Optimised mean fields for atoms. V. g-Hartree ab initio calculation of ionisation energies

For pt.IV see Physica, vol.131, A, p.363 (1985). The g-Hartree method is adapted to the direct ab initio calculation of transition energies in atoms. For the elements He (Z=2), Li (Z=3), Be (Z=4), Ne (Z=10), Mg (Z=12) and Ar (Z=18) all ionisation energies have been computed and found to agree with available experimental data within the computational errors. The systematic aspect (which is a truly second-order determination of the optimal mean field and contains no semi-phenomenological partial-summation prescriptions such as the self-energy summations in the Schwinger-Dyson approach) is emphasised and is shown to match experimental data significantly better than second-order (in the same strict sense) Brueckner-Hartree-Fock calculations. A detailed comparison of the method with other published approximation schemes shows a systematic improvement over the results obtained in conventional many body theories.