Electron pair annihilation

Electron pair annihilation, n LMi,SMs), and creation, n ( LMiSMs), operators can be defined such that tt creates a normalized two-electron state with the specified orbital and spin angular momenta when applied to the vacuum... 

Radiation, Annihilation—Photons produced when an electron and a positron unite and cease to exist. The annihilation of a positron-electron pair results in the production of two photons, each of 0.51 MeV energy. 

This association has its counterpart that was also variously described as an encounter complex, a nonbonded electron donor-acceptor (EDA) complex, a precursor complex, and a contact charge-transfer complex.10 For electrically charged species such as anion/cation pairs (which are relevant to ion-pair annihilation), the pre-equilibrium association results in contact ion pairs (CIP)7 (equation 3)... 

These traps, (Fig. 6) and similar effects in the motion of holes and other charges through polymers, would eventually be correlated also with such structural probes as positron lifetimes in macromolecular solids. Extensive recent studies of positron lifetime are based on positronium decay. In this, the lifetime of o-positronium (bound positron-electron pair with total spin one) is reduced from about 140 nanoseconds to a few nanoseconds by "pick-off annihilation" in which some unpaired electron spins in the medium cause conversion quenching of orthopositronium to para-positronium. The speed of the t2 effect is supposed, among other things, to represent by pick-off annihilation the presence of defects in the crystalline lattice. In any case, what amounts to empty space between molecules can then be occupied by orthopositronium.(14,15,16) It is now found in linear polyethylene, by T. T. Wang and his co-workers of Bell Laboratories(17) that there is marked shift in positron lifetimes over the temperature range of 80°K to 300°K. For... 

Improvements in current, established technologies and the introduction of new ways to test materials, nondestmctively are expected to continue apac. One promising method is positron annihilation. The positron is the antiparticle of the electron thus apositron/electron pair is unstable and will annihilate. In this process, two gamma rays at approximately 180 to one another are emitted from the center of the mass of the pair. A very slight departure from 180° is directly proportional to the transverse component of the momentum, of the pair. The momenta of the electrons involved in such collisions can be calculated from the geometry and intensity of the gamma rays. The dynamics of the clcctron/positron system underlie the use of the technique for the study of defects in materials,... 

Pair production has a threshold energy of 1.022 MeV because two particles are created, one electron and one positron. Thus, some energy is stored in or used to create the mass of the pair. Notice the total electric charge is conserved because the electron charge is — le and the positron charge is +le. One of the unique features of this process is that the energy that went into the creation of the two particles will be released when the positron comes to rest and annihilates with an electron. The annihilation process is... 

The experimental techniques involved in measuring the angular correlation and the Doppler broadening of the two annihilation gamma-rays were introduced in section 1.3. These techniques rely on the fact that the motion of the positron-electron pair immediately prior to annihilation causes the two gamma-rays to be emitted in directions differing... 

Positron is the antiparticle of electron and is another kind of fermion having the same mass me and spin s = 1 /2 as electron and the charge +e opposite to the electron s. A physical system containing a positron e+ and electrons e can change the number of its constituent particles due to the electron-positron pair annihilation, which occurs when they occupy a common position. The simplest example is positronium Ps, a hydrogen-like bound... 

Pair annihilation of a positron e+ and an electron e by y-ray emission was briefly explained in Section 1.3. There, the hydrogen-like system ePe, or positronium Ps, was described quantum mechanically as a QBS having a finite lifetime r because of an absorption potential —z Vabs- This potential also causes positron flux loss, or positron absorption, in collisions with atoms. 

Due to the longer lifetime of the arene radical ration in the SSIP, 37 undergoes isomerization to 38 yielding after return electron transfer and collapse of the reactive intermediates the Hetero Diels Alder adducts 40 and 41 in a. ratio of ra. 1 2.5. There is also experimental evidence for some participation of an ion pair annihilation leading directly to 40 and 41. 

The difference between the Fermi energies /xeh == f2 — fi is the free energy per electron-hole pair of the ensemble, also called the chemical potential of electron-hole pairs. It is free of entropy and we may therefore hope to transfer it into electrical energy without losses. If electron-hole pairs are not allowed to leave the 2-level system, i.e., under open-circuit conditions, they have to recombine and emit one photon per pair annihilation. These photons carry the free energy of the electron-hole pairs, and /n7 = /ieh = f2 — fi is recognised as their chemical potential. 

Antiparticles have been detected experimentally, but annihilate rather rapidly if they encounter their counterpart particle. For instance, in pair annihilation, a positron (e+ ) encountering an electron (e ) ... 

V. Nucleophilic and Electron-Transfer Processes in Ion-Pair Annihilation.. 96... 

Electron donors (D) and acceptors (A) constitute reactant pairs that are traditionally considered with more specific connotations in mind, such as nucleophiles and electrophiles in bond formation, reductant and oxidant in electron transfer, bases and acids in adduct production, and anion and cations in ion-pair annihilation (12). In the latter case, the preequilibrium formation of contact ion pairs (CIP), that is,... 

The formulation in Scheme 4 derives from the ion-pair annihilations via the known behavior of 19- and 17-electron carbonylmanganese radicals (67). Accordingly, the initiation by electron transfer is included in the generalized mechanism for Mn-Mn bond formation (Scheme 4). The... 

The presence of 1 equivalent of TPP1 OTf- with the chromium anion TpCr(CO)3- as the tetrabutylammonium salt in dichloromethane results in the loss of the carbonyl bands of the anion at 1890 and 1740 cm-1. Their complete replacement by the sharps, band at 2018 cm-1 and the broad E band (1898 and 1838 cm-1) of the 17-electron radical TpCr(CO)3- indicates that the ion-pair annihilation proceeds to completion. Variation of the pyrylium cation, by the replacement of TPP+ with a weaker acceptor such as tri-p-anisylpyrylium triflate (TAP+ OTf-), consistently results in lower conversions of the carbonylmetal anions. For example, the treatment of TpMo(CO)3 with the TAP+ salt leads to a light red solution of TAP (Am 560 nm) (92) and a greatly diminished concentration of TpMo(CO)3- as judged by the reduced carbonyl absorbances in comparison with that obtained from TPP+ at the same concentration. Even with this weaker acceptor cation, however, the strong chromium anionic donor TpCr(CO)3- is completely oxidized by 1 equivalent of TAP+ to form TpCr(CO)3- in essentially quantitative yields. 

Indeed, the 17-electron radicals in Eq. (43) with M = Mo and W can both be readily collected as red and orange crystals merely when the ion-pair annihilation is carried out in acetonitrile solutions. 

NUCLEOPHILIC AND ELECTRON-TRANSFER PROCESSES IN ION-PAIR ANNIHILATION... 

The formation of 6a is particularly diagnostic, since this unique carbon-carbon bonded reductive dimer was demonstrated by Wrighton and coworkers to arise via the transient 19-electron radical ( -cyclohexa-dienyl)Fe(CO)3 by regiospecific coupling at a ligand center (105). Furthermore the 17-electron radical CpMo(CO)3- is the precursor to the accompanying oxidative dimer [CpMo(CO)3]2 (7), as described in the earlier anodic studies of CpMo(CO)3 (106). Accordingly these products (6 and 7) of ion-pair annihilation are referred to hereafter as radical (homo) dimers. 

The generalized mechanism for ion-pair annihilation as presented in Scheme 11 involves the rather circuitous route for radical-pair production [involving Eqs. (55) and (56), certainly in comparison with the direct electron-transfer pathway (Scheme 8)]. In other words, why do ion pairs first make a bond and then break it, when the simple electron transfer directly from anion to cation would achieve the same end The question thus arises as to whether electron transfer between Fe(CO)3L+ and CpMo(CO)3 is energetically disfavored. The evaluation of the driving force for the electron transfer process obtains from the separate redox couples, namely,... 

The overall driving forces for electron transfer [— AG = (E + is ,)] for ion-pair annihilation in THF between mo and feL+ (i.e., cations 1, 2, 3, and 4) are AG — 3.2, 3.9, 5.3, and 6.0 kcal/mol, respectively, based on the electrochemical measurements (115). Such driving forces all easily lie within the isoergonic bounds for the facile electron transfer between feL+ and mo-. Moreover, the differences in driving forces are not sufficient to strongly distinguish the cations 1 and 2 from their cyclic analogs 3 and 4 for the consideration of simultaneous nucleophilic addition and electron transfer, as presented in possibility (c) above. 

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