Radial Configurational Interaction in Helium and Similar Atomic Systems

The spherically symmetric component of the ground-state wave functions of the two-electron series (${\mathrm{H}}^{-}$, He, ${\mathrm{Li}}^{+}$, ${\mathrm{Be}}^{2+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$) has been investigated by using the orthonormal complete set of ($2q+2$)-order associated Laguerre functions as radial orbitals in the method of superposition of configurations. The results for the total energies and the corresponding expansion coefficients demonstrate the excellent convergence properties of these functions. They are also useful practically since only one single-orbital exponent is used. Applied to excited quantum states, they indicate a more slowly convergent process.