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Sudden limit

The situation presented in fig. 29 corresponds to the sudden limit, as we have already explained in the previous subsection. Having reached a bend point at the expense of the low-frequency vibration, the particle then cuts straight across the angle between the reactant and product valley, tunneling along the Q-direction. The sudden approximation holds when the vibration frequency (2 is less than the characteristic instanton frequency, which is of the order of In particular, the reactions of proton transfer (see fig. 2), characterised by high intramolecular vibration frequency, are being usually studied in this approximation [Ovchinnikova 1979 Babamov and Marcus 1981]. [Pg.71]

When both vibrations have high frequencies, Wa, coq, the transition proceeds along the MEP (curve 1). In the opposite case of low frequencies, rUa.s the tunneling occurs in the barrier, lowered and reduced by the symmetrically coupled vibration q, so that the position of the antisymmetrically coupled oscillator shifts through a shorter distance, than that in the absence of coupling to qs (curve 2). The cases (0 (Oq, < (Oo, and Ws Wo, (Oq, characterized by combined trajectories (sudden limit for one vibration and adiabatic for the other) are also presented in this picture. [Pg.92]

We have tacitly assumed that the photoemission event occurs sufficiently slowly to ensure that the escaping electron feels the relaxation of the core-ionized atom. This is what we call the adiabatic limit. All relaxation effects on the energetic ground state of the core-ionized atom are accounted for in the kinetic energy of the photoelectron (but not the decay via Auger or fluorescence processes to a ground state ion, which occurs on a slower time scale). At the other extreme, the sudden limit , the photoelectron is emitted immediately after the absorption of the photon before the core-ionized atom relaxes. This is often accompanied by shake-up, shake-off and plasmon loss processes, which give additional peaks in the spectrum. [Pg.62]

However, we must underline that this simple relation is only valid in the sudden limit, Erot excitation function and therefore the final state distribution depends on the energy E, the reduced mass m, and last but not least the anisotropy parameter 0(7).+ More of the interrelation between the anisotropy of the PES and the final rotational state distribution follows in Chapter 10. [Pg.126]

Grinberg, H., Freed, K.F., and Williams, C.J. (1987). Three-dimensional analytical quantum mechanical theory for triatomic photodissociation Role of angle dependent dissociative surfaces on rotational and angular distributions in the rotational infinite order sudden limit, J. Chem. Phys. 86, 5456-5478. [Pg.391]

So far, we have fairly extensively discussed the general aspects of static and dynamic relaxation of core holes. We have also discussed in detail methods for calculating the selfenergy (E). Knowing the self-energy, we know the spectral density of states function A (E) (Eq. (10)) which describes the X-ray photoelectron spectrum (XPS) in the sudden limit of very high photoelectron kinetic energy (Eq. (6)). We will now present numerical results for i(E) and Aj(E) and compare these with experimental XPS spectra and we will find many situations where atomic core holes behave in very unconventional ways. [Pg.37]

In summary, the model allows for two types of interactions between the mirror spaces, the weak kinematical perturbation and the adiabatic and sudden limits equivalent to Eq. (17) or Eqs. (29)-(34). The overwhelming rate of particles over antiparticles in the Universe is inferred in this picture once the particular particle state has been selected. The Minkowski metric of the special theory of relativity is represented here by a non-positive definite metric, Eq. (8), bringing about a quantum model with a complex symmetric ansatz. Although the latter permits general symmetry violations, it is nevertheless surprising that fundamental transformations between complex symmetric representations and canonical forms come out unitary. [Pg.131]

The current interest in alcohols as motor fuels is rooted in the search for alternate fuels to replace our suddenly limited petroleum-based fuels. The fact that methyl alcohol (methanol) can be produced from a variety of sources, including coal and garbage, has focused considerable attention on this material as a possible alternate fuel. The fact that the tech-... [Pg.245]

In the strict kinematic limit in which no forces act, one takes the time derivative of Eq. (3) to conclude that the transformation Eq. (3) also relates the initial and final velocities. Often however there is a strong repulsion between the products and in the sudden limit this force gives rise to an impulsive change of the velocities. It follows that the velocities transform as... [Pg.33]

WKB-phase shifts are used for the isotropic part of the potential and phase shifts in the sudden limit for the anisotropic part (Cross, 1967) produced cross sections which are also in quantitative agreement with the experimental results (Buck et al., 1975). It proved necessary to introduce a large P,-contribution to the potential in order to get this agreement for the scattering of symmetrical top molecules on atoms. Thus this type of measurements seems to provide a reliable method for the determination of the anisotropic part of the potential. [Pg.377]

Fast Variables Near Sudden Limit Physics... [Pg.195]

Near Sudden Limit Physics and a Nonclassical Concept of Dissipation... [Pg.196]

We have emphasized in this chapter that Arrhenius principle implies that liquid phase chemical reactions occur in a nonclassical fast variable near sudden limit timescale regime rather than in the slow variable near adiabatic regime of standard irreversible statistical mechanics. Despite this, the traditional theories of liquid phase reaction dynamics [7-10] are of the slow variable type. [Pg.217]

Xho d sateUit The principal multiplet of the d final state for CuO is known to fall at 12.5 with a smaller one around 10 eV (15). The intensity of the d final state can be enhanced by the Cu 2p 3d resonant excitation process followed by an Auger decay (15). This process is resonant between 72-80 eV. The HTSC s exhibit a similar behavior (j ). The satellites in CuiO and Cu do not have non-resonant components (IS) because the UPS for CuiO and Cu reflect the one-hole DOS. However, the VB XPS of CuO and the HTSC s can and do show a significant nonresonant d satellite (see Figure 1) (23) indeed, it should grow as one approaches the sudden limit. This possibility makes it even more difficult to interpret the XPS data for the HTSC s, since the d satellite at 12.5 in the VB XPS falls at or near the same energy as the Ba spin-orbit split 5p features, which have been very controversial. [Pg.90]

The SCP-IOS model is the semiclassical approximation of Miller and Smith applied to the reaction-path Hamiltonian. It has the appealing feature that it behaves qualitatively correctly both in the adiabatic limit, which is the situation if the transverse vibrational motion is much faster than motion along the reaction coordinate, and also in the sudden limit, which is the case if reaction-coordinate motion is much faster than transverse vibrational motion. For the case of a coll inear atom-diatom reaction it becomes the Hofacker-... [Pg.34]

A sudden rotationally averaged cross section may be derived analogously. In the sudden limit all reagent rotational states collapse to the ground rotational state and the summation over j states is replaced by integration over an angle. Thus... [Pg.159]

Suppose that the two potential surfaces are dissimilar. Then the Franck-Condon factors are less than imity and you get different probabilities for making transitions to final v" vibrational levels depending on the vibrational overlap. We shall make repeated use of the Franck-Condon principle in imderstanding which vibrational levels are populated in various dynamical processes. In Section 9.2 we will generalize the principle so that it also applies to excitation as a result of a collision (where we need not be in the sudden limit). [Pg.267]

The model used here for electronic friction can be improved by using Kohn-Sham one-particle wavefunctions instead of those based on the Bloch potential. Also the solution of the many-electron problem can be improved. Instead of using the sudden limit, we may, with present computer facilities, integrate the eqs. (11.43) for a system involving 100 to 10(X) electrons. [Pg.182]


See other pages where Sudden limit is mentioned: [Pg.477]    [Pg.66]    [Pg.99]    [Pg.141]    [Pg.126]    [Pg.183]    [Pg.130]    [Pg.182]    [Pg.705]    [Pg.374]    [Pg.8]    [Pg.272]    [Pg.92]    [Pg.265]    [Pg.359]    [Pg.372]    [Pg.372]    [Pg.373]    [Pg.374]    [Pg.420]    [Pg.595]    [Pg.180]   
See also in sourсe #XX -- [ Pg.265 , Pg.372 ]




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