Survey of the lanthanides

It has further been argued by Band and Fomichev [623] who have performed Dirac-Fock calculations of the transition from collapsed to decol-lapsed orbitals that a coexistence of states in the same atom, due to the formation of hybrid states, can occur One thus forms a picture in which it could also happen, in cases of fluctuating valence, that two different valence states would coexist on the same site [624]. 

However, Bringer s conclusion is at variance with the results of Band et al. [624]. It is also important to note that the centrifugal model does not require the occurrence of two distinct potential wells for orbital contraction to take place it is sufficient that there should be an inner potential well of finite range, connected to an outer well of much longer range. The main influence of the barrier (when it occurs) is to ensure a fuller spatial segregation of the collapsed and decollapsed states. This is how the Hartree-Fock version of the Mayer-Fermi theory for free atoms accounts for d-electron contraction, in which case a repulsive barrier actually does not form, and localisation becomes even more term- and configuration-dependent. 

A classification of lanthanide or rare-earth elements based on the number of 4/ electrons in the atomic and condensed phases is presented in table 11.2. 

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