Coefficient of spontaneous emission

A being the radiative rate (labeled in such a way because it coincides with the Einstein coefficient of spontaneous emission) and Anr being the nonradiative rate, that is, the rate for nonradiative processes. The solution of the differential equation (1.16) gives the density of excited centers at any time r ... 

In the standard theory the integrated coefficient of spontaneous emission of a transition between two manifolds / and is given by... 

Excited state lifetimes are related to the Einstein coefficients of spontaneous emission Amn and can be approximately calculated from the expression... 

Aba is the Einstein coefficient of spontaneous emission and Bba is the Einstein coefficient of induced emission. 

P+ and P are the probabilities for absorption and emission, respectively B+ and B are the coefficients of absorption and of induced emission, respectively A- is the coefficient of spontaneous emission and p v) is the density of radiation at the frequency that induces the transition. Einstein showed that B+ = B, while A frequency dependence, spontaneous emission (fluorescence), which usually dominates in the visible region of the spectrum, is an extremely improbable process in the rf region and may be disregarded. Thus the net probability of absorption of rf energy, which is proportional to the strength of the NMR signal, is... 

Spontaneous emission That mode of emission which occurs even in the absence of a perturbing external electromagnetic field. The transition between states, n and m, is governed by the Einstein coefficient of spontaneous emission, Anm-See also stimulated emission. 

Bnm Einstein s coefficient of (stimulated) absorption Bmn Einstein s coefficient of stimulated emission Amn Einstein s coefficient of spontaneous emission... 

Bnm = Einstein coefficient of Absorption Bmn = Einstein coefficient of Induced Emission Amn = Einstein coefficient of Spontaneous Emission (from one pole to the other in the order given)... 

The radiation field induces also a transition from the upper to the lower state (stimulated emi.ssion). The rate is w = B p, where B is the Einstein coefficient of stimulated emission. The rate of spontaneous emission is w" = A, with A the coefficient of spontaneous emission (note the absence of p in this expression). This is... 

Einstein coefficient of spontaneous emission from state nto m arccos(jc) the smallest angle whose cosine is x a sample absorption coefficient (m" )... 

Using highly correlated MCSCF-Cl wave functions for the A rij and X states, the transition moment function for the A - X transition has been calculated which in turn allowed the evaluation of Einstein coefficients of spontaneous emission A, (v = 0,1 v" = 0,1,2), absorption oscillator strengths f v (v = 0,1 v" = 0,1), and radiative lifetimes for A Ili, v = 0,1 of PH and PD. The v = 0 lifetime Xrad = 399 ns for PH (390 ns for PD) is shorter than the experimental value, probably because the large correlation energy contributions to the transition moment have not been sufficiently accounted for in the calculation [32]. 

R = Bp, where p is the density of electromagnetic radiation and Bis the Einstein B coefficient associated with absorption. The rate of induced emission is also given by Bp, with the coefficient B of induced emission being equal to the coefficient of absorption. The rate of spontaneous emission Is given by A, where A is the Einstein A coefficient of spontaneous emission. The A and B coefficients are related byA = 8nhv B/( , where h is the Planck constant, v is the frequency of electromagnetic radiation, and c is the speed of light. The coefficients were put forward by... 

As discussed in [22], the spherical symmetry of is destroyed when these ions are situated in solids, so that a multiplet term level can be split up to 2/ + 1 crystal field levels for a non-Kramers ion. Due to the parity selection mle for pure electronic transitions in solids, the 41 (i) 4 (f) transition between states i and f is ED forbidden to first order. Parity describes the inversion behavior of the wavefunction of an electronic orbital, so that s,d... orbitals have even parity whereas p,f... orbitals are odd. The spectral feature representing the pure electronic transition is termed the electronic origin or the zero phonon line. An ED transition requires a change in orbital parity because the transition dipole operator (pe) is odd, and the overall parity for the nonzero integral involving the Einstein coefficient of spontaneous emission, A(ED) ... 

In addition, Einstein recognized that a system can go from an excited state to a lower-energy state spontaneously if there is a spontaneous emission of a photon of the right frequency. This spontaneous emission is dependent on the concentration of species in the excited state but not dependent on the photon density p v). The rate of spontaneous emission is characterized by A, the Einstein coefficient of spontaneous emission ... 

The constant A is the Einstein coefficient of spontaneous emission. It can be shown that the coefficients of stimulated absorption and emission are equal and that the coefficient of spontaneous emission is related to them by... 

The Einstein coefficient of spontaneous emission, A = 3.7 0.6 s thus Xrad = 0-27 0.04 s, was determined by measuring the absolute a A->>X emission rate using a calibrated (emission intensity from the O + NO reaction) optical detection system and the absolute NH(a A) concentration using an ESR spectrometer the NH(a A) molecules were generated by the reaction FH-NH2NH + HF in a fast-flow reaction chamber equipped with these two detection systems [3]. 

The ultimate single molecule detection limit is set by the probability with which a typical chromophore can emit a photon within a sub-picosecond time window. Even for the best chromophores with large transition dipoles and correspondingly high radiative rates this probability is low. The instantaneous brightness of a fluorophore is determined by the coefficient of spontaneous emission and hence by the extinction coefficient of the molecule. For an excellent molecular emitter with a radiative lifetime of 1 ns, such as for example the S2 state of porphyrins (smax = 600 000), the probability of emission within the initial 100 fs following excitation is only approximately 0.1%. Therefore, the molecule must be excited approximately 1000-times in order for one photon to be emitted with the specified 100 fs time window. Naturally, more than one photon must be collected in order to determine the dynamics of the system of interest and the collection efficiency of even the best microscope is far from 100%. 

In the case of emission, A(J,J ) is also known as Einstein s coefficient of spontaneous emission, and the sum of all probabilities for all radiative transitions is equal to the inverse of the radiative rate constant, Icr, in turn the reciprocal of the emissive state lifetime, Tr. 

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