Spontaneous pair production

Temperature > 10 K. This was the temperature during the first few minutes after the Big Bang. At this temperature the thermal motion of the protons and neutrons is so violent that even the strong nuclear forces cannot hold them together. Electron-positron pairs appear and disappear spontaneously and are in thermal equilibrium with radiation. (The threshold for electron-positron pair production is about 6 x 10 K.)... 

Example 9.1 At a temperature T, the average energy hv of a thermal photon is roughly equal to kT. As discussed in Chapter 2, at high temperatures electron-positron pairs will be spontaneously produced when the energy of photons is larger the than the rest energy 2mc of an electron-positron pair (where m is the mass of the electron). Calculate the temperature at which electron-positron pair production occurs. 

Ko within which any vacancy-interstitial pair will spontaneously recombine and (ii) to subthreshold energy transfers inducing athermal migration and annihilation of interstitials (with a cross-section Frenkel-pair production rate obeys the following relation ... 

Considering that /Tarninornercury(II) tetrafluoroborates are polar enough to undergo nucleophilic attack by the lone electron pair of an amine, ether or alcohol in the case of the 1,3-cyclooctadiene, 179, it has been assumed that the first formed 1,4-adduct can give the reaction product by displacement of mercury by amine with direct participation of the nucleophile in an assisted breakage of the anti C—Hg bond (path a) or by spontaneous reduction of mercury in the intermediate allylic organomercurial (path b) (equation 157). 

The tosyl protecting group of 4a is removed with sodium naphthalide at -60 °C, and an intramolecular nucleophilic attack of the nitrogen lone pair to the epoxide takes place spontaneously to afford the pyrrolidine hydroxy ester as a labile reaction product, which is immediately protected as the corresponding silyl ether 3a in 68%... 

There are at least three possible mechanisms for the spontaneous breakdown of hemiorthoesters, hemiacetals, and related species. Firstly, there may be a rapid and reversible ionization equilibrium followed by hydronium-ion catalysed breakdown of the anion (9) (Gravitz and Jencks, 1974). A necessary condition for this mechanism to be valid is that k2 calculated from kHi0 and Ka should fall below the diffusion controlled limit of c. 10loM 1s 1. The second mechanism (10) is similar to this but involves formation of the anion and hydronium ion in an encounter pair which react to give products faster than the diffuse apart (Capon and Ghosh, 1981). With this mechanism therefore the ionization equilibrium is not established and the rate constant for... 

First, we note that the charge ordering of the solvent can impose itself on the distribution of products in reaction. Chiappe and Pieraccini [40] report that in their study of electron transfer between Micheler s ketone and tetracyanoethene, they observed that the formation of a radical ion pair to be preferred over formation of a single, neutral complex. Such a preference is only observed for the most highly polar molecular liquids, and is analogous to the spontaneous ionization of metal atoms in fused salts noted above. This represents a novel phenomenon for moderately polar solvents, though its generality is unclear at this time. 

The time-resolved spectroscopic studies thus show that the charge-transfer excitation of CIP results in the simultaneous production of the reactive 17-electron carbonylmetal radicals [Mn(CO)5-, Co(CO)4 , etc.] together with the reduced acceptor radical (Cp2Co, Q-, NCP-, etc.). Furthermore, the time scale of the CT photoexcitation indicates that these radicals are initially formed as geminate pairs within the solvent cage. (50). The absence of productive photochemistry on steady-state irradiation of contact ion pairs alone in solution (i.e., without added phosphine) is consistent with the spontaneous return of the transient radicals to the ground state intact, for example,... 

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