Electron-positron pair creation

A more appropriate spin-orbit coupling Hamiltonian can be derived if electron-positron pair creation processes are excluded right from the beginning (no-pair approximation). After projection on the positive energy states, a variationally stable Hamiltonian is obtained if one avoids expansion in reciprocal powers of c. Instead the Hamiltonian is transformed by properly chosen... 

Electron-Positron Pair Creation in Relativistic Heavy-Ion Collisions... 

Let us first summarize the results of the field-theoretical description of pair creation. For details we may refer to Eichler and Meyerhof (1995) and Strayer et al. (1990). Electron-positron pair creation can be viewed as an excitation of an electron from the (occupied) negative energy continuum into a positive enetgy bound or continuum state... 

Soff, G. (1980) Electron-positron pair creation and K-shell ionisation in relativistic heavy ion collisions. In Proc. XVIII Winter School, Selected Topics in Nuclear Structure, Bielsko-Biala, Polen, p. 201. 

Moreover, electron-positron pair creation and other proce.s.ses ( radiative corrections ) de.scribed by quantum electrodynamics which has quantized degrees of freedom for both the fermions and the electromagnetic field are usually not included in the theory, although the chaige-conjugated degrees of freedom are still there. Therefore the literature often refers to the no virtual pair or, in short, no pair approximatioa Very few calculations go beyond this approximation. " Nevertheless. the no-pair operator based on the DCB Hamiltonian provides an exellent approximation to the full theory, generally sufficient for the determination of relativistic effects in the electronic structure of neutral atoms and molecules. 

Note that the mechanism of ion-pair formation by y particles is not the same as that by a or 0 particles. A y ray itself will not leave behind it a trail of ion pairs but rather collides with free or bound electrons imparting to them all or part of its electromagnetic energy (photoelectric and Compton effects). These secondary electrons are then responsible for formation of ion pairs in matter through which y radiation passes. In cases where the energy of radiation exceeds 1.02 Mev, another process is possible, the creation of electron->positron pairs. 

A further term, which has no analogue in hydrogen, arises in the fine structure of positronium. This comes from the possibility of virtual annihilation and re-creation of the electron-positron pair. A virtual process is one in which energy is not conserved. Real annihilation limits the lifetimes of the bound states and broadens the energy levels (section 12.6). Virtual annihilation and re-creation shift the levels. It is essentially a quantum-electrodynamic interaction. The energy operator for the double process of annihilation and re-creation is different from zero only if the particles coincide, and have their spins parallel. There exists, therefore, in the triplet states, a term proportional to y 2(0). It is important only in 3S1 states, and is of the same order of magnitude as the Fermi spin-spin interaction. Humbach [65] has given an interpretation of this annihi-... 

To not leave the reader with the impression that these extensions are trivial, let us recall that a relativistic reformulation caimot ignore the virtual creation of electron-positron pairs nor the fact that the Breit interaction involves the exchange of transverse photons. 

Note that in both the old and the new definition creation of an electron-positron pair requires approximately twice the rest mass energy and does not influence the total charge. A nice feature of the new formalism is, however, that one may also describe processes that create a positron without generating an associated electron. 

The simplest approximation to this Fock space theory consists in projecting the n-particle Hamiltonian to electronic states, i.e. to ignore the creation of virtual electron-positron pair states, whence the name no-pair theory. The next step after a no-pair theory would be a formalism, in which an n-electron state mixes, e.g. with an (n -1- l)-electron-1-positron state etc.. Not the particle number, but the charge is a constant of motion. In this way one takes care of vacuum polarization, which is a real physical effect. It is, however, not recommended to treat it in such a brute-force way, but rather to use the apparatus of QED. 

Paul Dirac factorized the left side of this equation by treating it as the difference of squares. This gave two continua of energy separated by a gap of width 2monegative energy) continuum is fuUy occupied by electrons (i.e., a vacuum), while the upper continuum is occupied by the single electron (our particle). If we managed to excite an electron from the lower continuum to the ujqier one, then in the upper continuum, we would see an electron, while the hole in the lower continuum would have the properties of a positive electron (positron). This corresponds to the creation of the electron-positron pair from the vacuum. 

Figure 5.1 Sketch of the spectrum of the Dirac Hamiltonian for a free electron (a) and a bound electron in a Coulombic potential attractive for electrons [see chapter 6] (b). In (c) creation of an electron-positron pair is illustrated according to Dirac s hole theory, where all negative-energy states are assumed to be occupied for the vacuum state.

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