# Scattering (physics)

In physics, scattering is generally understood to mean the deflection of an object through interaction with another local object ( scattering center ), more specifically the deflection of particle or wave radiation . Examples are the scattering of light on atoms or fine dust , of electrons on other electrons or of neutrons on atomic nuclei .

The strength of a scatter is indicated by the scatter cross section . The name comes from the fact that the cross-section of the classic scattering of mass points on a hard sphere is exactly the same as the cross-section of the sphere.

A distinction is made between elastic and inelastic (or inelastic) scattering:

Inelastic scattering in the narrower sense means that the incident particle is still present after the collision, albeit with reduced energy; In a broader sense, absorption processes (processes in which the incident particle "disappears") are sometimes counted among the inelastic scattering processes.

When it comes to the scattering of waves, a distinction is also made between coherent and incoherent scattering. In the case of coherent scattering, there is a fixed phase relationship between the incoming and the scattered wave (see reflection ), in the case of incoherent scattering there is not. If coherent rays are coherently scattered, the scattered rays can interfere with each other. This is particularly useful in X-ray diffraction .

The theoretical description of scattering is the task of scattering theory . Experiments in high-energy physics are generally referred to as scattering experiments, even when z. B. new particles arise ( deep inelastic scattering ). They provide information about the shape of the interaction potential . Ernest Rutherford showed on the basis of kinematic relationships in the scattering of alpha particles on atoms that these must contain a heavy nucleus .

In contrast to scattering, diffraction is a deflection of radiation due to the property of a wave front, spreading in all directions at the edge of an obstacle. In the case of refraction , the deflection of the radiation is based on the change in the speed of propagation with a change in the density or the composition of the propagation medium , most clearly at phase boundaries .

## Scatter angle, forward and backscatter

The scattering angle  is the angle by which the scattered particle is deflected. As a forward scattering scattering processes are referred to, in which there is only a small deflection (less scattering angle). Backscattering or backscattering refers to scattering processes with a scattering angle between and (see also kinematics (particle impact) ). ${\ displaystyle \ theta}$${\ displaystyle 90 ^ {\ circ}}$${\ displaystyle 180 ^ {\ circ}}$

If both collision partners have a mass other than zero, the scattering angle in the center of gravity system is often considered in scattering experiments in nuclear and particle physics . From a theoretical point of view, this is more important than the scattering angle in the laboratory system .

In many cases the forward scattering is much stronger than the scattering in other directions, so it has a comparatively large differential cross section . An example familiar from everyday life is the scattering of light by dust particles in the air: if you look almost in the direction of the light source (for example, when sunlight falls into a dark room), the dust particles can be clearly seen as bright points. Something similar happens with fine water droplets.

The scatter in the backward direction ( ) is usually weaker in the context of classical physics than in all other directions, but due to quantum mechanical effects or interference effects it can be stronger than the scatter in neighboring directions. Coherent backscattering is also responsible for the high brightness of the full moon. ${\ displaystyle \ theta = 180 ^ {\ circ}}$

## Classic spread

The classical mechanics differs collisions between rigid bodies of the scattering at a potential. For orbital movement of a point mass in a potential that decreases linearly with distance, there are always equations that describe a conic section : hyperbola, parabola, or ellipse. A positive, i.e. repulsive, potential always leads to hyperbolas. Attractive potentials lead to ellipses if the energy of the collision partner is not large enough. In this sense the movement of a comet is also the scattering at the gravitational potential of the sun.

## Interaction between electromagnetic radiation and matter

Elastic dispersion
Inelastic scattering
Compton scattering

The following is a schematic illustration of the interaction of a photon with an atom. The horizontal lines represent the discrete excited states of the atom, which the electron shown as a point can occupy. The bottom line corresponds to the energetic basic state.

### Thomson scattering

The coherent interaction with a (quasi) free electron is called Thomson scattering. However, the energy of the scattered photon does not change.

### Compton scattering

As Compton scattering is called the incoherent process, in which a photon is scattered at a free or only weakly bound electron. When an atom is scattered by the electron, it is ionized by this process and a photoelectron and a photon of reduced energy are emitted. This scatter is elastic because the sum of the kinetic energy before and after the collision is identical. For an inelastic process, kinetic energy would also have to be converted into internal energy, with internal degrees of freedom being excited, which an electron does not have.

### Rayleigh scattering

The scattering process is coherent, i.e. it maintains coherence . The energy ( h  is Planck's quantum of action ,  the frequency) of the incident photon is too small to excite the atom. The scattering takes place on bound electrons, whereby the energy of the scattered photon does not change. In the classic limit case, that is, a large wavelength of the photon compared to the Bohr radius of the atom, one speaks of Rayleigh scattering . A special feature is that the scattering cross-section  σ depends very strongly on the frequency and increases proportionally to . A frequency that is twice as high is scattered 2 4 times (= 16 times) more, this is the cause of the sky blue and the sunset. ${\ displaystyle E = h \ nu}$${\ displaystyle \ nu}$${\ displaystyle \ nu ^ {4}}$

### Raman scattering

With Raman scattering, which is inelastic in itself, a discrepancy between the energy of the scattered light quantum and the energy of the incident light quantum is observed . The energy difference is exactly the excitation energy of a rotation or oscillation of the molecule (in the first order Raman effect). This energy difference is given off to the atom or is absorbed by the photon. The energy of the scattered photon is then (energy transfer to the molecule) or (energy absorption from the light quantum). ${\ displaystyle E = h \ nu}$${\ displaystyle \ Delta E}$${\ displaystyle h \ nu - \ Delta E}$${\ displaystyle h \ nu + \ Delta E}$

### Resonance absorption, spontaneous emission, fluorescence and phosphorescence

If the energy of an incoming photon corresponds exactly to the difference between two discrete energy levels , the photon is absorbed by the atom (one also speaks of resonance absorption ). The atom is then in an excited state that can decay through various channels. Followed within a short time, the emission of a photon of similar frequency, it is called fluorescence . The energy of the fluorescence photon can be lower than the radiated energy due to non-radiating relaxation processes in the atom. The lifetime of the excited state (s) is typically a few nanoseconds (see fluorescence lifetime ). If the dwell time is significantly longer than a few nanoseconds, then one speaks of phosphorescence (phosphorescence transitions are often spin-forbidden transitions). Note that in both cases the emitted and absorbed photon do not have a fixed phase relationship, so it is an incoherent scattering process. ${\ displaystyle \ Delta E}$

### Stimulated emission

stimulated emission

With stimulated emission , an existing excited atom is excited to emit a second, coherent photon by a photon irradiated with the appropriate energy.

### Photo effect

Photo effect

An absorption process in which an electron takes over the full energy of the photon is known as the photoelectric effect . For this, a certain bond strength of the electron is necessary for reasons of kinematics ; therefore the cross-section for the photoelectric effect is greatest in the innermost shell (K-shell) of heavy atoms.

This is actually not a scattering process, but rather an absorption process, since afterwards there is no longer a scattered photon. In photoelectron spectroscopy , one looks at the triggered photoelectrons, distinguishing among other things the excitation with UV and X-rays ( UPS or XPS ).

## Multiple scattering

The lateral expansion of a thin pencil beam of charged particles at the potential of the nuclei of a medium is described by the Molière theory . The first order is a Gaussian beam profile. However, multiple scattering leads to higher terms, which lead to a higher kurtosis , that is, an increased expansion of the beam. See also Molière radius .

## Resonance scattering

For low potential wells of the size of the Compton wavelength , resonant scattering occurs, which is coherent but out of phase. The phase difference provides information about the potential depth.

## Deep inelastic scattering

From the angular distribution of the collision partners, the energies after the collision and the course of the cross-section for different input energies, data on composition ( parton ), shape ( form factor ), potential behavior ( Yukawa potential ) and coupling constants can be obtained. In addition, the phase diagram of the nuclear matter can be measured (see Quark-Gluon-Plasma ).

## literature

• Gustav Mie: Contributions to the optics of cloudy media, especially colloidal metal solutions . In: Annals of Physics . tape 25 , no. 3 , 1908, pp. 377–445 , doi : 10.1002 / andp.19083300302 (free full text).
• Ludvig Lorenz: Lysbevaegelsen i og uden for en af ​​plane Lysbolger belyst Kugle. Det Kongelige Danske Videnskabernes Selskabs Skrifter, 6. Raekke, 6. Bind, 1890, 1, pp. 1-62.
• Ludvig V. Lorenz: Sur la lumière réfléchie et réfractée par une sphère transparente . In: Œuvres scientifiques de L. Lorenz, revues et annotées par H. Valentiner . Librairie Lehmann et Stage, Copenhagen 1898, p. 403-529 .