Spontaneous radiative relaxation

The first term is due to spontaneous radiative relaxation and nonradiative phonon relaxation as described in eq. (13), where / , is the probability of ion i in the excited state. The second term is due to energy transfer induced by ion-ion interaction, where W es and W A are rates of resonant and phonon-assistant energy transfer, which depend on distance between donor and acceptor RtJ. For resonant energy transfer... 

Radiative relaxation from an excited state /J of a lanthanide ion usually occurs in various lower lying state giving rise to several lines in the emission spectrum. For example, the red luminescence of Eu is a result of transitions from its Dq state to all of the lower lying Fj levels. The spontaneous emission probability, A, of the transition /J is related to its dipole strength according to... 

The model of Fig. 9.1 may thus represent the decay of an excited molecular state with no photons, 1) = x, 0 ), to the continuum of states /) = g, 1r) that combine the ground molecular state with a continuum of single photon states of the radiation field. The relaxation 11) /) is then the process of spontaneous emission, and the rate will then )deld the radiative relaxation rate of the corresponding excited molecular state, as discussed in detail in Section 3.2.3. 

The radiative transitions of the previous descriptions have all been spontaneous Relaxation from the excited state to the ground state and emission of photons occur without external aid. In contrast, a stimulated emission occurs when the half-life of the excited state is relatively long, and relaxation can occur only through the aid of a stimulating photon. In stimulated emission, the emitted photon has the same direction as, and is in phase with, the stimulating photon. The example of Cr +-doped AI2O3 that we utilized earlier for our description of the color of ruby works equally well for a description of stimulated emission. Recall that the presence of chromium in alumina alters the electronic structure, creating a metastable state between the valence and conduction bands. Absorption of a blue-violet photon results in the excitation of an electron from... 

The possibility of deactivation of vibrationally excited molecules by spontaneous radiation is always present for infrared-active vibrational modes, but this is usually much slower than collisional deactivation and plays no significant role (this is obviously not the case for infrared gas lasers). CO is a particular exception in possessing an infrared-active vibration of high frequency (2144 cm-1). The probability of spontaneous emission depends on the cube of the frequency, so that the radiative life decreases as the third power of the frequency, and is, of course, independent of both pressure and temperature the collisional life, in contrast, increases exponentially with the frequency. Reference to the vibrational relaxation times given in Table 2, where CO has the highest vibrational frequency and shortest radiative lifetime of the polar molecules listed, shows that most vibrational relaxation times are much shorter than the 3 x 104 /isec radiative lifetime of CO. For CO itself radiative deactivation only becomes important at lower temperatures, where collisional deactivation is very slow indeed, and the specific heat contribution of vibrational energy is infinitesimal. Radiative processes do play an important role in reactions in the upper atmosphere, where collision rates are extremely slow. 

In direct gap GaAs, an excited electron at the bottom of the conduction band can relax spontaneously back into a hole in the valence band by emitting a photon at the band gap energy. This electron-hole radiative recombination process can only occur in Si if momentum is conserved, i.e., the excited electron wave vector must be reduced to zero. This, in pure Si, occurs via the transfer of momentum to a phonon that is created with equal and opposite wave vector to that of the initial state in the conduction band. Such a three-body process is quite inefficient compared with direct gap recombination.1218 This is why Si is such a poor light emitter. 

According to Judd-Ofelt theory, one can evaluate the radiative lifetime of any excited state of interest via Einstein spontaneous emission coefficients. The rate of relaxation, A, from an initial state fJ) to final state if J ) through radiative processes is given by (Condon and... 

Luminescence lifetime depends upon radiative and nomadiative decay rates. In nanoscale systems, there are many factors that may affect the luminescence lifetime. Usually the luminescence lifetime of lanthanide ions in nanociystals is shortened because of the increase in nomadiative relaxation rate due to surface defects or quenching centers. On the other hand, a longer radiative lifetime of lanthanide states (such as 5Do of Eu3+) in nanocrystals can be observed due to (1) the non-solid medium surrounding the nanoparticles that changes the effective index of refraction thus modifies the radiative lifetime (Meltzer et al., 1999 Schniepp and Sandoghdar, 2002) (2) size-dependent spontaneous emission rate increases up to 3 folds (Schniepp and Sandoghdar, 2002) (3) an increased lattice constant which reduces the odd crystal field component (Schmechel et al., 2001). 

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