Cross section pair production

A low ion pair yield of products resulting from hydride transfer reactions is also noted when the additive molecules are unsaturated. Table I indicates, however, that hydride transfer reactions between alkyl ions and olefins do occur to some extent. The reduced yield can be accounted for by the occurrence of two additional reactions between alkyl ions and unsaturated hydrocarbon molecules—namely, proton transfer and condensation reactions, both of which will be discussed later. The total reaction rate of an ion with an olefin is much higher than reaction with a saturated molecule of comparable size. For example, the propyl ion reacts with cyclopentene and cyclohexene at rates which are, respectively, 3.05 and 3.07 times greater than the rate of hydride transfer with cyclobutane. This observation can probably be accounted for by a higher collision cross-section and /or a transmission coefficient for reaction which is close to unity. 

The reaction rate coefficients in the above equations may be related to reaction rates per pair of particles 2/, in nuclear physics (e.g., Fowler et al., 1975 Harris et al., 1983) by k = Xj/(1 + 5/ ), where 8 = 0 except for i= , for which 5/ = 1. That is, for Reactions 2-145 and 2-147 in which two identical particles collide to react, the definition of k is half of defined by nuclear physicists and for reactions in which different particles collide, the definition of k is the same as Xij. The reaction rate coefficients depend on temperature in a complicated way (Table 2-3) and may be calculated as the average value of the product of relative velocity times cross section. The concentrations of the intermediate species can be derived as follows. From Equation 2-155, 145 [ H] = ki4e[ H]pH]. That is. 

Figure 17.14 Summary of the relative importance of the three mechanisms by which photons interact with matter. The curves indicate the locations in the atomic number-photon energy plane at which the cross section for Compton scattering is equal to that for photoelectric absorption, left side, or is equal to that for pair production, right side.

In his intervention Blackett treated the discovery of the positron in cosmic rays by C. D. Anderson in 193246 and its confirmation by Blackett and Occhialini,47 who had introduced, for the first time, the technique of triggering a vertical cloud chamber by means of the coincidence between two Geiger counters, one placed above, the other below the chamber. Blackett also discussed a number of papers by Meitner and Philipp, Curie-Joliot, Blackett, Chadwick and Occhialini, and Anderson and Nedder-meyer,48 all appearing almost at the same time, on the production of positrons in various elements irradiated with the -/-rays of 2.62 MeV energy of The. These were the first observations of electron-positron pair production. He also pointed out that the observed production of positrons has a cross section larger than the nuclear dimensions, and therefore, most probably, does not originate from a nuclear process. 

The electronic quantum state ofthe pair H,ls> H+>= in> remains invariant at all distances. The electron transfer will not take place in a direct manner because the electronic parity is equal for both channels. The interconversion process requires aTS with parity -1. Among the states available to a system decomposable in one electron and two protons (or proton deuterium, etc) there are the hydrogen molecule ion species. The first electronic excited state (leu) ofthe molecular ion H2+ provides an "intermediate" (Q-state) for the interconversion once angular momentum conservation rules are fulfilled. The state (lau) is found above the in> and out> states leading to resonance in the cross section. This state may either relax to the (lrg) state yielding the hydrogen molecule ion and emitting a photon as this state is 2.8eV below dissociation, or it may take the product channels. This is a FC-like process. The reaction (27) is a prototype of electron transfer (ET). Thus, for any ET reaction whose in> and out> asymptotic electronic states share the same parity, the actual interconversion would require the mediation of a TS. 

The formation of the alkaline earth cyanide is the major pathway in the reaction M + BrCN. The other channel (giving MBr + CN) is observed for the reactions of Ba and Sr. The ratio of the cross section is o(BaCN)/ a(BaBr) 25-100 and a(SrCN)/o(SrBr) 250-1000 [363]. It was not possible to measure internal state distribution for the alkaline earth salts, but for the CN product of the minor channel, the vibrational distribution was found to be N(d = 1)/N(p = 0) <. 0.2 and Txot = 1250K for Ba + BrCN and TIot = 750 K for Sr + BrCN. The reaction dynamics appear to be consistent with an electron jump mechanism which would favour the breakup of the M+(BrCN) ion pair to give MCN + Br. 

Since v = (2E /fi )l/2, the in-plane scattering of AB at various values of E can be represented by the concentric circles with radius u AB, which are shown in Figure 1.5. If uAB > C, then the complete lab distribution of AB ranges over 4n steradians and is easy to resolve. On the other hand, if ab < C, the scattering is confined to a cone defined by a small angle about C. This may occur either because E is small, or because mAB mc-If the reaction is appreciably exothermic, then v and therefore u AB and u c, can have a wide distribution of values, even when v and C are precisely defined. A detector at a laboratory angle 0 observes products with a spread of lab velocities each corresponding to a different pair of values for u and 0. Consequently, the lab-c.m. transformation of the differential cross sections, which is now represented [50] by the expression... 

A-z-k) in the lab system, respectively, wave function of TT+TT bound state with the Coulomb potential only squared at the origin with the principal quantum number n and the orbital momentum Z = 0, Pb is the Bohr momentum in 2, dan/dpidp2 is the double inclusive production cross section for tt+tt -pairs from short lived sources without taking into account 7r+7T Coulomb interaction in the hnal state, p and P2 are the 7t+ and 7t momenta in the lab system. The momenta of 7t+ and 7t mesons obey the relation Pi P2 The A2W are produced in states with different principal quantum numbers n and are distributed according to n Wi = 83%, W2 = 10.4%, W3 = 3.1%, W >4 = 3.5%. The probability of A2tt production in K, K, p, p, xp and T mesons decay were calculated in [34]. 

Basically, one distinguishes between pair creation, where the electron and positron are produced in free (continuum) states and pair creation with an electron in a bound state of one of the ions, for example, in a K-shell state. The latter process is also called bound-free pair production. Pair creation with electron capture into a bound state of the ion changes the charge state of the ion represents one of the major loss processes affecting the stability of ion beams in relativistic heavy-ion colliders. The corresponding cross-section for electron capture is of the order of 100 bam for RHIC energies in U92+(100 GeV/u) -I- U92+(100 GeV/u) collisions and determines the lifetime of ionic charge states in the beam and then the luminosity. 

Table 1.1 Cross-sections for free electron-positron pair production. Collision energies are given in units of GeV per nucleon (GeV/u).

We are limited in this modeling process by the accuracy with which measurements can be made and by the accuracy of the fission yields and neutron reaction cross sections which are used to interpret the results. As an example consider the Nd- Nd fission product pair, which has been used as an indicator of thermal neutron fluence because the capture cross section for the former is large and for the latter is small. The thermal cross section for l53Nd has recently been listed as 325 ( 10) barns (20), and more recently as 266 barns (11). Using the 325-barn value we deduce an age of about 2 to 27T billion years from neodymium to uranium ratios in the Oklo reactors, while an age of about 1.8 billion years is obtained using the 266-barn figure. 

If the ground state of the colliding pair should come close to an ionic one, the ion pair becomes a possible exit channel. A. P. M. Baede in Article 10 describes the measurement of interpretation of the energy dependence of the total and differential cross section for ion production in the 1-10 eV region where the process reaches its peak efficiency. A longer established... 

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