Resonance processes

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3.13.81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Leimard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by pennanent dipole-dipole interaction). 

Resonant processes of some importance include resonant electronic to electronic energy transfer (E-E), such as the pumping process of the iodine atom laser... 

Another near resonant process is important in the hydrogen fluoride laser, equation (A3.13.37), where vibrational to vibrational energy transfer is of interest ... 

Non-resonant processes include vibration-translation (V-T) processes with transfer probabilities decreasing... 

Electron attachment. A resonance process whereby an electron is incorporated into an atomic or molecular orbital of an atom or molecule. 

Doktorov A. B. The impact approximation in the theory of bimolecular quasi-resonant process, Physica A 90, 109-36 (1978). 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

A second type of neutralization occurs through a resonance process, in which an electron from the sample tunnels to the empty state of the ion, which should then be at about the same energy. Resonance neutralization becomes likely if the electron affinity of the ion is somewhat larger than the work function of the sample, or if the ion has an unfilled core level with approximately the same energy as an occupied level in the target atom. The latter takes place when He+ ions come near indium, lead or bismuth atoms. The inverse process can lead to reionization. 

First, the solvent evaporates, leaving behind formula units of the formerly dissolved salt. Next, dissociation of the formula units of salt into atoms occurs—the metal ions atomize, or are transformed into atoms. Then, if the atoms are easily raised to excited states by the thermal energy of the flame, a resonance process occurs in which the atoms resonate back and forth between the ground state and the excited states. 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

The electron could also be captured by the neutral to form a negative radical ion. However, electron capture (EC) is rather unlikely to occur with electrons of 70 eV since EC is a resonance process because no electron is produced to carry away the excess energy. [10] Thus, EC only proceeds effectively with electrons of very low energy, i.e., from thermal electrons up to a few electronvolts (Chap. 7.4). However, the formation of negative ions from electron impact may occur with analytes containing highly electronegative elements. 

Because the cross section of a resonance process is expressed by the Breit-Wigner formula, the energy-integrated cross section is written as follows ... 

There are three possible mechanisms whereby an excited atom or ion can undergo an electronic transition near a metal surface (1) de-excitation involving the emission of radiation, (2) de-excitation involving a two electron Auger process, and (3) a resonance process whereby an electron is transferred from the metal to an equivalent energy level in the ion or a similar transition where the electron goes from the ion to the metal. However, Schekhter has shown that the probability... 

The equilibria of all reactions under such conditions are displaced toward exothermic processes, even those that lead to the formation of highly ordered systems. Furthermore, one should bear in mind the possibility of a kind of autoregulation of the predominant direction of such spontaneous reactions processes with a relatively small heat release (closer to resonance processes ) could proceed with higher probability and, as the complexity of the molecules formed increases, the probability of the dissipation of the evolved energy among the intramolecular degrees of freedom becomes more pronounced. Therefore it seems possible that at very low temperatures under the conditions of initiation by cosmic rays, even most complex molecules can be formed with a small, but still measurable, rate, and that slow exothermic low-temperature reactions can play some part in the processes of chemical and biological evolution. 

Permission to use published material was granted by Finnigan MAT, American Society of Mass Spectrometry, John Wiley and Sons, Inc., Journal of Chemical Education, and Organic Magnetic Resonance. Processing software was furnished by Herbert Thiele (Bruker Instrument Corp.). 

Since the backup ions other than aluminum are of a size similar to the terbium ion, it is reasonable to assume that the structure of the glass matrix over the whole series is the same. Therefore, the concentration dependence of the lifetime is unequivocally due to terbium ions being packed closer and closer together. Pearson and Peterson postulate that, as the ions are situated closer and closer together, the quenching mechanism of Dexter and Schulman (45) becomes operative. That is, the excitation jumps from ion to ion by a resonance process until it reaches a sink. 

The maximum in the CM X p(ECM) spectra is predicted at around 0.28 eV, as compared to 0.6 eV in the diatomic case. Unfortunately, the experimental observation of this maximum in the triatomic case is obscured by the elastic scattering. But clearly a much more resonant process is observed in the Na quenching by C02 and NzO illustrated in Fig. 27. A similar observation has been made for HzO, however, the latter does not quench... 

Near the resonances the cross section of vibrational excitation increases by several orders of magnitude. From the physical standpoint we can divide each resonance process into three stages. At the first stage the incident electron is captured by the electron shell of the molecule, forming an intermediate negative molecular ion. The second stage is the vibrational motion of the nuclei of the newly formed ion, which eventually leads to the third stage of the process—the decay of the intermediate ion. 

Depending on the kind of the intermediate molecular ion, all resonance processes can be divided into two groups.116 The first group is the so-called shape resonances, where the electron is trapped in a potential well formed in the ground electron state of the molecule by centrifugal or polarization forces. The lifetime of such states is between 10 15 and 10 s. 

For this work, the molecular structures derived using an AMI semiempirical method (20) served as input for an INDO SCF procedure (27), which generated the unoccupied molecular orbitals. (Note The summation in equation 2 over the vibrational subspace of each electronic state is approximated as unity and is valid for all off-resonance processes.) The dipole moment matrix and transition energies corresponding to these Cl states were calculated and inserted directly into equation 2. 

This estimation concerns water. In nonassociated liquids, mu, I or still less (GT, VIG see also Sections V.D.2 and V.D.3). This result indicates that in this case resonant processes are very damped in a liquid. 

To rephrase, the vector space spanned by [BBgv 1gv = 1 defines the N-element resonance Q-eigenchannel space, which alone describes the resonance processes, if the background S matrix is independent of E. The vector space complement to it defines the (N0 - N)-element nonresonance Q-eigenchannel space, which is totally unassociated with the resonance... 

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