Collective moleculelike model

A second implication of the collective, moleculelike model concerns the states with excitation in the bending mode. The bending mode of the linear rotor-vibrator is of course doubly degenerate. Hence, there are two independent states with one quantum of bending, which should be very similar to one another and should differ markedly from the state with no excitation as with all first excited vibrational states, their probability distributions should be zero at the potential minimum where the density of the unexcited state is a maximum. In this case, the implication is that the two first excited bending states... 

Beginning less than 10 years ago, the independent-particle model for atoms was challenged, first for a specific set of rather exotic states of helium and, more recently, for the ground and ordinary excited states of the alkaline earth atoms Be, Mg, Ca, Sr, and Ba. Evidence has been building that the quantization in these two-electron and quasi-two-electron atoms corresponds to collective, moleculelike behavior, rather than to independent-particle-like behavior. 

In this chapter we review the recent history of and evidence for collective, moleculelike behavior of valence electrons in atoms and indicate some of the questions that will have to be explored in order to resolve the question of how well the electrons in atoms are described by independent-particle or collective models. We then turn the question around and ask whether atoms in a molecule could, under suitable circumstances, display independent-particle behavior, with their own one-particle angular momenta behaving like nearconstants of the motion. The larger question that emerges is then one of whether few-body systems—the valence electrons of an atom, the atoms that constitute a small polyatomic molecule, and perhaps others such as the nucleons in a nucleus, all of which have heretofore seemed nearly unrelated— share characteristics to the extent that we can devise a unifying picture of the dynamics of few-body systems that will expose their commonalities as well as their obvious differences. 

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