Convergence of the partial wave expansion of the He ground state

The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12 resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite in angular momentum using expansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ..., gave an energy accurate to 10^(-7) Hartree and a value of <delta> accurate to about 0.5%. Improved estimates of <E> and <delta>, accurate to 10^(-8) Hartree and 0.01% respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infty limit. Round-off errors were the main impediment to achieving even higher precision since determination of the radial and angular limits required the manipulation of very small energy and <delta> differences.