A fraction of the radial correlation energy is computed for the first-row atoms in the ground state as well as selected excited states. The same type of computation is reported for the ions of the isoelectronic series from Ne to A8+. The wavefunction we have used is a linear combination of three determinants: One is the standard Hartree-Fock determinant, and the other two contain orbitals shrunken or expanded relative to those in the Hartree-Fock determinant. In the paper we discuss the technique needed to obtain the determinants and the physical interpretation of the results. The large fraction of correlation energy (over 20% for the Ne atom) obtained with such a small expansion (two determinants added to the HartreeFock determinant) is explained as a consequence of rejecting the orthogonality constraints among the orbitals. The results of this work seems to indicate that different techniques should be used in order to solve the different effects which are lumped together under the name of "correlation energy.".