Einstein coefficient of absorption

Einstein coefficient of absorption for the pump wavelength calculated as B 531 In(lO) / where c is the velocity of light and is Avogadro s number. Other details of the modeling may be found in reference 3. 

Now we can introduce the energy density p (v m) to transform this result into the Einstein coefficient of absorption, viz. the probability that the molecule (or atom) will absorb a quantum in unit time under unit radiation density. The probability of absorption in the Einstein expression is given by B m p (v m). Under the influence of the radiation polarized In x-directions, the relationship between the field strength E in x-direction and the radiation density is deduced as follows ... 

The Einstein coefficient of absorption of radiation for the longitudinal (along the z axis) and the transverse (perpendicular to the z axis) electromagnetic fields can be obtained from these matrix elements and are given by... 

Special Topic 2.1 Einstein coefficients of absorption and emission... 

The expressions for the y and z directions are similar. Thus we obtain for the Einstein coefficient of absorption B , m the equation... 

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 UV-VIS spectrum, usually an A or log A vs. plot, in a first approximation reflects the discrete electronic states as absorption maxima at different v ,ax positions which are correlated with the molecular structure and geometry. The extinction coefficient e or more likely the integral absorption / e(v) dv, which is approximately the product of times the halfwidth AVi/2> gives information on the transition dipole moment or the Einstein coefficient of absorption or induced emission B n, which are interrelated by... 

The change in energy flux as it passes through the sample is given by Equation (16.17), where the Einstein coefficient of absorption Bjj is defined... 

The quotient of the second-order kinetic rate constant over the energy of transition is called the Einstein coefficient of absorption, denoted B.. and expressed in m j s . Precise, quantum-mechanical calculations give the following equation for the absorption coefficient (wavenumber basis) ... 

Lissamine molecules in the vicinity of gold nanoparticles because the [H oportionality of Einstein coefficients of absorption and emissiai must hold as long as absorption and emission occur without a Stokes shift. We find that the absorption cross section is changed by 30% for nanoparticles of 30 nm radius. This effect is ready included in the fluorescence quenching efficiency above and will be included in a similar way in the analysis of the following time resolved measurements. 

The quantity Bn n- = (8a3/3h2)Einstein coefficient of absorption. Per unit radiation density it is equal to die transition probability. The Einstein coefficient depends on the molecular structure and may, eventually, be used to characteri2e molecular properties on the basis of experimentally determined intensities of the respective transitions. 

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