Abstract
In order to understand the transferred hyperfine structure of the trigonal centres of Yb3+ in CaF2 it is essential to know their ground state wavefunctions accurately. For this purpose an estimate of the crystal field parameters must be made. The authors calculations of the crystal field parameters and the ground state wavefunctions are discussed. The limited data available from optical and EPR studies make it necessary to construct models of the crystal fields of these centres by comparison with one another and with the well known cubic centre. The most suitable model for each centre has been selected using a least squares fit to the available data, followed by chi 2 tests of significance. A good model of the T2 centre has been found giving accurate ground state wavefunctions. For the T1 and T3 centres the models are not so good, but give adequate accuracy. The estimates of the crystal fields have allowed us to make predictions of the positions of all the energy levels of the Yb3+ (4f13) configuration in these centres.

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