Positron annihilation valences

It should be noted that there are some experimental measurements (such as positron annihilation) which are apparently inconsistent with these valences. The difficulty arises from the fact that, although this valency scheme is useful and is consistent with many experimental facts, it is an over simplified description of the electronic nature of cerium and its alio tropes. This problem is dealt with in the discussions concerning the various models proposed to explain the a y transformation and the electronic nature of a, a and y phases (sections 5.1-5.7). 

Measurements of the Doppler broadening of the annihilation radiation produced by various molecules has been related to annihilation at specific sites within molecules by Iwata, et al. [15]. Prom the observed 7-ray spectra, the line width of the dominate peak, which comes from valence electrons, was extracted. Thus, for each molecule there is a single measured quantity, the fine width. For a series of hydrocarbons, the observed fine widths were found to be linear in the fraction of electrons in C-C (or C-H) bonds. Each type of bond was assumed to contain two electrons. Prom a linear fit of this data, fine widths for the C-C and C-H bonds were extracted and found to be 2.06 and 2.42 keV, respectively. These agree reasonably with an old theoretical estimate in which the positron density was assumed to be constant over the molecule [16]. ... 

For DBES data three main factors contribute to the S parameter in polymers (1) free-volume content, (2) free-volume size, and (3) chemical composition. First, larger free-volume content contributes to a larger S value. DBES measures radiation near 511 keV where a major contribution comes from p-Ps. This p-Ps contribution is only 1/3 the o-Ps intensity as that in I3 of PAL data. Second, when p-Ps is localized in a defect with a dimension fix, the momentum Ap has a dispersion according to the Heisenburg uncertainty principle AxAp > h/4n. The S parameter from DBES spectra is a direct measure of the quantity of momentum dispersion. In a larger size hole where Ps is localized, there will be a larger S parameter due to smaller momentum uncertainty. Therefore, in a system with defects or voids, such as polymers, the S parameter is a qualitative measure of the defect size and defect concentration. The value of the S parameter also depends on the momentum of the valence electrons, which annihilate with the positrons. The absolute value of the S parameter therefore, may differ from polymer to polymer. Third, the S parameter depends on the electron momentum of the elements. As the atomic number of the elements increases, the electron momentum increases, and thus the S parameter decreases. Fortunately, in chemicals of... 

Here is an intriguing idea the polarization approximation should be an extremely good approximation for the interaction of a molecule with an antimolecule (built from antimatter). Indeed, in the molecule we have electrons in the antimolecule positrons, and no antisjmunetrization (between the systems) is needed. Therefore, a product wave function should be a very good starting point. No valence repulsion will appear, and the two molecules will penetrate like ghosts. Soon after the annihilation takes place and the system disappear . 

Fig. 3.4. (a) The electric field dose to the proton (composed of three quarks) is so strong that it creates matter and antimatter (shown as electron-positron pairs). The three quarks visible in scattering experiments represent the valence quarks, (b) One of the radiative effects in the QED correction of the c order (see Table 3.1). The pictures show the sequence of the events from left to the right A photon (wavy line on the left) polarizes the vacuum and an electron-positron pair (solid lines) is created, and the photon vanishes. Then the created particles annihilate each other and a photon is created, (c) A similar event (of the order in QED), but during the existence of the electron-positron pair the two particles interact by exchange of a photon, (d) An electron (horizontal solid line) emits a photon, which creates an electron-positron pair, that annihilates producing another photon. Meanwhile the first electron emits a photon, then first absorbs the photon from the annihilation, and afterwards the photon emitted by itself earlier. This effect is of the order c in QED. 

When a positron enters a solid, it thermalizes in a time much shorter (few picoseconds) than its lifetime (few hundred of picoseconds). At the time of annihilation, the positron has diffused over a certain distance (few hundreds of nm). This diffusion process is critical to determine the state of the electron-positron pair at the time of annihilation the positron migrates in a region energetically favorable, namely the interstitial region of the lattice. The positron might also be trapped if it reaches a defect and experiences a longer lifetime. Otherwise, it annihilates with an electron in the valence or conduction band. Observing the annihilation radiation provides information on the electronic structure in momentum space. 

In a real system, the positron exists in different states. It may annihilate either with valence or conduction electrons of the bulk. These processes give rise to a bulk annihilation rate Ab. It may also be trapped in various defect states Dj where the electron density is smaller than in the bulk, i.e. a single vacancy, a cluster of vacancies, dislocations, impurities etc. Each defect state will be characterized by an annihilation rate Dj- In a vacancy-like defect the trapped-positron lifetime is increased compared to free positrons aimihilating in the bulk, as the electron density is locally reduced. Each defect state leads to a different lifetime Tdj = 1/Ap,. 

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