Molecules, large Fermi resonance

The relatively large number of experiments on vibrational relaxation compared to other means of access to the molecular dynamics (such as translational, rotational, or electronic relaxation) stems from the richness of vibrational structure. A molecule composed of N atoms presents 3N — 6 vibrational modes and still only three translational degrees of freedom. In addition the vibrational overtone manifold cannot always be ignored due to accidental (strongly size-dependent) degeneracy and Fermi resonance with fundamental modes. 

Let us now consider what is the analog of a Fermi resonance in a molecule when we consider the crystals. In going over from an isolated molecule to a crystal, the branches of optical phonons appear. In the region of overtone and sum frequencies, several bands of many-particle states arise and, if anharmonicity is sufficiently strong, bands of states with quasiparticles bound to one another (for instance, biphonons) will also appear. Thus, in crystals a large number of... 

Bond distances obtained in infrared and Raman studies are normally ro or r distances. Although data from the infrared are now, in general, precise enough to obtain distances, the large amounts of pure rare isotopic species required to obtain these distances preclude the substitution technique, and only a handful of partial r, structmes have been obtained by optical methods. In these tables, whenever both r and ro stractmes have been derived for a given molecule, only the r structure is listed. UtKertainties in r parameters are not easily estimated since for polyatomic molecttles the study of several vibration-rotation bands is required and quite often the data used come from several different laboratories and have been obtained over a period of years. The derivation of r parameters also often necessitates certain assunqttions regarding the effects of perturbations, especially Fermi resonances. The limitations of ro parameters have been detailed above in Section 1.4.1. 

The isotopic shift of a given vibrational frequency will be small if the atoms replaced by the isotopes participate only to a small extent in the vibration, but the shift will be large if these atoms play a major role. Thus, the shift an isotope produces can be used as a measure of the extent to which a particular atom participates in a vibration, provided no factors other than the change in mass are involved in the observed shift. A phenomenon such as Fermi resonance may be enhanced when an isotope is substituted into a molecule, if the shift brings frequencies more nearly into coincidence. 

Therefore, the problems which faced the would-be designers of chain reactors early in 1941 were (1) the choice of the proper moderator to uranium ratio, and (2) the size and shape of the uranium lumps which would most likely lead to a self-sustaining chain reaction, i.e., give the highest multiplication factor. In order to solve these problems, one had to understand the behavior of the fast, of the resonance, and of the thermal neutrons. We were concerned with the second problem which itself consisted of two parts. The first was the measurement of the characteristics of the resonance lines of isolated uranium atoms, the second, the composite effect of this absorption on the neutron spectrum and total resulting absorption. One can liken the first task to the measurement of atomic constants, such as molecular diameter, the second one, to the task of kinetic gas theory which obtains the viscosity and other properties of the gas from the properties of the molecules. The first task was largely accomplished by Anderson and was fully available to us when we did our work. Anderson s and Fermi s work on the absorption of uranium, and on neutron absorption in general, also acquainted us with a number of technics which will be mentioned in the third and fourth of the reports of this series. Finally, Fermi, Anderson, and Zinn carried out, in collaboration with us in Princeton, one measurement of the resonance absorption. This will be discussed in the third article of this series. 

The experiments in followed a different approach to achieve mBEC [35]. For the halo dimers are less stable because of less favorable short-range three-body interaction properties. Therefore the sample is first cooled above the Feshbach resonance, where a is large and negative, to achieve a deeply degenerate atomic Fermi gas. A sweep across the Feshbach resonance then converts the sample into a partially condensed cloud of molecules. The emergence of the mBEC in is shown in Figure 9.16. 

---