Pair production

Pair production has a threshold energy of 1.022 MeV because two particles are created, one electron and one positron. Thus, some energy is stored in or used to create the mass of the pair. Notice the total electric charge is conserved because the electron charge is — le and the positron charge is +le. One of the unique features of this process is that the energy that went into the creation of the two particles will be released when the positron comes to rest and annihilates with an electron. The annihilation process is 

A neutron will move through material along a straight line with a constant energy until it encounters a nucleus and induces a nuclear reaction. Thus, neutron attenuation follows an exponential law similar to that for photons. Written in terms of an energy-dependent attenuation length, p, we have 

Example Problem Calculate the average thermal neutron capture cross section and the mean free path for LiF, a solid crystalline material at room temperature with a density of 2.635 g/cm3 and a molar mass of 25.94 g/mol. Lithium has two stable isotopes 6Li (7.5%) and 7Li (92.5%) with thermal neutron capture cross sections of ct thermal = 39 mb and 45 mb, respectively. Fluorine is monoisotopic, 19F, with (Tthermal = 9.6 mb. 

Notice that half the atoms are fluorine and half the atoms are lithium, but the lithium atoms are split unevenly between A = 6 and A = 1. The fractions of each isotope must reflect this distribution. 

Rearranging the equation above relating the mean free path and the total reaction cross one has 

Pair production is an interaction between a photon and a nucleus. As a result of the interaction, the photon disappears and an electron-positron pair appears (Fig. 4.20). Although the nucleus does not undergo any change as a result of this interaction, its presence is necessary for pair production to occur. A y-ray will not disappear in empty space by producing an electron-positron pair.  

Conservation of energy gives the following equation for the kinetic energy of the electron and the positron  

The available kinetic energy is equal to the energy of the photon minus 1.022 MeV, which is necessary for the production of the two rest masses. Electron and positron share, for all practical purposes, the available kinetic energy, i.e.. 

Pair production eliminates the original photon, but two photons are created when the positron annihilates (see Sec. 3.7.4). These annihilation gammas are important in constructing a shield for a positron source as well as for the detection of gammas (see Chap. 12). 

The probability for pair production to occur, called the pair production coefficient or cross section is a complicated function of E and Z (see Evans and Roy Reed). It may be written in the form 

The cross-section for the interaction, k, depends upon and Z in a complicated manner which can be expressed as  

It is more than likely that the electron with which the positron annihilates will be bound to an atom. It is necessary, therefore, for some energy to be shared with the atom in order to remove the electron. This means that the energy available to be shared between the annihilation quanta will be lower than expected. For example, in aluminium the annihilation radiation has been estimated to be 510.9957 keV instead of the theoretical 511.0034keV. In everyday gamma-ray spectrometry, the difference is unlikely to be noticed. What is certainly noticeable is the extra width of annihilation gamma-ray peaks due to Doppler broadening, the reason for which I explained in Chapter 1 (Section 1.2.2). 

A more useful coefficient in practical terms is the mass-attenuation coefficient, the ratio of attenuation coefficient to the density of the material  

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In addition to Compton scattering, y-rays having energies above 1022 keV interact with matter by a process called pair production, in which the photon is converted into a positron and an electron. The y-ray energy in excess of the 1022 keV needed to create the pair is shared between the two new particles as kinetic energy. Each j3 -particle is then slowed down and annihilated by an electron producing two 511-keV photons. 

Rays of the highest energy can interact in a third way with matter, namely by pair production. In this process, which begins at about 106 ev and becomes dominant as the energy increases, the 7-ray disappears in the field of a nucleus or of an electron, and there is produced an electron-positron pair. Owing to the energy requirement, pair production is impossible with x-rays commonly used for analytical purposes. 

Electron penetration, of aluminum, 176 of x-ray target, 8, 9 Electron-positron pair production, 290 Element determinations,. bibliography, 328-331... 

P-10 gas, 45, 219 Pair production, 290 Palladium, determination by x-ray emission spectrography, 328 Particle size, effect of variations of, in mineral analysis, 200 Philips Autrometer, 252-256, 280 Philips Electronics gas analyzer, 135 Philips Electronics improved Coolidge tubes, 248, 252, 253... 

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

Pair Production—An absorption process for x- and gamma radiation in which the incident photon is absorbed in the vicinity of the nucleus of the absorbing atom, with subsequent production of an electron... 

Figure 3 shows another example where colliding-beam experiments have produced results in excellent agreement with each other. This particular reaction is the recombination of ions with electrons producing ion-pair products, i.e. ... 

The concentration of small ions in the atmosphere is determined by 1) the rate of ion-pair production by the cosmic rays and radioactive decay due to natural radioactive substances, 2) recombination with negative ions, 3) attachment to condensation nuclei, 4) precipitation scavenging, and 5) transport processes including convection, advection, eddy diffusion, sedimentation, and ion migration under the influence of electric fields. A detailed differential equation for the concentration of short-lived Rn-222 daughter ions including these terms as well as those pertaining to the rate of formation of the... 

Radon daughter ions and the ionization caused by the decay chains of radon and thoron in indoor air play important roles both from the contribution made by the daughter product positive ions to internal dose and from the effects of ion-pair production on the indoor atmospheric electrical parameters. 

Pair production, in which the photon is annihilated in a nuclear interaction giving rise to an electron-positron pair, which carries the energy of the photon less twice the rest energy of the electron. 

There are three methods of attenuating (reducing the energy level of) gamma-rays photoelectric effect, compton scattering, and pair production. 

The ion pair production is independent of the radiation, causing the initial ionization. 

Find the number density of positrons resulting from pair production by y-rays in thermal equilibrium in oxygen at a temperature of 109 K and a density of 1000 gmcm-3, using the twin conditions that the gas is electrically neutral and that the chemical potentials of positrons and electrons are equal and opposite. (At this temperature, the electrons can be taken as non-relativistic.) The quantum concentration for positrons and electrons is 8.1 x 1028 T93/2 cm-3, the electron mass is 511 keV and kT = 86.2 T9 keV. 

Paint technologies, 18 54-55, 56 Paint viscosity, measuring, 18 69 Paired comparison test, 11 512 Paired synthesis, of phthalide and 4.4-butylbenzaldehyde, 9 680-681 PAI resins, properties of, 10 215t Pair production process, 21 313 Palatinit, 12 44... 

The triplet carbenes fluorenylidene 20 and anthronylidene 24, which can be generated from the diazoalkanes by photolysis, show a similar behaviour. Fluorenylidene in cyclohexane yields 9-cyclohexenyl-fluorene 27, and 9,9 -difluo-renyl 22 which are clearly formed by an abstraction-recombination process Another example is anthronylidene 24 in cyclohexane or toluene, which yields the products 25,26,27 resulting from an abstraction-recombination process Benzene, on the contrary, failed to give the radical pair product 20... 

A particularly interesting feature of the theory [9] is the incorporation of deviations from Coulomb scattering due to the nonvanishing size of the projectile nucleus. The very fact that the theory is based on the Dirac equation and that spin dependences enter nontrivially indicates that quantum mechanics is essential here. Moreover, at the highest energies considered, pair production becomes important, i.e., an effect that does not have a classical equivalent [57]. 

Figure 5 X-ray mass attenuation coefficients for aluminum as a function of photon energy. At low energies, photoelectric absorption predominates. At higher energy, incoherent (Compton) scatter becomes almost the exclusive contributing mode. Eventually, pair production dominates at very high energies (above 10 MeV).

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