Positron production, from

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. 

Note that <727 — 00 as v — 0, although the annihilation rate, which is proportional to the product W27, remains finite. At low incident positron energies the two gamma-rays are emitted almost collinearly, the energy of each being close to me2 (= 511 keV). Annihilation of a small fraction of the positrons emanating from the radioactive source can occur at relativistic speeds and then it is necessary to use the full equation (1.2). 

When using an electron accelerator, fast positrons are produced by pair production from bremsstrahlung gamma-rays generated as the high energy electrons from the accelerator slow down in matter, whereas with cyclotrons and reactors, very intense primary positron sources are produced directly. Slow positron beams are then produced and transported using similar techniques to those described previously in this section. 

The primary cosmic rays propagate through the interstellar medium (ISM) until they either escape into extragalactic space, or are removed by interaction or energy losses in the ISM. Their interstellar equilibrium intensity may be recorded with a detector which is usually carried above the earth s atmosphere on spacecraft or balloon. Secondary cosmic rays are those that are generated as products from interactions of the primaries in the ISM positrons and antiprotons mostly come from interactions of primary protons, while the secondary nuclei such as Li, Be, B, and the elements just below iron, which cannot be produced by primary nucleosynthesis, are the products of spallation reactions of heavier primaries in the ISM. The overall arriving cosmic-ray intensity represents a mix of primary and secondary particles. 

The time-dependence of the energy levels in a supercritical heavy-ion collision is depicted in Figure 8.33. An electron (or hole) which was in a certain molecular eigenstate at the beginning of the collision can be transfered with a certain probability into different states by the dynamics of the collision. This can lead to the hole production in an inner shell by excitation of an electron to a higher state and/or hole production by ionization of an electron to the continuum. Further possibilities are induced positron production by excitation of an electron from the lower continuum to an empty bound level and direct pair production [59]. 

Irene Joliot-Curie (daughter of Pierre and Marie Curie) and her husband Frederic Joliot-Curie observed that when aluminum-27 is bombarded with alpha particles, neutrons and positrons (positive electrons) are emitted as part of the products. When the source of alpha particles is removed, neutrons cease to be produced, but positrons continue to be emitted. This observation suggested that the neutrons and positrons come from two separate reactions. It also indicated that a product of the first reaction is radioactive. After further investigation, they discovered that, when aluminum-27 is bombarded with alpha particles, phosphorus-30 and neutrons are produced. Phosphorus-30 is radioactive, has a half-life of 2.5 minutes, and decays to silicon-30 with the emission of a positron. The equations for these reactions are... 

Because the water produced is not radioactive, methyl acetate foms by the first reaction, where all of the oxygen-18 ends up in methyl acetate. 55. 2 neutrons 4 / particles 57. Strontium. Xe is chemically unreactive and not readily incorporated into the body. Sr can be easily oxidized to Si +. Strontium is in the same family as calcium and could be absorbed and concentrated in the body in a fashion similar to Ca. The chemical properties determine where radioactive material may be concentrated in the body a how easily it may be excreted. 59. a. unstable beta production b. stable c. unstable positron production or electron capture d. unstable, positron production, electron capture, or alpha production. 61. 3800 decays/s 63. The third-life will be the time required for the number of nuclides to reach one-third of the original value (No/3). The third-life of this nuclide is 49.8 years. 65. 1975 67. 900 g 5u 69. 7 X 10 m/s 8 X 10- J/nu-clei 71. All evolved 02(g) comes from water. 79. 77% and 23% 81. Assuming that (1) the radionuclide is long lived enough that no signiheant decay occurs during the time of the experiment, and (2) the total activity is uniformly distributed only in the rat s blood, V = 10. mL. 83. a. 1 C b. N, c, N, UQ, and =N c. -5.950 X 10 J/mol H 85. 4.3 X 10- 87.-H Ne - g Bh -H 4 Jn 62.7 s [Rn 7 5f 6d ... 

Like positron emission, electron capture is never observed directly. However, after electron capture, the product atom is missing one of its 1 J electrons, as shown schematically in Figure 22-6b. When an electron from an outer orbital occupies this vacancy in the 1 orbital, a photon is emitted whose energy falls in the X-ray region of the... 

When a positron is emitted from a nucleus, it can combine with an electron to produce energy. Show that the following equations, when combined, yield exactly the number of electrons required for the product nucleus. 

The first reaction is a fusion of two protons to produce a 2H nucleus, a positron (e+) and a neutrino (ve). The second reaction is a proton capture with the formation of 3He and a y-ray. In the third reaction two 3He nuclei fuse to give 4He and two protons. The total energy released in one cycle is 26.8 MeV or 4.30 x 10-12 J. An important product of this process is the neutrino and it should provide a neutrino flux from the Sun that is measurable at the surface of the Earth. However, the measured flux is not as big as calculated for the Sun - the so-called neutrino deficit... 

FIGURE 34-3 Positron emission tomography using 13NH3 showing increased brain ammonia uptake in a patient with liver cirrhosis and mild hepatic encephalopathy. CMRA, cerebral metabolic ratio for ammonia HE, hepatic encephalopathy PS, permeability/surface area product. (With permission from reference [9].)... 

At very high temperatures, above 3 or 4 billion k, silicon is consumed so quickly that positron emission and electron capture reactions which might modify the n/p ratio are largely short-circuited. The weak interaction does not have time to convert any appreciable fraction of protons into neutrons during the brief period of thermonuclear combustion. It follows that, starting with matter that is initially dominated by nuclei containing equal numbers of neutrons and protons, such as oxygen-16 and silicon-28, the final products must conserve Z = N, unless they move away from nuclear stability beyond calcium-40, the last stable a element. 

The step 1 product was flow cast on a 25-pan positron emission tomography (PET) film so that the final film thickness was 20 pan then dried at 120°C for 5 minutes. The film was then peeled from the PET film, held onto a metal pin frame, and dried at 150°C for 5 minutes, 200°C for 5 minutes 250°C for 5 minutes, 350°C for 5 minutes, and the product isolated having a Tg of 270°C. 

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