Theoretical Studies of Lanthanide and Actinide Spectra*

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Abstract
In the present paper I have sought to explore the role and feasibility of theoretical calculations in the interpretation of the energy levels of the rare earths and their associated electronic properties. I have attempted to show that the density of states places a fundamental limitation on establishing a unique correlation between the experimental and theoretical energy levels in rare earths. For most rare-earth electron configurations containing five or more electrons (or holes) outside closed shells, the density of states is sufficiently high as to preclude the possibility of a unique correlation except for those levels built upon the lowest energy states of the fN core. The levels of the fN(N = 5 to 9) configurations follow the Wigner statistical distribution quite closely, with the result that most of the electronic properties that distinguish the character of one level from another are smeared out. It is suggested that whenever the density of states is high, the energy levels and their associated properties will be statistically distributed.