Oscillator strengths and lifetimes

N. Vaeck, M. Godefroid, J.E. Hansen, MCHF oscillator strength and lifetime calculations in neutral Calcium, J. Phys. B 24 (1991) 361. 

Table 6.2 lists some of the physical data for the hydrated electron. Most of these data are experimental. The molar volume is calculated, as experimental measurements are not reliable. The oscillator strength and the natural lifetime against reaction with water molecules are lower bounds, whereas the salvation time is possibly an upper bound. 

There are numerous needs for precise atomic data, particularly in the ultraviolet region, in heavy and highly ionized systems. These data include energy levels, wavelengths of electronic transitions, their oscillator strengths and transition probabilities, lifetimes of excited states, line shapes, etc. [278]. 

A medium with bound electrons can be regarded as an ensemble of oscillators each of which is characterized by three parameters its natural frequency oscillator strength/, and the damping constant y(, which equals the inversed lifetime of the corresponding state ("y, = 1 /r,). The well-known expression for the permittivity of the medium91,95 can be presented in the form89... 

Table 7 Calculated S-T transition moments from the ground state (So) to the three lowest triplet states (Tn) at the ground state geometry, oscillator strengths (/), radiative lifetimes (rn), and vertical transition energy (En). From Ref. [70].

In contrast to polyenes the aromatic molecules exhibit not only the Ti — So absorption, but also the longlived T — So emission, which gives rise to phosphorescence phenomena of rigid solvents and crystals. This is another important field of applications of spin-orbit quadratic response theory. Such calculations refer to lifetimes, transition moments, oscillator strengths and polarization directions for the radiative decay of molecular triplet states. These quantities may either be averaged over the triplet levels or refer to specific triplet spin sublevels depending on the conditions for the relevant experimental measurements. 

Kurita et al. 2 Takeda et al. 3 and Parthenopoulos and Rentzepis11 used picosecond laser photolysis techniques to study the photochromic processes of furyl fulgide. They found that the excited states of furyl fulgide and its colored form were singlet states and had n,n characteristics. Takeda et al.13 reported from theoretical studies that the values of the oscillator strength and the radiation lifetime (/r) were... 

Aft initio MRD Cl study of ground and excited Cj. Calculation 75 of lifetimes associated with a number of band systems Aft initio SCF and MRD Cl calculations of the oscillator 76 strengths and lifetimes of the Phillips system (A Il -X iiJ)... 

As meteoric material is evaporated, a number of high energy gas-phase collision processes occur. These processes, examples of which are listed in Fig. 1, involve both collisions between neutrals and neutrals and ions. Metal atoms, Me, are abundant in all meteoric bodies, and play an important role for several reasons (i) Metal atoms and ions frequently have low lying excited states with high oscillator strengths and are, therefore, easily identified and traceable (ii) Metal atoms have low ionization potentials and can be ionized fairly efficiently in high velocity neutral collisions (iii) Atomic metal ions have very long lifetimes with respect to ion-molecule reactions and electron-ion recombination compared with molecular ions, which rapidly dissociatively recombine with electrons. 

The transition energies are not sharp but rather have finite widths due to thermal vibrations in the solid. Thus, the wave functions and the density of states can be treated as functions of energy. The wave functions can be normalized with respect to energy and a Dirac delta function used for the density of final states to insure conservation of energy. Then Einstein s A and B coefficients can be used to relate the transition matrix elements to experimentally measurable quantities such as oscillator strengths and luminescence lifetimes. For electric dipole-dipole interaction the energy transfer rate becomes... 

The spectroscopic properties and chemistry of aprotic Nd + laser liquids plus references to earlier studies are discussed by Brecher and French (V7). The oscillator strengths and fluorescence lifetimes are comparable to those in solids with quantum efficiencies near unity. Since fluorescence line-widths are smaller than in glasses, the stimulated emission cross sections are larger (1 8), although still less than in crystals. Aprotic liquid laser materials and references are listed in Ref. 19. Thus far only Nd3+ has been used as the laser ion although other lanthanide ions could also be used. 

The L absorption spectra in lanthanide vapors may be interpreted through this type of approximation. Figure 8 models an atomic Lm absorption spectrum through a superposition of a lifetime broadened distribution of atomic oscillator strengths and an arctan shaped continous absorption. Due to the relatively large core hole... 

For most practical purposes the oscillator strengths and the connected radiative transition probabiUties obtained from the absorption spectra correspond to some average values due to the total number of sites. This is also true for the nonradiative transition probabilities, which are obtained from the measured average lifetimes and average quantum efficiencies of fluorescence. 

Radiative transition probabilities, branching ratios /3, lifetimes, oscillator strengths, and peak cross sections for holmium(III) in ZBLA glass at 300 K [Reisfeld et al. (1985a) when no other reference is given]. 

There are numerous examples of calculated transition probabilities, oscillator strengths, or lifetimes for small molecules in the literature. Convergence patterns with respect to the size of the AO basis set and the theoretical treatment for selected transitions in diatomic molecules are treated in Partridge et al. ... 

The vast majority of single-molecule optical experiments employ one-photon excited spontaneous fluorescence as the spectroscopic observable because of its relative simplicity and inlierently high sensitivity. Many molecules fluoresce with quantum yields near unity, and spontaneous fluorescence lifetimes for chromophores with large oscillator strengths are a few nanoseconds, implying that with a sufficiently intense excitation source a single... 

The oscillator strength of the longest wavelength absorption band of BMPC (1.1, [25]) is very similar to those of two previously studied carbocyanines (DOC and DTC) [45] so that we can expect that, for BMPC as well as for EK)C and DTC, the radiative constant (kp) is equal to 2-3x10 s". Combining this value with the fluorescence quantum yield of BMPC in methanol, 4)p= 5.3x10", we can estimate its room-temperarnre fluorescence lifetime to be = 2 ps. 

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