The exchange effect

The angular dependence of l(r) in eqn. (63) has not been discussed very widely. However, the pre-exponential factor, A, will depend on the mutual orientation of donor and acceptor molecules. For instance, in aromatic molecules the sign of the wave function changes as the molecular plane is crossed and, consequently, energy transfer between an aromatic donor (acceptor) and an acceptor (donor) in its molecular plane should be slower than for other orientations. Adamczyk and Phillips [182] have discussed this further (Sect. 3.5). 

Since much of the following statistical mechanical analysis follows the outlines developed above for dipole—dipole energy transfer and is similar to electron tunnelling (recently reviewed by Rice and Pilling [39]), the following discussion has been compressed a little. 

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In designing a unit, each side of the exchanger is independently tailored to the duty required, and the exchanger effectiveness (discussed in Section 9.9.4) can range from 2 5 per cent to values in excess of 98 per cent without fundamental design or construction problems arising. Countercurrent, co-current and cross flow contacting can be employed individually or in combination. 

The principal use of this method is in the rating of an existing exchanger. It can be used to determine the performance of the exchanger when the heat transfer area and construction details are known. The method has an advantage over the use of the design procedure outlined above, as an unknown stream outlet temperature can be determined directly, without the need for iterative calculations. It makes use of plots of the exchanger effectiveness versus NTU. The effectiveness is the ratio of the actual rate of heat transfer, to the maximum possible rate. 

Nuclear spin exchange has also been observed (80) between nuclei in semiconductors of the heavier elements, such as InSb, GaSb, GaAs, and InAs, and considerable exchange broadening of these NMR lines has been observed. Anderson (81) has given a treatment of the exchange effect in semiconductors. 

Bc3 cluster the 3-body forces cannot be approximated solely by the Axilrod-Teller term. The reasons for the satisfactory approximation of many-body energy by the Axilrod-Teller term in the bulk phases of the rare gases were discussed by Meath and Aziz . As follows from precise calculations of the 3-body interaction energy in the Hcg , Neg and Ara trimers, both the Axilrod-Teller and the exchange energies are important. Nevertheless, in some studies of many-body interactions, the exchange effects are still neglected and the many-body contribution is approximated by only dispersion terms, for example see... 

Though the true electron spin operators were employed here as well as in the Breit-Pauli Hamiltonian, the phenomenological Spin Hamiltonian, in which the spin coupling is an exchange effect, is in sharp contrast to the Breit-Pauli Hamiltonian, that is including the (magnetic) spin-spin interactions. Since the exchange effect is an effect introduced by the Pauli principle imposed on the wave function, we may write the electron-electron interaction as an expectation value,... 

Because the dependence on the distance of separation of donor and acceptor is similar for both energy transfer by the exchange effect and for electron transfer by tunnelling, this section can be abbreviated, the more so since the subject has been reviewed recently by Rice and Pilling [39]). 

Hie thermodynamic properties of fluids consisting of light molecules sometimes departs markedly from those of heavier molecules. These departures, the so-called quantum effects, result from two different phenomena, the exchange effect and the diffraction effect... 

The classical interaction, that is, without the exchange effect, here gives a very slight attraction, which would, however, only lead to a heat of dissociation of about 10 kcal. 

The Vsr part accounts for the monomers shape factor in the potential. It mainly includes the exchange effects. However, other effects, such as the overlap-dependent electrostatic interaction, may also be conveniently absorbed in Vsr. Following Buckingham, Fowler and Hutson [14], Vsr may be adequately modeled by a Bom-Mayer exponential form ... 

The origin of these interactions, called exchange, was first realized by Heisenberg and Dirac in 1926. The interpretation of the exchange effect as formally equivalent to the coupling between spins permits the use of a vector-coupling scheme to model the quantitative behavior of coupled spins with the... 

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