Transition probabilities and lifetimes

The computation of transition probabilities using MBPT is an arduous task, since an explicit wave function is not obtained in the calculation of the corresponding term values thus the correlation corrections, implicit in the effective Hamiltonian 

Extensive numerical MCSCF studies have been carried out on energy levels, transition probabilities and lifetimes for phosphorus-like and for silicon-like ions (Fritzsche et al. 1998a, 1999 Kohstall et al 1998) as well as on electric-dipole emission lines in Ni II (Fritzsche et al. 2000a). 

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In 1957, this team of brothers-in-law started working together on Townes s idea for an optical maser. They found atoms that they felt had the most potential, based on transitional probabilities and lifetimes. However, there was still one major problem In the visible light portion of the electromagnetic spectrum, atoms don t remain in an excited state as long as... 

Converting the absorption lines into abundances requires knowledge of line positions of neutral and ionized atoms, as well as their transition probabilities and lifetimes of the excited atomic states. In addition, a model of the solar atmosphere is needed. In the past years, atomic properties have seen many experimental updates, especially for the rare earth elements (see below). Older solar atmospheric models used local thermodynamic equilibrium (LTE) to describe the population of the quantum states of neutral and ionized atoms and molecules according to the Boltzmann and Saha equations. However, the ionization and excitation temperatures describing the state of the gas in a photospheric layer may not be identical as required for LTE. Models that include the deviations from LTE (=non-LTE) are used more frequently, and deviations from LTE are modeled by including treatments for radiative and collision processes (see, e.g., [27,28]). 

As mentioned in the introduction, transition probabilities (and lifetimes) are important in astrophysics for determination of elemental abundances, in plasma physics for diagnostics of gaseous discharges, in spectrochemistry for abundances and diagnostics and in laser isotope separation where the choice of possible transitions and levels depends heavily on transition probabilities and lifetimes. 

The implementation of the relativistic MR-MP procedure, using G spinors, and the procedure for calculating transition probabilities with relativistic MR-MP wavefunctions are outlined in the next two sections. In section 1.4, relativistic MR-MP calculations of term energy separations, transition probabilities, and lifetimes are presented. 

In order to be able to make reliable predictions for systems with heavy elements, an efficient relativistic theory is needed. In chapter one, Y. Ishikawa and M.J. Vilkas provide a review of multireference MoDer-Plesset (MR-MP) perturbation theory. They present a detailed overview of implementation of tiie metiiod and describe a procedure for calculating transition probabilities between the ground and excited states. The chapter is augmented by examples of relativistic MR-MP calculations of term energy separations, transition probabilities and lifetimes. 

Oq and 02 being the scalar and tensor polarizability constants, respectively, can be determined experimentally and calculated theoretically. For J = 0 or 1/2, for which the formula breaks down, there is only a scalar effect. The Stark effect can be seen as an admixture of other states into the state under study. Perturbing states are those for which there are allowed electric dipole transitions (Sect.4.2) to the state under study. Energetically close-lying states have the greatest influence. A theoretical calculation of the constants Oq and 02 involves an evaluation of the matrix elements of the electric dipole operator (Chap.4). Investigations of the Stark effect are therefore, from a theoretical point of view, closely related to studies of transition probabilities and lifetimes of excited states. (Sects. 4.1 and 9.4.5). In Fig. 2.13 an example of the Stark effect is given different aspects of this phenomenon have been treated in [2.31]. 

W.L. Wiese Atomic transition probabilities and lifetimes, in Progress in Atomic Spectroscopy, Pt.B, ed. by W. Hanle, H. Kleinpoppen (Plenum, New York 1979) p.llOl... 

W.L. Wiese Atomic transition probabilities and lifetimes. In Progress... 

The intensities of spectroscopic lines are also important. They reflect the relative concentration of resonance nuclei at certain sites although one also has to take into account the transition probabilities and lifetimes of the energy states of the system investigated. The correspondence between the number and intensities of frequencies and the number of non-equivalent sites occupied by a resonant atom in a crystal lattice is very helpful in a preliminary structure study made with the use of NQR. 

The statistical adiabatic channel model (SACM) " is one realization of the laiger class of statistical theories of chemical reactions. Its goal is to describe, with feasible computational implementation, average reaction rate constants, cross sections, and transition probabilities and lifetimes at a detailed level, to a substantial extent with state selection , for bimolecular reactive or inelastic collisions with intermediate complex formation (symbolic sets of quantum numbers v, j, E,J. ..)... 

The intensities of spectral lines are proportional to the transition probabilities of the corresponding atomic or molecular transitions. Sections 2.7 and 2.9 cover some experimental and theoretical methods for the determination of transition probabilities and lifetimes of excited states. 

Hence verify that the transition probabilities and lifetimes given in Table 4.3 are correct. 

Langer and Doltsinis [45] have calculated nonadiabatic surface hopping trajectories for 10 different initial configurations sampled from a ground state AIMD runs at 100 K. They later extended their study to a total of 16 trajectories [41, 42], From a mono-exponential fit to the 5) population a lifetime of 1.3 ps is obtained (see Table 10-1 the average transition probability and its standard deviation leads to the interval [0.6...1.1...3.5] ps. Thus methylation appears to result in a slightly longer excited state lifetime. 

There is presently a large volume of literature devoted to the properties of isoelectronic diatomic molecules. Interest in these molecules comes from diverse areas of physics and chemistry. However, most of such literature reports calculations of lifetimes, transition probabilities, and energy levels. To the lesser extent, there have also been calculations and experiments on polarizabilities, NMR chemical shifts, harmonic and higher order force constants, and so on. 

Deactivation of electronic excited slates may also involve phosphorescence. After inlersystem crossing to the triplet state, further deactivation can occur cither by internal or external conversion or by phosphores cencc. A triplet — singlet transition is much less probable than a singlet-singlel conversion. Transition probability and excited-state lifetime are inversely related, Thus, the average lifetime of the excited triplet stale with respect to emission is large and ranges from 10 to 10 s or more. Emission from such a transition may persist for some time after irradiation has ceased. 

By scanning the probe laser over one or more rotational branches of the product, the relative intensities of the lines in this excitation spectrum may be used to determine product rotational (and/or vibrational) state distributions. In order to arrive at fully quantitative answers, corrections have to be made for relative transition probabilities, fluorescence lifetimes of the excited state, and any wavelength-dependent detection functions (such as the detection system spectral response). But once this has been done, one can deduce the ground state distribution function(s) by examining the so-called excitation spectrum of a molecular species. For thermal equilibrium conditions, the level population /V, can be described using a Boltzmann distribution function with temperature as the most important parameter in its most general form this is... 

The oscillator strengths can be measured by several experimental techniques. One of them uses the measurement of absorption profiles or dispersion profiles. Lifetime measurement (see Sect. 2.10), which give direct values of transition probabilities and therefore information on the natural line width of a transition (see Sect. 3.1) are a valuable source for the determination of oscillator strengths. 

In the proposed book there is an emphasis cm luminescence lifetime, which is a measure of the transition probability and non-radiative relaxation from the emitting level. Luminescence in minerals is observed over a time interval of nanoseconds to milliseconds. It is therefore a characteristic and a unique property and no two luminescence emissions will have exactly the same decay time. The best way for a combination of the spectral and temporal nature of the emission can be determined by time-resolved spectra. Such techniques can often separate overlapping features, which have different origins and therefore different luminescence lifetimes. The method involves recording the intensity in a specific time window at a given delay after the excitation pulse where both delay and gate width have to be carefully chosen. The added value of the method is the energetic selectivity of a laser beam, which enables to combine time-resolved spectroscopy with powerful individual excitation. 

N.P. Penkin Experimental determination of electronic transition probabilities and the lifetimes of the excited atomic and ionic states, in Atomic Physics 6, ed. by R. Damburg (Plenum, New York 1979) p.33... 

Fermi level. In a coarse approximation the p-level distribution can be assumed to correspond to that of a Fermi gas of free electrons, or even simpler, to that of a rectangular shaped distribution of equally spaced states (Richtmyer et al. 1934). Assuming equal transition probabilities and a Lorentzian lifetime broadening, the K absorption coefficient follows an arctan curve as a function of energy (cf. fig. 7, Ho) ... 

The shorter lifetime in the glass ceramic is probably due to the effect of the oxide matrix incorporating the nanoparticles. Indeed, several studies have proved that the oxide glassy matrix interacted with the rare-earth ions situated inside the nanosized crystallites and influenced their spectroscopic properties [65, 66]. Indeed, those Er ions close to the nanocrystallite/glass interface are in distorted sites. As the distortions lower the symmetry, this could result in an increase in the electric dipole transition probability and consequently decrease the radiative lifetime. Moreover, those Er " " ions close to the surface of the crystallites can be sensitive to the presence of oxide ions in their coordination polyhedron, inducing multiphonon nonradiative contribution to the Er " " de-excitation and lowering the lifetime. 

According to (2.58,59) the oscillator strength can be determined experimentally from measurements of absorption and dispersion profiles of spectral lines (see Sect.2.7.2). Another, widely used method derives transition probabilities and oscillator strengths from measurements of spontaneous lifetimes of excited levels. This will be discussed in the next section. 

Duquette [22] has measured branching ratios from intensity-calibrated emission spectra recorded by Fourier transform spectroscopy and determined transition probabilities using lifetimes x measured by the method given in [16] (see above). 

From the results contained in Table 4,2 the transition probabilities and radiative lifetimes of hydrogenic energy levels can be calculated using equations (4,30) and (4.26)... 

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