Annihilating pair, kinetic energy

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. 

Ekln(i) Mean kinetic energy of the annihilating positron-electron pair... 

The bounce shock heats up deleptonized matter and rapidly spends most of its kinetic energy to destroy nuclei and produce plenty of free nucleons (n, p). Modified URCA-processes [38] becomes important e + p n + ve, e++n —> p+ue and pair-neutrino annihilation takes place e++e — ve IL-At the typical collapse temperatures T 10 MeV a lot of z/s is produced [168] However, at densities p 1012 g/cm3 the mean free path of 10 MeV neutrinos is by 5-6 orders of magnitude smaller than the size of the proto neutron star (R 50 km) so the opaque neutrinosphere forms. Most of the core collapse neutrinos diffuse out of the neutrinosphere on a time scale 10 seconds. First calculations of v spectra in core collapse SN were performed by D.K. Nadyozhin [108, 109] We should note that subsequent detailed calculations (e.g. [101] and references therein) did not change much these spectra. Thus, the modest 10% fraction of the total neutrino energy released in the core collapse ( 1053 ergs) would be sufficient to unbind the overlying stellar envelope and produce the phenomenon of type II supernova explosion. 

The fourth mode of interaction for y-rays with an absorber involves conversion in the Coulomb field of the nucleus of a y-ray into an electron and a positron (Fig. 6.18). This process is termed pair production since a pair of electrons, one positive and one negative, is produced. The process can be considered as the inverse phenomenon of positron annihilation. Since the rest mass of an electron corresponds to 0.51 MeV, the y-ray must have a minimum value of 1.02 MeV to interact by pair production. As the energy of the y-ray is increased beyond this value, the probability of pair production increases (see Fig. 6.17, where p is denoted k). The excess energy (above the 1.02 MeV) appears as the kinetic energy of the electron pair. 

In (1) a ic.b Kjaic and b f are boson creation and annihilation operators for the a and b Hartree-Fock particle states with momentum hn and kinetic energy K-h k /2m. pa and pb denote the densities of the component holon gases while pa and pb denote their respective chemical potentials. In equilibrium, pa=Pb-Pt where u is determined by the condition that the statistical average of A Eic (a icaic b Kbic) be equal to p=pa+pb=N/A, the total number of holons per unit area (N , A ). V is taken to satisfy V<pairing interaction. Finally, V is restricted to operate between holons with k[Pg.45]

Since the positron is the antiparticle of the electron, an encounter between them can lead to the subsequent annihilation of both particles. Their combined rest mass energy then appears as electromagnetic radiation. Annihilation can occur via several mechanisms direct transformation into one, two, or three photons or the formation of an intermediate, hydrogen-like bound state between the positron and the electron, known as a positronium (Ps). The extent to which each annihilation mechanism contributes depends on the kinetic energy of the positron-electron pair. 

For pair production the y-rays must have energy greater than 1.02 MeV. The incident ray reacts with electrons and is completely absorbed. Ejection of a positron and an electron (the pair ) takes place. The energy of the ray, if in excess of 1.02 MeV, is transferred to both the members of the pair as kinetic energy. The positron is not long-lived. It combines with a ftee electron and is annihilated with y-ray emission. 

The kinetic energy of the annihilating pair is typically a few electron volts (eV). In their center-of-mass frame, each photon energy is exactly moC = 511keV, and the two photons go strictly in opposite directions that is, the emission direction is collinear to conserve linear momentum (Figure 27.1). Because of the nonzero momentum of the pair, which is due mainly to the finite momentum of the electron of the material medium, the photons deviate from collinearity in the laboratory frame. The momentum conservation law for the transverse component of the momentum yields a result ... 

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