The mechanism of orbital collapse

For (b) and (c), resonances can appear in the continuum, drop below threshold and turn into bound states as the potential becomes more attractive 

the double-well potential originates (i) from the presence of the centrifugal barrier and (ii) from the existence of an atomic core. These are sufficiently general for the double-well potential to develop slowly and deepens systematically with increasing atomic number [204]. 

We turn now to the mechanism of orbital collapse, which is not immediately obvious from the numerical calculations of the various authors quoted above. It has been explained by Connerade [210, 211] using analytic potentials and elementary quantum theory. The key feature to note is the difference in nature between different kinds of potential in quantum mechanics. This is illustrated in fig. 5.9(a). First, we have the familiar Coulomb well or long range potential. This, as we have seen in chapter 2, gives rise to Rydberg series containing an infinite number of 

The third kind of well we need to consider is the asymmetric short range well, shown in fig. 5.9(c) this well shares most of the properties of the symmetric short range well, except for (i) it can, in fact, be completely empty of states, a fact which is of crucial importance in the present context. Asymmetric short range wells include the asymmetric square well with one hard wall, (whose ground state is made up from the first excited state of the symmetric well), the Morse potential, the Lennard-Jones potential, etc, several of which will be of interest to us. 

The inner well of the double-valley potential of fig. 5.8 has the characteristics of a short range potential. It was speculated by Connerade [210] 

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