Rydberg states of many-electron systems

In these units, R, = 109737 cm-1 and (for H) Rjj = 109678 cm-1 which shows how small the mass correction is, even for the lightest atom. 

Finally, true frequency units can be used directly, an option usually preferred by laser spectroscopists, if the value just given is multiplied by c, yielding R = 3.2898274 x 1015 Hz the MHz and GHz are then popular measures for the bandwidth of high resolution lasers, while the kHz can be used to express the bandwidth of a truly excellent narrow band laser. 

It is a remarkable fact that many-electron atoms, molecules and, indeed, any nearly spherical compact assembly of charged particles can, even in the presence of internal excitations, exhibit Rydberg series of energy levels (an example is shown in fig. 2.2, i.e. apparently infinite manifolds of levels En obeying the formula  

This formula is very close to (2.1), apart from the introduction of He. and n. The similarity is in some ways deceptive because it conceals some essential differences, which are worth spelling out. 

For a many-electron system, even if one is concerned with only the lowest ionisation threshold and even if one neglects the spin-orbit interaction, it is no longer true that a single Rydberg series occurs. As noted in section 2.1, it is a remarkable feature of the two-body problem that, although 

---