Interacting resonances

We evaluate the pseudoinverse matrix w (o) of the transition rates (4.2.28) between energy states of a harmonic oscillator which interacts resonantly with a phonon reservoir. With this aim in view, it is necessary to 1) write... 

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

D. Sokolovski, S.K. Sen, V. Aquilanti, S. Cavalli, D. De Fazio, Interacting resonances in the F+H2 reaction revisited Complex terms, Riemann surfaces, and angular distributions, J. Chem. Phys. 126 (2007) 084305. 

G.F. Gribakin, J.A. Young, C.M. Surko, Positron-molecule interactions Resonant attachment, annihilation, and bound states, Rev. Mod. Phys. 82 (2010) 2557. 

The data presented in Table 26 indicate that the resonance effect of the u-CHsO and p-CH30 increase the rate augmentation by the phenyl ring. However, the m-CH30 does not interact resonatively with the reaction center, as shown by the elimination rate of HC1 which is similar to that of the unsubstituted phenylethyl chloride. 

Fingerprints of the Pairing Interaction Resonance Peak and Kink... 

A number of physical studies have been performed on Mn111 porphyrins in an attempt to understand their electronic structure. The visible spectra of such compounds have been of particular interest. For most metal porphyrins the visible spectrum is insensitive to the nature of the coordinated metal and this has been interpreted as indicating little interaction between the metal and the porphyrin 7r-orbitals in such compounds. However this is not the case for Mn111 porphyrins which exhibit metal-dependent charge transfer absorptions. This dependence appears to reflect significant n orbital-Mn"1 interaction. Resonance Raman and linear dichroism spectral studies are also consistent with this conclusion.667... 

SFG using femtosecond lasers allows all the resonances within the broad (-200 cm" ) bandwidth of the IR pulse to be probed simultaneously, without scanning the infrared source. To obtain spectral resolution in an SFG spectrum, the IR polarization is upconverted with a narrowband (-8 cm" ) visible beam, which is prepared by pulse shaping the output of a femtosecond laser. Only the frequency components of the pulse that interact resonantly with the vibrational modes are enhanced, resulting in an SFG spectrum [28, 29]. Owing to the use of femtosecond... 

The first part of the chapter contains a brief summary of Wigner s scattering theory, presented so as to emphasise the underlying similarity with the closely related approach of MQDT (chapter 3). This is followed by a discussion of the properties of S-, R- and K-matrices, in which we give the motivation for choosing one or the other, depending on the application in hand. Finally, we turn to some explicit applications of K-matrix theory to cases of interacting resonances in atomic physics. 

A specific advantage of using the K-matrix approach in the present context is that the transition to a numerical treatment of the equations can be postponed until quite a late stage, thus allowing the full algebraic structure of the interacting resonances to be displayed. 

Wigner s theory is most useful for studying cases of Rydberg series of interacting features in which an intruder appears. There are several distinct effects in the spectra of interacting resonances which result from perturbations, and are readily described by K-matrix theory. We first list them, and then discuss each one in turn. 

Although most suitable for use with lasers, Thermionic diodes have also been successfully applied to synchrotron radiation studies by using wiggler magnets to enhance the intensity of the beam [390]. Last but not least, one should mention the important category of atomic beam experiments, complemented by the techniques of photoelectron and photoion spectroscopy. All these techniques are suitable for the experimental study of interacting resonances. We turn now to their theoretical description, which will be illustrated by experimental examples. 

Thus, laser spectroscopy, and in particular ionisation spectroscopy involving several photons, allow one to study the mechanism of autoionisation itself, as opposed to testing the quality of atomic wavefunctions used to obtain pre-diagonalised states. Thereby, interest in the subject of interacting resonances and their parametric representation is enhanced (see in particular section 8.20). 

Fig. 5.10. Reaction profile, model of two intersecting parabolas. The activation energy is if the reaction energy AE is zero (solid parabola on the right). If the reaction energy AE is negative (dotted parabola on the right) AE is smaller than AEq and the transition state, i.e. the intersection of parabolas, is closer to the reactants. A modification of the simple model in which the two potentials interact (resonance energy H) is shown as dash-dotted line...

The almost Breit-Wigner profiles correspond to the almost exponential decays of the two weakly interacting resonances in (c) and (d). The interference between the two resonances in (b) is similar to the interferences appearing in Fano profiles (Section 2.2.3, Figure 1.6). 

Paidarova, Ph. Durand, Modeling quantum resonances 1. Dynamics of interacting resonances, in J. Maruani, R. Lefebvre, E. Brandas (Eds.), Advanced Topics in Theoretical Chemical Physics, Vol. 12 Progress in Theoretical Chemistry and Physics, Kluwer Academic, Dordrecht, 2003, p. 271. 

F.X. Gadea, P. Durand, T. Gonz ez-Lezana, G. Delgado-Barrio, P. Villareal, Effective resolvent applied to interacting resonances, Eur. Phys. J. D 15 (2001) 215. 

P. Avan, Interacting Resonances in Atomic Spectroscopy, Ph.D. Thesis, Universite de Paris VI, 1976. 

J.-P. Connerade, A.M. Lane, Interacting resonances in atomic spectroscopy. Rep. Prog. Phys. 51 (1988) 1439. 

Figure 8.2 Time dependence of the probability Pe(t) of observing the spontaneously decaying two-level system in its excited state at the center of a closed spherical cavity The number of resonantly interacting field modes is of the order of rR/ 7rc and depends on the size of the cavity R. For FR/c = 10 (upper figure) a spatially localized photon wave packet is generated by spontaneous emission and can be reabsorbed again by the two-level system at the center of the cavity at later times. For FR/c = 1 (lower figure) only a small number of cavity modes interact resonantly and the two-level system performs approximate Rabi oscillations governed by the vacuum Rabi frequency.

Such concepts as configuration interaction, resonance, hybridization, and exchange are not real physical phenomena, but only artifacts of the approximations used in the calculations. Likewise, the concept of orbitals is but an approximation, and, strictly speaking, orbitals do not exist. 

Justification for using two-plate quadrupolar excitation has been reported by several groups including Jackson et al. who demonstrated the qualitatively similar results of a mixture of PEG 1000 and PEG 1500 undergoing both two-plate and four-plate ion axialization. The authors note that despite the complex dynamics and interacting resonances produced from a two-plate excitation, the results show similar efficiencies in their ability to cool ions. 

We have neglected here the effect of level widths on the mixing coefficients, which is unimportant in the case of strong perturbations. This effect may play a role for weakly interacting, resonant levels (see below). 

When interacting resonantly with a photon, an atom or molecule changes from one energy level to another while in an excited energy state it can also decay spontaneously to a lower state. The probability of an atom or molecule changing states depends... 

Since the nuclear resonant scattering is a coherent elastic process it is impossible to identify the scattering atom in the sample. Instead, for each individual resonant nucleus there is a small probability that this nucleus is excited. The summation of all these small amplitudes gives the total probability amplitude for a photon to interact resonantly with the nuclei. If the incident radiation pulse is short compared to the nuclear lifetime Tq. these probability amplitudes exhibit the same temporal phase. As a result, a collectively excited state is created, where a single excitation is coherently distributed over the resonant atoms of the sample [44]. The wave function of this collectively excited state is given by a coherent... 

MODELING QUANTUM RESONANCES I. DYNAMICS OF INTERACTING RESONANCES... 

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