Positron principle

External fields are introduced in the relativistic free-particle operator hy the minimal substitutions (17). One should at this point carefully note that the principle of minimal electromagnetic coupling requires the specification of particle charge. This becomes particularly important for the Dirac equation which describes not only the electron, but also its antiparticle, the positron. We are interested in electrons and therefore choose q = — 1 in atomic units which gives the Hamiltonian... 

Eowler JS,Wolf AP (1986) Positron emitter-labelled compounds priorities and problems. In Phelps M, Mazziotta J, Schelbert H (eds) Positron emission tomography and anto-radiography principles and applications for the brain and heart. Raven Press. New York,... 

If the kinetic balance condition (5) is fulfilled then the spectrum of the L6vy-Leblond (and Schrodinger) equation is bounded from below. Then, in each case there exists the lowest value of E referred to as the ground state. In effect, this equation may be solved using the variational principle without any restrictions. On the contrary, the spectrum of the Dirac equation is unbounded from below. It contains the negative ( positronic ) continuum. Therefore the variational principle applied unconditionally would lead to the so called variational collapse [2,3,7]. The variational collapse maybe avoided by properly selecting the trial functions so that they fulfil the boundary conditions specific for the bound-state solutions [1]. 

Camici P, Ferrannini E, Opie LH. Myocardial metabolism in ischemic heart disease basic principles and application to imaging by positron emission tomography. Prog Cardiovasc Dis 1989 32 217-238... 

Huang, S.C., Phelps, M.E. Principles of tracer kinetic modeling in positron emission tomography and autoradiography. In Phelps. M.E.. Mazziota. J., Schelbert H. (eds) Positron Emission Tomography and Autoradiography Principles and Applications for the Brain and Heart. Raven Press, New York, 1986. 

Another type of symmetry of importance in elementary particle physics is that entitled charge conjugation. This principle slates that if each particle in a given isolated system is replaced by its corresponding anliparticle, then no difference can be observed. For example, if. in a hydrogen atom, the proton is replaced by an anti-proton and the electron is replaced hy a positron, then this antimatter atom will behave exactly like an ordinary atom, so long as it does not come inlo contact with ordinary atoms. 

As a final point in the introduction, it is interesting to note that the analogous process of positron capture by neutron excessive nuclei should be possible in principle. However, such captures are hindered by two important facts First, the number of positrons available for capture is vanishingly small in nature, and second, both the nucleus and the positron are positively charged and will repel one another. Compare this to the situation for electron capture in which the nucleus is surrounded by (negative) electrons that are attracted to the nucleus, of course, and the most probable position to find any s electrons is at the nucleus (r = 0). 

The next paper was by Dirac on the Theory of the Positron. In the following discussion Niels Bohr made a long intervention on the correspondence principle in connection with the relation between the classical theory of the electron and the new theory of Dirac. 

The new proposed deuteron model is founded on the principles of SLRT and QMT. In Ref. 4, where QMT is presented, it is shown that, if the electron in the hydrogen atom is excited to the state of the potential quantum number, n = 794 then, the electron turns into a positron. The consequence is very unusual the hydrogen atom turns into a system of one proton and one positron, which is undoubtedly a very odd example of CP violation. This has been obtained as a result of theoretical analysis based on the QMT principles. If this is experimentally proved, then atoms with very unusual physical characteristics will certainly be obtained, and a rather exotic regime of matter could be expected. 

The recent advances in producing, trapping and cooling antiprotons and positrons opened the possibility of antihydrogen formation in laboratory. This may allow the studies of antimatter and tests of fundamental physical principles such as charge - parity - time ( CPT ) invariance or the weak equivalence principle (WEP) for antiparticles. Such experiments are planned at the newly built CERN AD (Antiproton Decelerator) within ASACUSA, ATRAP and ATHENA projects, which have just started their operations. 

Measurements of daPs/dQ for positron-argon scattering have also been made by Finch et al. (1996a, b) and Falke et al. (1995, 1997) and for positron-krypton scattering by Falke et al. (1997). The principle of the experiments, involving the detection of the positronium in coincidence with an atomic ion, is illustrated schematically in Figure 4.28. More details of the system used by Finch et al. (1996a), which has also been used to study the differential ionization cross section, can be found in section 5.6. 

Fig. 4.28. Schematic illustrating the principle of angle-resolved measurements of positronium formation in positron-gas collisions (following Falke et at, 1997). Reprinted from Journal of Physics B30, Falke et al, Differential Ps-formation and impact-ionization cross sections for positron scattering on Ar and Kr atoms, 3247-3256, copyright 1997, with permission from IOP Publishing.

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