11 - The hydrogen lines

Summary

The hydrogen lines deserve special consideration, not only because they are the strongest lines, but also because they are a very important tool in analyzing stellar spectra. The reason is that they are broadened by the so-called ‘molecular’ Stark effect, that is by the electric fields due to the passing ions. When a radiating atom or ion finds itself in an electric field, the energy levels are shifted to slightly different values of the excitation energy _n or χ_exc The emitted lines therefore occur at slightly different wavelengths. Even more important is that for the hydrogen atom the different orbitals contributing to the energy level with a main quantum number n, are normally degenerate, i.e., when there is no external force field they all have the same excitation energy (this is, of course, indicated by the statistical weight for each level). In the presence of an external force field this degeneracy is removed, so that in an external field the different orbitals contributing to a given level with main quantum number n now occur at slightly different values for the excitation energy. This in turn means that, instead of one line being emitted in the force free case, there are now several lines emitted or absorbed at slightly different wavelengths. Fig. 11.1 shows the different components which are observed for the different Balmer lines.

This shifting of the energy levels in the electric field of the neighboring ions has mainly two effects. First, it shortens the lifetime of the undisturbed level which, according to equation (10.15), results in a broadening of the undisturbed energy level.