Diamagnetic Shift and Splitting of Rydberg Levels in Atoms

Second-order contributions of diamagnetic interaction to the energy shift and splitting are studied in the basis of the angular momentum eigenfunctions for two kinds of Rydberg states in atoms: (i) hydrogen-like degenerate states and (ii) nondegenerate Rydberg states with small magnetic quantum number, m ? 3, in many-electron atoms. General formulae are presented for calculations of higher order energy corrections in degenerate states with the use of reduced Green's function. The analytical expressions are derived for the second-order radial matrix elements of operator r2 and for the second-order diamagnetic susceptibilities of hydrogen-like states with m ? n-5. The quasiclassical quantum defect method is used to calculate the irreducible components ?nl(p) of the diamagnetic susceptibility ?nlm(2) for Rydberg states of alkali atoms. The numerical results are presented for susceptibilities of degenerate hydrogen substates, and for susceptibilities of alkali atoms in Rydberg s-, p-, d-states. The asymptotic dependence of susceptibilities in alkali atoms on the effective principal quantum number ? is determined numerically and the deviation from that of the hydrogen-like states is discovered. The data is also presented for the scaling parameters cl(p), determining the irreducible parts of the diamagnetic susceptibilities in states with high ?, according to the asymptotic formula ?nl(p) = cl(p)?11.