Resonances heavy-particle

The chemical importance of heavy-particle Feshbach resonances cannot be overstated. They are present In unlmolecular rearrangements, both thermal ones and those which occur In organic photochemical reactions. In mass spectroscopic Ion fragmentations, and In blmolecular collisions which proceed through long-lived Intermediates. 

Table III. Heavy-Particle Feshbach Resonance Examples...

Recent years have seen the development of a number of methods for direct calculation of complex resonance energies, both In the context of electron scattering from atoms and molecules and In the context of heavy-particle scattering. This article Is not Intended as a review of that literature. Rather, I present here a brief summary of some of our own work together with a description of a few other approaches with the intention of exhibiting the common theme they employ. That theme is a generalized complex variational... 

The reverse of step 2 corresponds to a vibrational Feshbach resonance, which has never been observed experimentally for heavy-particle systems. The forward process, on the other hand, can be observed quite easily. One generally needs a supersonic molecular beam In order to achieve low enough temperatures to form A B without having macroscopic condensation of the sample, and a detector which... 

The method of perturbed stationary state (PSS) was applied to the heavy particle collision of symmetrical resonance by Buckingham and Dalgarno, Matsuzawa and Nakamura, and Kolker and Michels. Although the essential idea of our method is the same as in these papers, except for the inclusion of four levels, we include a brief description of the PSS method for later discussion. 

The expressions presented are valid only provided the inequalities (44) and (45) hold. However, for reactions involving heavy particle transfer but without electron transfer from one reactant to another, it may be expected that the electron resonance integral will be large, owing to large overlap of the electronic wave functions, and the inequality (44) will be violated. 

The motion of a heavy particle when accompanied by a screening cloud of band electrons was first studied by Kondo (1984) and later by Kagan and Prokofev (1986) as a model for muon diffusion in metals. Liu (1987) and Kagan and Prokofev (1987) independently proposed that the same mechanism applies in heavy-fermion systems. The idea is that the f band is formed by the hopping of an f hole whose motion is accompanied by the screening cloud. Just like the band problem in the spin fluctuation resonance model, the hopping is the result of the hybridization interaction. Consequently, the dispersion of the f band is again solved from eq. (52) where Gf(to) is now calculated from the f hole spectrum in eq. (57) (Liu 1987, 1988) ... 

Here, all the three particles are assumed to have a unit charge. The value of j3 is 6 for H with an infinitely heavy nucleus and is 8 for Ps. With the values of a from these analytic formulas, and hence f, Eq. (80) played an essential role in the analysis of the Feshbach series of resonances in muonic... 

---