Mid Sweden University

It has earlier been shown that the use of a self consistent multipole electrostatic model to derive the crystal field parameters (CFP) actually gives the correct curve shape when the CFP are plotted against the various rare-earth ions (S. Edvardsson, M. Klintenberg, The use of CI calculated polarizabilities to study rare-earth CFP dependencies in the laser host RE:YLF. Mater. Sci. Forum, 1999;315-317:407). It is also known that the electrostatic contribution is important for the lower order parameters. In this connection; our primary interest is to revisit this model and investigate theoretically some aspects of the dipole polarizability (alpha(D)). A few approximations were done in the earlier calculations: the treatment of unfilled shells, the neglect that also higher order terms of the type A(10)r(t)C(0)(t) contribute with t odd (not only the A(10)r(1)C(0)(1) term), correlation effects and second order contributions in perturbation theory. The solutions of the inhomogeneous Schrodinger equation are solved by a powerful numerical method. The problem is reformulated and results instead in a simple linear equation system (symmetric tridiagonal matrix) which is stable and fast to solve. The various theoretical results will be used in future applications.