[ General Glossary, Quantum Glossary, Atomic Glossary ]
Hydrogenic Scaling

There are several straight-forward scaling laws associated with hydrogen-like ions. Amongst these, the most important are the following:

Energy Levels

The energies of the levels are well approximated by the Bohr atom. Thus the energies of the lines (Eik) due to transistions between the ground-state (ie ni = 1 shell; the K-shell) and the nk > 1 shells (ie L-, M-, N-shells etc), are well approximated by
Eik = Ebf [1 - (nk)-2]
where Ebf is the energy of the bound-free absorption edge.

The first few factors are given in the table to the right. See also a list of the bound/free transistion energies.

nk [1 - (nk)-2]
2 0.7500
3 0.8889
4 0.9375
5 0.9600
6 0.9722
7 0.9796
8 0.9844
9 0.9877

Oscillator Strengths

For transistions from the ground-state (ie ni = 1 shell; the K-shell) and the nk > 1 shells (ie L-, M-, N-shells etc), the oscillator strengths (fosc) for all hydrogen-like ions are (very, very nearly) the same as for H I.

The first few are given in the table to the right.

nk fosc
2 4.16x10-1
3 7.91x10-2
4 2.90x10-2
5 1.39x10-2
6 7.79x10-3
7 4.81x10-3
8 3.18x10-3
9 2.21x10-3

Furthermore, for nk > approx 15 , the strength is well aproximated by
fosc = 1.568 (nk)-3.
This is illustrated in the figure to the right.


See also More on Hydrogen-like Ions or