Photon angular momentum transfer

To each ionic state Jj and angular momentum transfer jx belongs a reduced scattering amplitude S jt) - the name for which originates from the formulation of photoionization as a half-scattering process. (In a scattering process with real particles the scattered particle still exists after the interaction, but in photoionization the primary incident particle, the photon, is annihilated.) The angular momentum transfer formulation allows a partition of the amplitudes into two classes, parity-favoured and parity-unfavoured, where... 

Optical tweezers have also been used to transfer various types of photon angular momentum to macroparticles, as was done long ago with the photon spin and atoms (Chapter 4). It is not out of place here to note that the photon angular momentum is, first, associated with the spin for circularly polarized light and has a magnitude of h = h/2Tt per photon. Second, there is an orbital angular momentum that is associated with the inclination of the wavefront an the laser beam (Allen et al. 1999). Unlike... 

Classically, a circularly polarized light beam with angular frequency w(= 2nv) transfers angular momentum at a rate of E/w, where E is the rate of energy transfer. Considered as a beam of photons, E = Nhui/2-n, so that the angular momentum of each photon is h/2n = h. 

In addition to energy, the semiconductor band gap is characterized by whether or not transfer of an electron from the valence band to the conduction band involves changing the angular momentum of the electron. Since photons do not have angular momentum, they can only carry out transitions in which the electron angular momentum is conserved. These are known as direct transitions. Momentum-changing transitions are quantum-mechanically forbidden and are termed indirect (see Table 28.1). These transitions come about by coupling... 

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. 

In fact, the / value usually does change during a rovibrational or rovibronic transition, even though the rotational state has relatively little impact on the overall transition energy. In electric-dipole transitions, the photon transfers one unit of angular momentum to the molecule, and this must be absorbed by the... 

As we have seen, the vector properties of molecular collisions offer much richer information than that provided by scalar properties, such as the total cross-section of a reaction or the energy content of the reaction products. To illustrate this point, consider a simple atom-transfer reaction, which will be abstractly written as A -f BC AB -I- C. For this process, we can readily identify four vectors. These are the initial relative velocity v of the reagents (A, BC), the final relative velocity v of the products (AB, C), the initial rotational angular momentum of the reagent molecule BC, denoted by j, and the final rotational angular momentum of the product molecule AB, denoted by j. Here we have assumed, for simplicity, that no photons are emitted or absorbed in the collision process, and that electronic or nuclear spin angular momenta are non-existent or are randomly oriented and do not couple to other angular momenta present. A simple example of such a case would be the atom-transfer reaction O -F CS CO + S. 

The first factor, called the 3J-symbol, depends on M, M and m = M - M. It can be expressed by the Clebsch-Gordon coefficients which describe the coupling of angular momenta for a system initially in a state (J,M). The photon transfers an angular momentum of with projection mji (m = 0, 1) and brings the system into a state (J M ). The second factor... 

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