It has earlier been shown that the Sternheimer method is appropriate in deriving crystal field parameters (CFP) for Pr3+ and Nd3+ doped in YLF or Nd3+ in YAG. In this connection, the dipole (αD) and quadrupole (αQ) polarizabilities for the whole rare-earth (RE) series will be presented. These are needed for the self consistent lattice summations performed. The various rare-earth wavefunctions needed for the computations are derived from the well known relativistic full Hartree-Fock code by R. D. Cowan. The main CFP behaviour for the various RE dopants in YLF are seen to agree fairly well with the experimentally fitted parameters. Covalency effects are, as expected, observed to be more important for higher order parameters. It is also seen that the contribution to the crystal field due to covalency is approximately constant for a given Btp. This observation is also supported by calculations of Newman. The shielding, nuclear antishielding factors and radial integrals for the whole RE series are also presented.