Article

Abstract

A method for calculating complete secular polynomials is discussedthat is based on the evaluation of matrix elementsof a specific Hamiltonian.Several Hamiltonians are presented and described in detail as well astheir physical significance. It is shown that theycan be transformed into an equivalent form in termsof raising and lowering operators, and the third componentof the spin operator. A basis set is definedand the action of a specific Hamiltonian on thebasis set is described in detail. Several Hamiltoniansare given explicitly and in matrix form. Results in terms of secularpolynomials for an anisotropic Hamiltonian with one anisotropyparameter and a Hamiltonian with two anisotropy parameters forseveral values of N are reported. These polynomialsthat have not appeared before are given in terms of both theenergy and anisotropy variables.PACS Nos.: 05.50+q, 75.10Dg, and 75.10 Jm