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The scattering cross-section, σ < sub > scat </ sub >, is a hypothetical area which describes the likelihood of light ( or other radiation ) being scattered by a particle.
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scattering and cross-section
In general, the scattering cross-section is different from the geometrical cross-section of a particle, and it depends upon the wavelength of light and the permittivity, shape and size of the particle.
The total amount of scattering in a sparse medium is determined by the product of the scattering cross-section and the number of particles present.
In terms of area, the total cross-section ( σ ) is the sum of the cross-sections due to absorption, scattering and luminescence
The Rayleigh scattering cross-section is given by
The Rayleigh scattering coefficient for a group of scattering particles is the number of particles per unit volume N times the cross-section.
the " scattering cross-section ") of one atom.
For ionized hydrogen, where is the Thomson scattering cross-section for the electron and is the mass of a proton.
The effectiveness of a material as a biological shield is related to its cross-section for scattering and absorption, and to a first approximation is proportional to the total mass of material per unit area interposed along the line of sight between the radiation source and the region to be protected.
For wavelengths of light at the energies of one of the Lyman transitions in hydrogen, the scattering cross-section is large, meaning that even for low levels of neutral hydrogen in the intergalactic medium ( IGM ), absorption at those wavelengths is highly likely.
Chung-Yao Chao studied the scattering of gamma rays in lead by pair production in 1930, without knowing that positrons were involved in the anomalously high scattering cross-section.
** The absorption cross section and scattering cross-section are closely related to the absorption and attenuation coefficients, respectively.
For example, the cross-section for Thomson scattering of a photon from an electron is equal to
When the total energy of the objects is close to the energy of the resonance they interact strongly, and their scattering cross-section becomes very large.
Plot of scattering cross-section versus normalized energy for various values of the parameter q illustrating the asymmetric Fano line-shape.
Fano showed that the total scattering cross-section assumes the following form,
In practice P or Q should be chosen such that the resulting background scattering phase or cross-section is slowly depending on the scattering energy in the neighbourhood of the resonances ( this is the so-called flat continuum hypothesis ).
The scattering cross-section can be further subdivided into coherent scattering and incoherent scattering, which is caused by the spin dependence of the scattering cross-section and for a natural sample, presence of different isotopes of the same element in the sample.
scattering and σ
The amount of Rayleigh scattering from a single particle can also be expressed as a cross section σ.
For that reason, the scattering and absorption cross sections σ < sub > S </ sub > and σ < sub > A </ sub > are defined and the total cross section is simply the sum of the two partial cross sections:
scattering and <
The strong wavelength dependence of the scattering (~ λ < sup >− 4 </ sup >) means that shorter ( blue ) wavelengths are scattered more strongly than longer ( red ) wavelengths.
λ < sup >− 4 </ sup > Rayleigh-type scattering can also be exhibited by porous materials.
The λ < sup >− 4 </ sup >- type scattering is caused by the nanoporous structure ( a narrow pore size distribution around ~ 70 nm ) obtained by sintering monodispersive alumina powder.
No dark matter signal has been found, but for WIMP masses of 24 Gev / c < sup > 2 </ sup > new stringent limits have been obtained on the spin-dependent cross section for WIMP scattering on < sup > 19 </ sup > F of 13. 9 pb ( 90 % CL ).
The intensity of Thomson scattering declines as 1 / m < sup > 2 </ sup > with the mass m of the charged particle that is scattering the radiation ; hence, the atomic nuclei, which are thousands of times heavier than an electron, contribute negligibly to the scattered X-rays.
Neutron scattering also has the remarkable property that the solvent can be made invisible by adjusting the ratio of normal water, H < sub > 2 </ sub > O, and heavy water, D < sub > 2 </ sub > O.
Since no energy is lost ( elastic, not inelastic scattering ), the wavelengths are the same as are the magnitudes of the wave-vectors | k < sub > in </ sub >|=| k < sub > out </ sub >|.
Both k < sub > out </ sub > and k < sub > in </ sub > have the same length, due to the elastic scattering, since the wavelength has not changed.
In this expression, W < sub > c, v </ sub >( E ) represents the product of the Brillouin zone-averaged transition probability at the energy E with the joint density of states, J < sub > c, v </ sub >( E ); φ is a broadening function, representing the role of scattering in smearing out the energy levels.
( QuickTime movies of this for H + H < sub > 2 </ sub > reactive scattering can be found on the Wyatt group web-site at UT Austin.
These predictions were confirmed by the experiments of Chang and Jones on commercial glasses and glass ceramics, where mean free paths were limited by " internal boundary scattering " to length scales of 10 < sup >− 2 </ sup > cm to 10 < sup >− 3 </ sup > cm.
Therefore, these processes are also known as Umklapp ( U ) processes and can only occur when phonons with sufficiently large q-vectors are excited, because unless the sum of q < sub > 2 </ sub > and q < sub > 3 </ sub > points outside of the Brillouin zone the momentum is conserved and the process is normal scattering ( N-process ).
The following table shows the scattering lengths for various elements ( in 10 < sup >− 12 </ sup > cm ).
This scattering mechanism is the primary cause of the blue color of the Earth's sky on a clear day, as the shorter blue wavelengths of sunlight passing overhead are more strongly scattered than the longer red wavelengths according to Rayleigh's famous 1 / λ < sup > 4 </ sup > relation.
The use of a coherent state to represent the superfluid component of < sup > 4 </ sup > He provided a good estimate of the condensate / non-condensate fractions in superfluidity, consistent with results of slow neutron scattering.
The neutron scattering lengths b < sub > H </ sub >
scattering and >
/ math > is the scattering angle.
scattering and >,
The cross section for the photoelectric process is proportional to Z < sup > 5 </ sup >, that for pair production proportional to Z < sup > 2 </ sup >, whereas Compton scattering goes roughly as Z.
From these two energies, E < sub > 1 </ sub > and E < sub > 2 </ sub >, the Compton scattering angle, angle θ, can be determined, along with the total energy, E < sub > 1 </ sub > + E < sub > 2 </ sub >, of the incident photon.
When three wavelengths (&# 955 ;< sub > 1 </ sub >, &# 955 ;< sub > 2 </ sub >, and &# 955 ;< sub > 3 </ sub >) interact in a nonlinear medium, they give rise to a fourth wavelength (&# 955 ;< sub > 4 </ sub >) which is formed by the scattering of the incident photons, producing the fourth photon.
* Johnson, W. R., and Guet, C., “ Elastic scattering of electrons from Xe, Cs < sup >+</ sup >, and Ba < sup > 2 +</ sup >, Phys.
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In practice, a bidirectional reflectance distribution function ( BRDF ) may be required to characterize the scattering properties of a surface accurately, although the albedo is a very useful first approximation.
Another source of background absorption, particularly in ET AAS, is scattering of the primary radiation at particles that are generated in the atomization stage, when the matrix could not be removed sufficiently in the pyrolysis stage.
This obviously also includes a reduction of the measured intensity due to radiation scattering or molecular absorption, which is corrected in the same way.
* Autocorrelation is used to analyze Dynamic light scattering data, which notably enables to determine the particle size distributions of nanometer-sized particles or micelles suspended in a fluid.
* The Small-angle X-ray scattering intensity of a nanostructured system is the Fourier transform of the spatial autocorrelation function of the electron density.
Some colloids are translucent because of the Tyndall effect, which is the scattering of light by particles in the colloid.
Multiple light scattering coupled with vertical scanning is the most widely used technique to monitor the dispersion state of a product, hence identifying and quantifying destabilisation phenomena.
As a rule of thumb, a scattering or a decay process is cosmologically important in a certain cosmological epoch if the time scale describing that process is smaller or comparable to the time scale of the expansion of the universe, which is with being the Hubble constant at that time.
Visible light has energy on the scale of 1 eV and is used as a scattering probe to measure variations in material properties such as dielectric constant and refractive index.
In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism.
Cosmologists refer to the time period when neutral atoms first formed as the recombination epoch, and the event shortly after of photons starting to travel freely through space rather than constantly scattering with electrons and protons in plasma is referred to as photon decoupling.
A cross section is the effective area which governs the probability of some scattering or absorption event.
A particular case is scattering.
The K-corona ( K for kontinuierlich, " continuous " in German ) is created by sunlight scattering off free electrons ; Doppler broadening of the reflected photospheric absorption lines completely obscures them, giving the spectral appearance of a continuum with no absorption lines.
A diaspora ( from Greek διασπορά, " scattering, dispersion ") is " the movement, migration, or scattering of people away from an established or ancestral homeland " or " people dispersed by whatever cause to more than one location ", or " people settled far from their ancestral homelands ".
In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc.
Multiple light scattering, coupled with vertical scanning, is the most widely used technique to monitor the dispersion state of a product that exists as an emulsion.
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