A Modified Perturbation Procedure for a Problem in Paramagnetism

A modified perturbation technique is described for problems in which second-order effects are comparable in magnitude with first-order effects, where orthodox methods break down. It is applied to the energy levels of paramagnetic ions in a crystal, giving an effective Hamiltonian in which the Stark splitting, the anomalous g-value and the temperature-independent paramagnetism are clearly exhibited.