Further limits optical and inner-shell excitations

If an approximate radial equation is constructed for a many-electron system, it must involve a non-Coulombic effective potential, because of the effects of electron-electron repulsion. Since the radial Schrodinger equation depends explicitly on , it is no surprise that the binding energy then depends on both n and , and so both must be specified for each electron when the configuration of the atom is written down. 

6 Further limits optical and inner-shell excitations 

Even if only the outermost or optical electron is excited, several Rydberg series of energy levels, distinguished by their value, can occur. Indeed, once the spin-orbit interaction is introduced, not only for the optical electron, but also (and, as it turns out, more importantly) for the core electrons, a large number of possible series and, indeed, more than one possible series limit can occur even if only the optical electron is excited. An example is shown in fig. 2.3. 

not only does a many-electron system exhibit many series of energy levels, but it also possesses many distinct series limits or ionisation potentials. These higher thresholds may correspond to the removal of one electron, but leave the singly charged parent ion in some excited state. Indeed, it is even possible to remove more than one electron by direct excitation, but this further complication will be excluded for the time being (see chapter 7). 

The first ionisation limit of a many-electron atom corresponds to the ground state of the corresponding or parent ion. Higher thresholds correspond to excited states of the parent ion. Apart from the special case of He, which has a hydrogenic parent ion, they are not simply related to fundamental constants. The many-electron Schrodinger equation must also be solved for the parent ion in order to determine the energies of the thresholds. 

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