HIGHER-ORDER DIAMAGNETIC CONTRIBUTIONS TO SHIFT AND SPLITTING OF ATOMIC LEVELS IN A MAGNETIC-FIELD

The contributions of the diamagnetic interaction to the magnetic field -induced shift and splitting of atomic levels in the first and second orders of perturbation theory are calculated. The tensor of the second -order diamagnetic susceptibility for a degenerate state of atom, chi( nlm)((2)), is decomposed into irreducible parts by analogy to the elec tric hyperpolarizability. The irreducible parts are written in terms o f the second-order radial matrix elements of the quadrupolar operator. Numerical calculations have been carried out for the ground and excit ed states of alkali atoms. For the states of the hydrogen atom with th e highest angular momenta l = n - 1, I = n - 2, and projections on the field vector m = +/-l, +/-(l - 1) (the nondegenerate states), the ana lytic expressions for the second-order diamagnetic susceptibilities, c hi(nlm)((2)), have been derived, providing the information on the asym ptotic behaviour of chi(nlm) for the high-momentum Rydberg states with n much greater than 1. The boundaries, for the use of perturbation th eory in the calculation of atomic energy in strong magnetic fields, ar e also discussed.