Two-electron Rydberg law for the ns21S0Wannier states of alkaline-earth atoms

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Abstract
The first quantitative calculations on ns2 1S0 Wannier states of alkaline-earth atoms Be through Ba are presented. The two-electron Hamiltonian built on a discrete basis is diagonalised to give the energy positions of the seven lowest members of each Wannier sequence. For each element, the energies are found to obey a two-electron Rydberg law depending on two parameters, a screening constant sigma ' and a quantum defect correction mu ' to the effective quantum number of the parent state ns. The parameters sigma ' and mu ' are nearly the same for each alkaline earth and, moreover, close to those obtained for helium. Treating each ns2 1S0 Wannier state as the lowest member of a Rydberg series converging to the parent state ns, quantum defects are calculated for each ns ms 1S0 series; the linear n dependence of the computed quantum defects accurately reproduces that observed experimentally in several nsms core-excited Rydberg series of Ca and Ba.

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