exemplified by an electron being fired at an atomic nucleus. In this case, the atom's exact position relative to the path of the electron is unknown and would be unmeasurable, so the exact trajectory of the electron after the collision cannot be predicted. Single scattering is therefore often described by probability distributions.

With multiple scattering, the randomness of the interaction tends to be averaged out by a large number of scattering events, so that the final path of the radiation appears to be a deterministic distribution of intensity. This is exemplified by a

backscattering that occurs when coherent radiation is multiply scattered by a random medium, is usually attributed to weak localization
.

Not all single scattering is random, however. A well-controlled laser beam can be exactly positioned to scatter off a microscopic particle with a deterministic outcome, for instance. Such situations are encountered in radar scattering as well, where the targets tend to be macroscopic objects such as people or aircraft.

Similarly, multiple scattering can sometimes have somewhat random outcomes, particularly with coherent radiation. The random fluctuations in the multiply scattered intensity of coherent radiation are called

speckles
. Speckle also occurs if multiple parts of a coherent wave scatter from different centers. In certain rare circumstances, multiple scattering may only involve a small number of interactions such that the randomness is not completely averaged out. These systems are considered to be some of the most difficult to model accurately.

The description of scattering and the distinction between single and multiple scattering are tightly related to wave–particle duality.

Theory

Scattering theory is a framework for studying and understanding the scattering of

boundary condition
, and then propagate away "to the distant future".

The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.

Attenuation due to scattering

Equivalent quantities used in the theory of scattering from composite specimens, but with a variety of units

When the target is a set of many scattering centers whose relative position varies unpredictably, it is customary to think of a range equation whose arguments take different forms in different application areas. In the simplest case consider an interaction that removes particles from the "unscattered beam" at a uniform rate that is proportional to the incident number of particles per unit area per unit time (), i.e. that

where Q is an interaction coefficient and x is the distance traveled in the target.

The above ordinary first-order differential equation has solutions of the form:

where Io is the initial flux, path length Δx ≡ x − xo, the second equality defines an interaction mean free path λ, the third uses the number of targets per unit volume η to define an area cross-section σ, and the last uses the target mass density ρ to define a density mean free path τ. Hence one converts between these quantities via Q = 1/λ = ησ = ρ/τ, as shown in the figure at left.

In electromagnetic absorption spectroscopy, for example, interaction coefficient (e.g. Q in cm−1) is variously called

absorption coefficient, and attenuation coefficient. In nuclear physics, area cross-sections (e.g. σ in barns or units of 10−24 cm2), density mean free path (e.g. τ in grams/cm2), and its reciprocal the mass attenuation coefficient (e.g. in cm2/gram) or area per nucleon are all popular, while in electron microscopy the inelastic mean free path[14] (e.g. λ in nanometers) is often discussed[15]
instead.

Elastic and inelastic scattering

The term "elastic scattering" implies that the internal states of the scattering particles do not change, and hence they emerge unchanged from the scattering process. In inelastic scattering, by contrast, the particles' internal state is changed, which may amount to exciting some of the electrons of a scattering atom, or the complete annihilation of a scattering particle and the creation of entirely new particles.

The example of scattering in

central potential. The scattering of two hydrogen atoms will disturb the state of each atom, resulting in one or both becoming excited, or even ionized
, representing an inelastic scattering process.

The term "deep inelastic scattering" refers to a special kind of scattering experiment in particle physics.

Mathematical framework

In mathematics, scattering theory deals with a more abstract formulation of the same set of concepts. For example, if a differential equation is known to have some simple, localized solutions, and the solutions are a function of a single parameter, that parameter can take the conceptual role of time. One then asks what might happen if two such solutions are set up far away from each other, in the "distant past", and are made to move towards each other, interact (under the constraint of the differential equation) and then move apart in the "future". The scattering matrix then pairs solutions in the "distant past" to those in the "distant future".

Solutions to differential equations are often posed on

continuous spectrum
is associated with scattering states. The study of inelastic scattering then asks how discrete and continuous spectra are mixed together.

An important, notable development is the

exactly solvable models
.

Theoretical physics

index of refraction
higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact.

In

fundamental particles
.

In regular

partial wave analysis, and the Born approximation
.

Electromagnetics

A Feynman diagram of scattering between two electrons by emission of a virtual photon

Mie scattering. Inelastic scattering includes Brillouin scattering, Raman scattering, inelastic X-ray scattering and Compton scattering
.

Light scattering is one of the two major physical processes that contribute to the visible appearance of most objects, the other being absorption. Surfaces described as white owe their appearance to multiple scattering of light by internal or surface inhomogeneities in the object, for example by the boundaries of transparent microscopic crystals that make up a stone or by the microscopic fibers in a sheet of paper. More generally, the

sheen
) of the surface is determined by scattering. Highly scattering surfaces are described as being dull or having a matte finish, while the absence of surface scattering leads to a glossy appearance, as with polished metal or stone.

Spectral absorption, the selective absorption of certain colors, determines the color of most objects with some modification by

nanoparticles can produce many different highly saturated and vibrant hues, especially when surface plasmon resonance is involved (Roqué et al. 2006).[17][18]

Models of light scattering can be divided into three domains based on a dimensionless size parameter, α which is defined as:

where πDp is the circumference of a particle and λ is the wavelength of incident radiation in the medium. Based on the value of α, these domains are:

  • α ≪ 1: Rayleigh scattering (small particle compared to wavelength of light);
  • α ≈ 1: Mie scattering (particle about the same size as wavelength of light, valid only for spheres);
  • α ≫ 1: geometric scattering (particle much larger than wavelength of light).

atmosphere.[19] The degree of scattering varies as a function of the ratio of the particle diameter to the wavelength of the radiation, along with many other factors including polarization, angle, and coherence.[20]

For larger diameters, the problem of electromagnetic scattering by spheres was first solved by

ellipsoids
. Closed-form solutions for scattering by certain other simple shapes exist, but no general closed-form solution is known for arbitrary shapes.

Both Mie and Rayleigh scattering are considered elastic scattering processes, in which the energy (and thus wavelength and frequency) of the light is not substantially changed. However, electromagnetic radiation scattered by moving scattering centers does undergo a

Doppler shift, which can be detected and used to measure the velocity of the scattering center/s in forms of techniques such as lidar and radar
. This shift involves a slight change in energy.

At values of the ratio of particle diameter to wavelength more than about 10, the laws of

geometric optics
are mostly sufficient to describe the interaction of light with the particle. Mie theory can still be used for these larger spheres, but the solution often becomes numerically unwieldy.

For modeling of scattering in cases where the Rayleigh and Mie models do not apply such as larger, irregularly shaped particles, there are many numerical methods that can be used. The most common are finite-element methods which solve Maxwell's equations to find the distribution of the scattered electromagnetic field. Sophisticated software packages exist which allow the user to specify the refractive index or indices of the scattering feature in space, creating a 2- or sometimes 3-dimensional model of the structure. For relatively large and complex structures, these models usually require substantial execution times on a computer.

Electrophoresis involves the migration of macromolecules under the influence of an electric field.[21] Electrophoretic light scattering involves passing an electric field through a liquid which makes particles move. The bigger the charge is on the particles, the faster they are able to move.[22]

See also

References

  1. ^ Newton, Isaac (1665). "A letter of Mr. Isaac Newton Containing his New Theory About Light and Colours". Philosophical Transactions. 6. Royal Society of London: 3087.
  2. ^ Herschel, William (1800). "Experiments on the Solar, and on the Terrestrial Rays that Occasion Heat". Philosophical Transactions. XC. Royal Society of London: 770.
  3. JSTOR 109101
    .
  4. ^ Merritt, Ernest (5 Oct 1898). "The Magnetic Deflection of Diffusely Reflected Cathode Rays". Electrical Review. 33 (14): 217.
  5. S2CID 4023635
    .
  6. ^ Rutherford, E. (1911). "The Scattering of α and β rays by Matter and the Structure of the Atom". Philosophical Magazine. 6: 21.
  7. ISBN 0-471-82857-2
  8. ISBN 978-3-540-62838-5
    .
  9. ISBN 3-540-50496-6
    .
  10. ^ "Zodiacal Glow Lightens Paranal Sky". ESO Picture of the Week. European Southern Observatory. Retrieved 2 December 2013.
  11. ISBN 978-0-387-98853-5
    .
  12. ISBN 978-0-387-98853-5
    .
  13. ISBN 978-0-8194-1934-7
    .
  14. ISBN 0-306-45223-5
  15. ISBN 3-540-62568-2
  16. ISBN 978-3-540-62838-5
    .
  17. ISBN 978-0-471-29340-8
    .
  18. doi:10.1016/j.jeurceramsoc.2005.12.024
    .
  19. ISBN 0-471-82857-2
  20. S2CID 4393904
    .
  21. ^ "Understanding Electrophoretic Light Scattering". Wyatt Technology.
  22. ^ "Light Scattering". Malvern Panalytical.

External links

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