The Goppert-Mayer-Fermi theory of orbital contraction

It seemed at first surprising that isolated and rather intense atomic transitions should be present in the solid. In order to establish the correctness of this interpretation, it was necessary to investigate the spectra of the corresponding free atoms which, largely for technical reasons, had escaped observation until then. They were not in fact uncovered until 1974 [189, 190], when the first observations of a giant resonance in a free atom were reported independently. 

Detailed observations and assignments of the giant resonances in many free atoms then followed rapidly, guided by the earlier observations for the solid. It was soon established experimentally that the quasiatomic giant resonances occur for nearly all solids for which the corresponding atomic transition exists, and that they may persist both in molecules and in ions. A detailed discussion of the properties of giant resonances in atoms, molecules and solids may be found in the book Giant Resonances in Atoms, Molecules and Solids [191], which summarises much of the research in this area prior to 1986. 

7 The Goppert-Mayer-Fermi theory of orbital contraction 

This idea was followed up by Goppert-Mayer [195] in 1941, who solved the radial equation for a number of elements in the d and / sequence. Unfortunately, she used the Thomas-Fermi model, which gives a fairly poor description of the radial potential and, as is now appreciated, does not account properly for the shell structure of the atom. Thus, although she found a certain number of interesting properties of 4/ elements (lanthanides), she was unable to account for the filling of the d subshells, and her paper did not therefore have the impact it might otherwise have achieved.1 

She had, through numerical calculations, uncovered that the effective radial potential experienced by 4/ electrons, namely 

---