The oscillator strengths reflect the fact that transitions are more likely between quantum mechanical states with similar wavefunctions – which give rise to strong lines – versus those with very dissimilar wavefunctions – which give rise to weak “forbidden” lines. But calculating wavefunctions is somewhere between difficult and impossible, and numerical approximation often don’t seem to resemble reality particularly well. Hence the tendency to use empirical lab measurements.
This is bringing back memories.
I am but a humble experimental chemist and know rather little quantitative about atomic spectroscopy, other than hydrogenic systems in the Schrödinger approximation. My DPhil research, was on robvibronic structure in the electronic spectra of Cu2 and CeO in the gas phase. More recently I helped the Exomol team with AlH. A beauty of that field of work is there is a plethora of rotational lines, by and large, and frequently a good number of vibrational bands. Fairly easy to measure the temperature also. With all those measurements fitting a potential curve is not entirely trivial, especially near dissociation, and very difficult when two states perturb each other. However, very accurate results are possible and it is (usually) straightforward to reverse engineer properties such as dipole moment, polarizability and so on. In particular, oscillator strengths — which is what this thread has done to refresh my RAM.
Thank you both.
(BTW, One state in AlH is barely bound and I failed to get a good enough approximatiom to the potential energy curve. Believe it or not, an ab initio calculation was the key to solving this one. It gave a fairly good PEC but a not particularly good absolute energy. The latter was known very precisely from the spectra and putting the two together gave excellent predictions for the oscillator strengths.)