The determination of ionisation potentials

the observation of Rydberg series allows ionisation potentials to be determined. This is done by fitting the Rydberg formula to the observed series members, and hence extracting the series limit. Since the assumption that p is a constant breaks down for the lower members, the simplest approach is to exclude them from the fit, and only to include series members for which p has settled down to a fairly constant value. This, however, is not the best approach, because even the lower members contain information on the nature of the variation of p with energy, which needs to be included if the most accurate value of the series limit is to be obtained. Note that p then ceases to be constant, and must be allowed to vary as a smooth function of energy. 

for example, the principal Rydberg series of He, i.e. the manifold of the strongest allowed transitions from the ground state  

The fitting of Rydberg series to high resolution data, when performed with sufficient accuracy, can reveal very fine details of atomic spectra. Thus, by carefully fitting the principal series of T , the influence of hy-perfine structure on the determination of the ionisation potential has been revealed [32]. 

---