Radial Limit in the Configuration-Interaction Method for the 1 1S State of the Helium Isoelectronic Sequence

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Abstract
Using the configuration‐interaction method with only radial configurations, precise radial limits are obtained for the ground state of the helium isoelectronic sequence for atomic numbers 1 thru 20. All matrix elements required in the calculation are shown to be obtainable from sums over integers, which eliminates all necessity of any multiple precision arithmetic in the computer calculation. Also, when the atomic number is varied, considerable saving in computer time is achieved by noticing that all Hamiltonian matrix elements are expressible in the form ZηA+η2B+ηC, where Z is the atomic number, η a nonlinear variational parameter, and A, B, and C are sums independent of Z and η.