Orthogonal polynomial expansions for effective interactions in the modified Lipkin model

B. D. Chang, Louisiana State University
J. P. Draayer, Louisiana State University


The effective interaction in a one-dimensional model is calculated in terms of an orthogonal polynomial (OP) expansion derived from spectral distribution considerations. Configuration densities are assumed to be gaussian. The results are compared with those of a Brillouin-Wigner (BW) perturbation expansion for the same model. While for a strong perturbation the BW series diverges, the OP expansion is shown to converge smoothly. © 1979.