Higher order diamagnetic contributions to shift and splitting of atomic levels in a magnetic field

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Abstract
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 (2)nlm, is decomposed into irreducible parts by analogy to the electric hyperpolarizability. The irreducible parts are written in terms of the second-order radial matrix elements of the quadrupolar operator. Numerical calculations have been carried out for the ground and excited states of alkali atoms. For the states of the hydrogen atom with the highest angular momenta, l=n-1, l=n-2, and projections on the field vector m=+or-1, +or-(l-1) (the nondegenerate states), the analytic expressions for the second-order diamagnetic susceptibilities, chi (2)nlm, have been derived, providing the information on the asymptotic behaviour of chi nlm for the high-momentum Rydberg states with n>>1. The boundaries, for the use of perturbation theory in the calculation of atomic energy in strong magnetic fields, are also discussed.

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