Closed summation of large perturbation orders: the s-d series for hydrogen in a magnetic field

Abstract

A 'method of the model series' is proposed which aims at making useful slowly convergent perturbation expansions. The large-order perturbation wavefunctions are covered in closed form with the help of a model series of proper asymptotic behaviour. The method is applied to Killingbeck's s-d expansion of the ground-state quadratic Zeeman effect. It produces accurate Zeeman energies at a moderate computational effort.