Second-order perturbation calculations for the hydrogenic Zeeman effect

Second-order perturbation calculations for the hydrogenic Zeeman effect are performed using the effective Hamiltonian of Delande and Gay (1984) and the hydrogenic basis separable in parabolic coordinates. Manifolds characterised by magnetic quantum numbers mod m mod =n-1, n-2, n-3, n-4 and an arbitrary principal quantum number n allow for a completely analytic determination of the first two Rayleigh-Schrodinger coefficients. For highly excited states. When mod m mod <or=n-5, the calculations of the coefficients include a numerical diagonalisation within the given subspace with fixed n and m. Comparisons with variational results are presented and the application of the method to calculation of zeroth-order bound-bound transition matrix elements is discussed.