Comparison of Correlated Wave Functions in the Helium Sequence

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Abstract
The method of calculating ground state energies of heliumlike atoms by use of a variational wave function is well known. The usual procedure is to start with an uncorrelated wave function multiplied by a correlation factor containing several variational parameters. The variational principle is then used to determine the parameters which give minimum energy. It has been the practice to use the same uncorrelated function and then compare the results when several different correlation factors were used. In this work, the same correlation factor is retained, and the effect of using two different uncorrelated functions is investigated. The correlation factor used was 1+c1r12+c2(r1−r2)2, where c1 and c2 are variational parameters. The uncorrelated wave functions used were hydrogenic functions and Hartree-Fock functions. Results are presented for the He-like ions with Z = 2−10, and it will be seen that the hydrogenic functions give the best results when electron correlation is included.

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