The angular distribution (cross-sections) of photons scattered from a single free electron is described by the Klein-Nishina formula. Cross-Section of Compton Scattering

Compton Scattering

Compton Scattering – Cross-Sections

The probability of Compton scattering per one interaction with an atom increases linearly with atomic number Z, because it depends on the number of electrons, which are available for scattering in the target atom. The angular distribution of photons scattered from a single free electron is described by the Klein-Nishina formula:where ε = E_{0}/m_{e}c^{2} and r_{0} is the “classical radius of the electron” equal to about 2.8 x 10^{-13} cm. The formula gives the probability of scattering a photon into the solid angle element dΩ = 2π sin Θ dΘ when the incident energy is E_{0}.

Cross section of compton scattering of photons by atomic electrons..Energies of a photon at 500 keV and an electron after Compton scattering.

See also:

Compton Formula

See also:

Compton Scattering

See also:

Compton Edge

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In spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. Radiation Dosimetry

Compton Scattering

Compton Edge

In spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. This feature is due to photons that undergo Compton scattering with a scattering angle of 180° and then escape the detector. When a gamma ray scatters off the detector and escapes, only a fraction of its initial energy can be deposited in the sensitive layer of the detector. It depends on the scattering angle of the photon, how much energy will be deposited in the detector. This leads to a spectrum of energies. The Compton edge energy corresponds to full backscattered photon.

See also:

Cross-Section of Compton Scattering

See also:

Compton Scattering

See also:

Inverse Compton Scattering

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Inverse Compton scattering is the scattering of low energy photons to high energies by relativistic electrons. Radiation Dosimetry

Compton Scattering

Inverse Compton Scattering

Inverse Compton scattering is the scattering of low energy photons to high energies by relativistic electrons. Relativistic electrons can boost energy of low energy photons by a potentially enormous amount (even gamma rays can be produced). This phenomenon is very important in astrophysics.

See also:

Compton Edge

See also:

Compton Scattering

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The sum of the three partial cross-sections is called the linear attenuation coefficient. Gamma rays attenuation. Radiation Dosimetry

The total cross-section of interaction of a gamma rays with an atom is equal to the sum of all three mentioned partial cross-sections:σ = σ_{f} + σ_{C} + σ_{p }

σ_{f} – Photoelectric effect

σ_{C} – Compton scattering

σ_{p} – Pair production

Depending on the gamma ray energy and the absorber material, one of the three partial cross-sections may become much larger than the other two. At small values of gamma ray energy the photoelectric effect dominates. Compton scattering dominates at intermediate energies. The compton scattering also increases with decreasing atomic number of matter, therefore the interval of domination is wider for light nuclei. Finally, electron-positron pair production dominates at high energies.Based on the definition of interaction cross-section, the dependence of gamma rays intensity on thickness of absorber material can be derive. If monoenergetic gamma rays are collimated into a narrow beam and if the detector behind the material only detects the gamma rays that passed through that material without any kind of interaction with this material, then the dependence should be simple exponential attenuation of gamma rays. Each of these interactions removes the photon from the beam either by absorbtion or by scattering away from the detector direction. Therefore the interactions can be characterized by a fixed probability of occurance per unit path length in the absorber. The sum of these probabilities is called the linear attenuation coefficient:

The attenuation of gamma radiation can be then described by the following equation.

I=I_{0}.e^{-μx}

, where I is intensity after attenuation, I_{o} is incident intensity, μ is the linear attenuation coefficient (cm^{-1}), and physical thickness of absorber (cm).

The materials listed in the table beside are air, water and a different elements from carbon (Z=6) through to lead (Z=82) and their linear attenuation coefficients are given for three gamma ray energies. There are two main features of the linear attenuation coefficient:

The linear attenuation coefficient increases as the atomic number of the absorber increases.

The linear attenuation coefficient for all materials decreases with the energy of the gamma rays.

Dependence of gamma radiation intensity on absorber thickness.The relative importance of various processes of gamma radiation interaction with matter.Linear Attenuation CoefficientsTable of Linear Attenuation Coefficients (in cm-1) for a different materials at gamma ray energies of 100, 200 and 500 keV.

The half value layer expresses the thickness of absorbing material needed for reduction of the incident radiation intensity by a factor of two. Radiation Dosimetry

Half Value Layer

The half value layer expresses the thickness of absorbing material needed for reduction of the incident radiation intensity by a factor of two. There are two main features of the half value layer:

The half value layer decreases as the atomic number of the absorber increases. For example 35 m of air is needed to reduce the intensity of a 100 keV gamma ray beam by a factor of two whereas just 0.12 mm of lead can do the same thing.

The half value layer for all materials increases with the energy of the gamma rays. For example from 0.26 cm for iron at 100 keV to about 1.06 cm at 500 keV.

The half value layer expresses the thickness of absorbing material needed for reduction of the incident radiation intensity by a factor of two. With half value layer it is easy to perform simple calculations.
Source: www.nde-ed.org

Table of Half Value Layers (in cm) for a different materials at gamma ray energies of 100, 200 and 500 keV.

Absorber

100 keV

200 keV

500 keV

Air

3555 cm

4359 cm

6189 cm

Water

4.15 cm

5.1 cm

7.15 cm

Carbon

2.07 cm

2.53 cm

3.54 cm

Aluminium

1.59 cm

2.14 cm

3.05 cm

Iron

0.26 cm

0.64 cm

1.06 cm

Copper

0.18 cm

0.53 cm

0.95 cm

Lead

0.012 cm

0.068 cm

0.42 cm

See also:

Pair Production

See also:

Gamma Ray Attenuation

See also:

Mass Attenuation Coefficient

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The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). Radiation Dosimetry

Mass Attenuation Coefficient

When characterizing an absorbing material, we can use sometimes the mass attenuation coefficient. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of gamma radiation can be then described by the following equation:

I=I_{0}.e^{-(μ/ρ).ρl}

, where ρ is the material density, (μ/ρ) is the mass attenuation coefficient and ρ.l is the mass thickness. The measurement unit used for the mass attenuation coefficient cm^{2}g^{-1}.For intermediate energies the Compton scattering dominates and different absorbers have approximately equal mass attenuation coefficients. This is due to the fact that cross section of Compton scattering is proportional to the Z (atomic number) and therefore the coefficient is proportional to the material density ρ. At small values of gamma ray energy or at high values of gamma ray energy, where the coefficient is proportional to higher powers of the atomic number Z (for photoelectric effect σ_{f} ~ Z^{5}; for pair production σ_{p} ~ Z^{2}), the attenuation coefficient μ is not a constant.

See also:

Half Value Layer

See also:

Gamma Ray Attenuation

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A neutrino is an elementary subatomic particle with infinitesimal mass and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin. Radiation Dosimetry

A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos belong to the family of leptons, which means they do not interact via strong nuclear force. Neutrinos are weakly interacting subatomic particles with ½ unit of spin. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). There are three types of charged leptons, each associated with neutrino, forming three generations (between generations, particle differ by their quantum number and mass). The first generation consist of the electron (e^{−}) and electron-neutrino (ν_{e}). The second generation consist of the muon (μ^{−}) and muon neutrino (ν_{μ}) The third generation consist of the tau (τ^{−}) and the tau neutrino (ν_{τ}). Each type of neutrino is associated with an antimatter particle, called an antineutrino, which also has neutral electric charge and 1/2 spin. Currently (2015), it is not resolved, whether the neutrino and its antiparticle are not identical particles.

Carrying no electric charge they are not affected by electromagnetic forces that act on another charged leptons, such as electrons. Since neutrinos belong to the family of leptons, they are not subject to the strong force. Neutrinos are subject to the weak force, which is of much shorter range than electromagnetic force and gravity force. Therefore, neutrinos are the most penetrating subatomic particles, capable of passing through Earth without any interaction. It is estimated neutrinos have interaction cross-sections about 20 orders of magnitude less than typical cross-sections of scattering of two nucleons (~10^{-47}m2 = 10^{-19}barn). It is estimated neutrino cross-section for interaction increases linearly with energy of incident neutrino.

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

Source: wikipedia.orgThe inside of a cylindrical antineutrino detector before being filled with clear liquid scintillator, which reveals antineutrino interactions by the very faint flashes of light they emit. Sensitive photomultiplier tubes line the detector walls, ready to amplify and record the telltale flashes.
Photo: Roy Kaltschmidt, LBNL
Source: Daya Bay Reactor Neutrino Experiment

Discovery of the Neutrino

Discovery of the Neutrino

The study of beta decay provided the first physical evidence for the existence of the neutrino. The discovery of the neutrino is based on the law of conservation of energy during the process of beta decay.

In both alpha and gamma decay, the resulting particle (alpha particle or photon) has a narrow energy distribution, since the particle carries the energy from the difference between the initial and final nuclear states. For example, in case of alpha decay, when a parent nucleus breaks down spontaneously to yield a daughter nucleus and an alpha particle, the sum of the mass of the two products does not quite equal the mass of the original nucleus (see Mass Defect). As a result of the law of conservation of energy, this difference appears in the form of the kinetic energy of the alpha particle. Since the same particles appear as products at every breakdown of a particular parent nucleus, the mass-difference should always be the same, and the kinetic energy of the alpha particles should also always be the same. In other words, the beam of alpha particles should be monoenergetic.

It was expected that the same considerations would hold for a parent nucleus breaking down to a daughter nucleus and a beta particle. Because only the electron and the recoiling daughter nucleus were observed beta decay, the process was initially assumed to be a two body process, very much like alpha decay. It would seem reasonable to suppose that the beta particles would form also a monoenergetic beam.

To demonstrate energetics of two-body beta decay, consider the beta decay in which an electron is emitted and the parent nucleus is at rest, conservation of energy requires:

Since the electron is much lighter particle it was expected that it will carry away most of the released energy, which would have a unique value T_{e-}.

But the reality was different. The spectrum of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background, however. Moreover virtually all of the emitted beta particles have energies below that predicted by energy conservation in two-body decays. The electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. When this was first observed, it appeared to threaten the survival of one of the most important conservation laws in physics!

To account for this energy release, Pauli proposed (in 1931) that there was emitted in the decay process another particle, later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

Production of Neutrinos

Neutrinos can be produced in several ways. The most powerful source of neutrinos in the solar system is doubtless the Sun itself. Billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6 x 10^{10} cm^{-2}s^{-1}) on the Earth’s surface. In the Sun, neutrinos are produced after fusion reaction of two protons during positive beta decay of helium-2 nucleus.

Each nuclear reactor is also very powerful source of neutrinos. In fact, antineutrinos. In a nuclear reactor occurs especially the β^{−} decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β^{−} decay, where the neutron is converted into a proton, an electron, and an electron antineutrino.

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

See also:

Fundamental Particles

See also:

Antineutrino

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