Transition probability spontaneous

As discussed above, for a single element planar transition tensor the angle-dependent two-photon transition probability is the squared modulus of the single photon cos 6 transition probability. Spontaneous emission from a two-photon excited molecular population occurs via the same —> So transition as in single photon fluorescence ... 

In a celebrated paper, Einstein (1917) analyzed the nature of atomic transitions in a radiation field and pointed out that, in order to satisfy the conditions of thermal equilibrium, one has to have not only a spontaneous transition probability per unit time A2i from an excited state 2 to a lower state 1 and an absorption probability BUJV from 1 to 2 , but also a stimulated emission probability B2iJv from state 2 to 1 . The latter can be more usefully thought of as negative absorption, which becomes dominant in masers and lasers.1 Relations between the coefficients are found by considering detailed balancing in thermal equilibrium... 

Application of the F-D theorem produced [122] several significant results. Apart from the Nyquist formula these include the correct formulation of Brownian motion, electric dipole and acoustic radiation resistance, and a rationalization of spontaneous transition probabilities for an isolated excited atom. 

Equation (A3.7) shows the equality between the probabilities of absorption and stimulated emission that we have already established for monochromatic radiation in Equation (5.15). Equation (A3.8) gives the ratio of tlie spontaneous to the induced transition probability. It allows us to calculate the probability A of spontaneous emission once the Einstein B coefficient is known. 

He points out that the variation of lifetime with glass matrix is due to at least two causes, the first being the changes in refractive index. If the wave functions of the ion remain essentially the same from host to host, the spontaneous-transition probability will increase with increasing refractive index because of the increase in density of final states. The second cause is configuration mixing of 4/ and 5d states, which must reflect the size and symmetry of the crystal field produced at the ion by the surroundings. 

Changing the base glass caused considerable changes in the -state mean life. To ascertain whether this was the result of variations in spontaneous emission matrix elements or radiationless transition probabilities, the peak absorption coefficient of the 4/9/2 —4F3/2 transition was plotted... 

The first term on the right-hand side is a gain term due to transitions between level m and n, the second a loss term Nn is the number of atoms in level n. The important new element introduced by Einstein was the discovery of spontaneous emission. The transition probability is the sum of two contributions ... 

Einstein s treatment of spontaneous emission uses occupation numbers and transition probabilities. On the other hand, quantum mechanics is based on probability amplitudes. The difference between these two points... 

A, A", symmetry species of Cg, 75 Amn, Einstein transition probability of spontaneous emission, 24, 38... 

These equations are similar to those of first- and second-order chemical reactions, I being a photon concentration. This applies only to isotropic radiation. The coefficients A and B are known as the Einstein coefficients for spontaneous emission and for absorption and stimulated emission, respectively. These coefficients play the roles of rate constants in the similar equations of chemical kinetics and they give the transition probabilities. 

Laser induced transition probabilities are often small. This is because the interaction time of the ions with the laser is short ( ns), and because the relevant matrix elements are small, or else the levels involved have large natural widths. A useful approximate expression for estimating signal strengths for an electric-dipole (El) transition from a metastable level 1) to a short lived level 2), followed by a spontaneous decay to a third level 13), when the interaction time is long compared to the lifetime of the second level is [8] ... 

In the Born-Oppenheimer approximation, the relative importance of channels (la) and (lb), together with their dependence on wavelength would depend upon the matrix elements for the transition between the electronic states, the Franck-Condon factors, the Honl-London factors, and upon the probabilities for spontaneous dissociation of the excited state formed. In principle, except for the last one, these are well known quantities whose product is the transition probability for that particular absorption band of Cs. When multiplied by the last quantity, and with an adjustment of numerical constants i becomes the cross section for the photolysis of Cs into Cs + Cs. It is the measurement of this cross section that lies at the focus of this work. 

The transition probability for the upward transition (absorption) is equal to that for the downward transition (stimulated emission). The contribution of spontaneous emission is neglible at radiofrequencies. Thus, if there were equal populations of nuclei in the a and f spin states, there would be zero net absorption by a macroscopic sample. The possibility of observable NMR absorption depends on the lower state having at least a slight excess in population. At thermal equlibrium, the ratio of populations follows a Boltzmann distribution... 

For the x-ray emission process, the transition probability( is also calculated from the dipole matrix similar to the case of the x-ray absorption, but the molecular state f in eq.(lO) is of occupied in this case. The transition probability corresponds to the spontaneous emission rate, then is given by Einstein formula as... 

B12 and 21 are the transition probabilities for absorption and stimulated emission, respectively, and 1 n2, n, and wT the analyte atom densities for the lowest state, the excited state, the ionized state and the total number densities, gi and g2 are the statistical weights, A2i is the transition probability for spontaneous emission and 21 the coefficient for collisional decay. Accordingly,... 

The Einstein transition probabilities for spontaneous emission are related to the absorption oscillator strengths through the well-known expression,... 

We are concerned with the dynamics of a molecule after optical excitation. If the state we excited is coupled only to the radation field, we will only see the exponential decay to that field by spontaneous emission, and this is too well known to warrant our interest. It is therefore necessary that the state we excite is coupled to other states. We then arrive at the conventional model for radiationless transitions a light (optical transition probability carrying) state s> coupled to a more or less dense manifold of background states fc>. In pyrazine, s> is the lBiu state and fc> is the set of vibronic states arising from the 3B3u state. In addition, the state s> may be coupled to another... 

We have been speaking of calculations of probabilities for spontaneous transition, whereas measurements are of relative intensities. Calculated intensities are obtained by multiplying the transition probabilities by the populations of the upper states. In gas discharges it is usually the case that all excited states of approximately the same excitation potential are equally populated—this is known as statistical population— but special conditions may sometimes lead to over- or under-population of some particular state. Thus abnormal intensities may reflect non-statistical populations. 

Transition probabilities, such as the Einstein spontaneous emission coefficient, Aij, axe defined so that, in the absence of collisions, nonradiative decay processes (see Chapters 7 and 8), and stimulated emission the upper level, i, decays at a rate... 

The ratio of the transition probabilities of spontaneous emission to stimulated emission at a frequency v is given by... 

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