Frozen excitation model

A molecular fluorescence model is presented which is particularly appropriate for short pulse excitation. The frozen excitation model treats the two rotational levels which are directly excited by the laser as an isolated system with constant total number density. Consider the four level molecular model illustrated in Fig. 1. The four level model was solved by Berg and Shackleford (5 ) for the case where steady state is established throughout all molecular levels. Levels le and 2e are the single... 

Using the frozen excitation model to analyze the data shown in Fig. 3, and calibrating the system via Rayleigh scattering (8J, a total OH number density of 4 x 1C>16 cm 3 was calculated for an assumed flame temperature of 2000 K in the methane-air torch. Nt was not compared directly with the results of absorption studies future flat flame burner studies will involve direct comparison of absorption and fluorescence. 

In Fig. 6.5a, the initial direction of K-electron rotation depends on the photon polarization vector, that is, clockwise (counterclockwise) direction for e+ (e ) excitation, which has been described in Sect. 6.3. However, the amplitudes of mt) temporally vary for both cases, due to the decrease of the overlap between the nuclear WPs moving on the relevant two adiabatic PESs as depicted later in Fig. 6.6. This is one of the characteristic behaviors that are absent in a frozen-nuclei model. As for nuclear motions, DCP vibrates during n-electron rotation as seen in Fig. 6.5b, but the behavior of Q(f) differs only slightly between e+ and e excitations. 

In contrast with previous studies on He2Cl2 cluster, in the present work localized structures are determined for the lower He2Br2 vdW states. Traditional models based on a He2Cl2 tetrahedron frozen stucture have failed to reproduce the experimental absorption spectrum, suggesting a quite delocalized structure for its vibrationally ground state. Here, based on ab initio calculations we propose different structural models, like linear or police-nightstick , in order to fit the rotationally resolved excitation spectrum of He2Cl2 or similar species. 

One example of non-IRC trajectory was reported for the photoisomerization of cA-stilbene.36,37 In this study trajectory calculations were started at stilbene in its first excited state. The initial stilbene structure was obtained at CIS/6-31G, and 2744 argon atoms were used as a model solvent with periodic boundary conditions. In order to save computational time, finite element interpolation method was used, in which all degrees of freedom were frozen except the central ethylenic torsional angle and the two adjacent phenyl torsional angles. The solvent was equilibrated around a fully rigid m-stilbene for 20 ps, and initial configurations were taken every 1 ps intervals from subsequent equilibration. The results of 800 trajectories revealed that, because of the excessive internal potential energy, the trajectories did not cross the barrier at the saddle point. Thus, the prerequisites for common concepts of reaction dynamics such TST or RRKM theory were not satisfied. 

In the one-electron transition model it is assumed that only one core electron is excited to an unfilled state present in the initial, unperturbed solid. The remaining electrons are assumed to be unaffected, remaining frozen in their original states. In essence the one-electron model describes the potential seen by the final-state electrons as nonoverlapping spherically symmetric spin-independent potentials (muffin-tin scatterers) centered around an atom from which the X-ray cross section from a deep core level of an atom to final states above the Fermi level can in principle be calculated for any energy above threshold. 

Virtually all non-trivial collision theories are based on the impact-parameter method and on the independent-electron model, where one active electron moves under the influence of the combined field of the nuclei and the remaining electrons frozen in their initial state. Most theories additionally rely on much more serious assumptions as, e.g., adiabatic or sudden electronic transitions, perturbative or even classical projectile/electron interactions. All these assumptions are circumvented in this work by solving the time-dependent Schrodinger equation numerically exact using the atomic-orbital coupled-channel (AO) method. This non-perturbative method provides full information of the basic single-electron mechanisms such as target excitation and ionization, electron capture and projectile excitation and ionization. Since the complex populations amplitudes are available for all important states as a function of time at any given impact parameter, practically all experimentally observable quantities may be computed. 

Table 3 lists the errors in excitation energies of Cs calculated with a relativistic ab initio one-valence electron PP and various forms of the cutoff-factor as well as with addition of a local potential. Clearly, for a given CPP the PP could be adjusted to reproduce (essentially exactly) the experimental energy levels, but then the PP without CPP does not model the frozen-core DHF AE case any more. 

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