# Spontaneous Emission

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## spontaneous emission

[spän′tan·ē·əs i′mish·ən]## Spontaneous Emission

the emission of electromagnetic radiation by atoms and other quantum systems in excited energy levels. In contrast to induced radiation, spontaneous emission does not depend on the effect of external electromagnetic radiation on the quantum system; the laws governing the emission depend entirely on the system’s properties, as is the case with such other types of spontaneous transformations as radioactive decay and the transformations of molecules in monomolecular reactions.

Spontaneous emission is observed during the spontaneous quantum jump of an excited system from a higher energy level *E _{i}* to a lower level E

_{k}. It is characterized by the frequency v

_{ik}of the emitted photon, with energy hv

_{ik}= E

_{i}– E

_{k}(where

*h*is Planck’s constant), and by the probability A

_{ik}, equal to the average number of such photons emitted by the quantum system per unit time. If the number of atoms or molecules in an excited energy level

*E*(the population of the level) is

_{i}*N*, then the power of spontaneous emission—the energy of the photons emitted per second—is

_{i}*N*; the power determines the intensity of spontaneous emission, which remains constant for constant

_{i}A_{ik}hv_{ik}*N*. If the initial number of excited systems is given as N

_{i}_{i0}and there is no further excitation, then as a result of spontaneous emission a decrease in

*N*will occur with time

_{i}*f*according to the law

*N*= N

_{i}_{i0}exp (–

*A*, where

_{i}t*A*is the total probability of spontaneous emission upon transitions of the system from energy level

_{i}*Ei*to increasingly lower energy levels

*E*. The larger the A

_{k}(A_{i}= ƩA_{ik})_{i}the faster the spontaneous emission attenuates with time and the shorter the lifetime Ƭ = 1/A

_{i}, in level

*E*.

_{i}The probability A_{ik} of spontaneous emission, which is the most important characteristic of the quantum transition between energy levels *Ei* and E_{k}, depends on the properties of both levels. For dipole radiation, A_{ik} is proportional to the cube of the transition frequency and the square of the dipole transition moment; in the visible region of the spectrum, A_{ik} is ~10^{8} sec^{–1}, corresponding to a lifetime of ~10^{–8} sec for excited energy levels. In spectroscopy the dimensionless probabilities f_{ik} = A_{ik}*/*A_{a} are often used in place of the probabilities A_{ik}. They are also referred to as oscillator strengths, and here A_{0} is the probability, taken as uni ty, that gives the same attenuation law for spontaneous emission as for the dipole radiation of an elastically bound electron accord ing to classical theory.

M. A. EL’IASHEVICH