Configuration interaction (CI) calculations in atoms with two valence electrons, carried out in the V (N−2) Hartree-Fock potential of the core, are corrected for core-valence interactions using manybody perturbation theory (MBPT). Two variants of the mixed CI+MBPT theory are described and applied to obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr. PACS numbers: 31.10.+z,
I. INTRODUCTIONAlthough Be, Mg, Ca, and Sr atoms have been studied theoretically for many years and numerous calculations are available in the literature, energy levels of those divalent atoms have been treated primarily with semiempirical methods and only a limited number of low-lying levels have been evaluated using ab-initio methods, which often do not provide sufficient precision or require extensive computer resources. Semiempirical methods, to their advantage, do not require significant computer resources and can be applied easily to a large number of levels; however, such theories have limited predictive power and accuracy. Although energies obtained using semiempirical methods agree well with one another and with experiment, oscillator strengths obtained by different semiempirical calculations are inconsistent [1]. Examples of semiempirical calculations can be found for Be in [1], for Ca in [2], and for Sr in [3]. Large-scale ab-initio configuration interaction (CI) calculations of energies and transition rates, although capable of high accuracy, have been performed only for a few low-lying levels in the Be [4,5] and Mg [6] isoelectronic sequences. The size of the configuration space in such CI calculations is limited by the available computer resources. Smaller-scale CI calculations, carried out in the frozen V (N−2) Hartree-Fock potential of the core, lead to poor results. We found, for example, that frozen-core CI calculations in Ca gave energies so inaccurate that it was difficult, if at all possible, to identify many closely spaced levels of experimental interest. Multi-configuration Dirac-Fock (MCDF) and Hartree-Fock (MCHF) methods have also been used to obtain energies and oscillator strengths in divalent atoms: MCHF for Be-like ions [7] and neutral calcium [8], and MCDF for Mg-like ions [9]. The accuracy of MCHF and MCDF calculations in neutral atoms is poor, basically because of computational limits on the number of con- * Electronic address: isavukov@nd.edu; URL: http://www.nd.edu/ isavukov † Electronic address: johnson@nd.edu; URL: http://www.nd.edu/ johnson