Electromagnetic radiation transition rate

Einstein coefficients Coefficients used in the quantum theory of radiation, related to the probability of a transition occurring between the ground state and an excited state (or vice versa) in the processes of induced emission and spontaneous emission. For an atom exposed to electromagnetic radiation, the rate of absorption is given by... 

Figures 2.13(a) and 2.13(b) illustrate the basis of a semiconductor diode laser. The laser action is produced by electronic transitions between the conduction and the valence bands at the p-n junction of a diode. When an electric current is sent in the forward direction through a p-n semiconductor diode, the electrons and holes can recombine within the p-n junction and may emit the recombination energy as electromagnetic radiation. Above a certain threshold current, the radiation field in the junction becomes sufficiently intense to make the stimulated emission rate exceed the spontaneous processes.

The solvent where a physico-chemical process takes place is a non-inert medium that plays prominent roles in chemistry. It is well-known that, for example, a small change in the nature of the solvent can alter the rate of a reaction, shift the position of a chemical equilibrium, modify the energy and intensity of transitions induced by electromagnetic radiation or cause protein denaturation. As a result, the possibility of describing the properties of solvents in terms of accurate models has aroused the interest of chemists for a long time. 

From the general considerations of transition intensities in Section 12.2, we know that the rate of absorption of electromagnetic radiation is proportional to the population of the lower energy state (N in the case of a proton NMR transition) and the rate of stimulated emission is proportional to the population of the upper state (Np). At the low frequencies typical of magnetic resonance, we can neglect spontaneous emission as it is very slow. Therefore, the net rate of absorption is proportional to the difference in populations, and we can write... 

All spectroscopic techniques involve production or deactivation of excited states, normally by the interaction between electromagnetic radiation and molecules. The excited states have finite lifetimes, determined by radiative and non-radiative relaxation to the ground state. Kinetic information can be obtained by comparison of the rates of these processes with those of chemical reactions in competition with them. We will consider two of these processes, involving nuclear spin and electronic excited states. However, the same ideas are applicable to other types of spectroscopic transition. 

The van der Waals interaction as described above can be interpreted as an effect caused by the modification of the boundary conditions imposed on the electromagnetic field around the atom. This affects the level width as well as its position the radiation rate is proportional to the density of vacuum modes which in turn depend on the boundary. Thus, an excited atom connected to lower states by an E1 transition moment parallel to the metallic surface will have its radiation rate reduced. If the distance d to the surface is less than X the rate is given approximately by... 

---