A fully numerical multiconfiguration Hartree-Fock program has been modified for performance of calculations on atomic quasibound states using the complex-coordinate (dilation) technique. We present single-configuration calculations for the lowest
2P\ifmmode^\circ\else\textdegree\fi{} states of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, along with results of some small-scale multiconfiguration investigations of the Mg resonance. An instability originating in difficulty satisfying orthogonality constraints prevents a full multiconfiguration treatment of this resonance. Single-configuration dilated Hartree-Fock calculations predict
2P\ifmmode^\circ\else\textdegree\fi{} shape resonances for all these systems, though recent extensive calculations show the Ca, Sr, and Ba ions to be bound. Nonetheless, we think it is significant that the dilated numerical method can easily carry out fully variational computations on these heavy atoms, and our results, in conjunction with those of other studies, shed light on the importance of electron correlation in its effect upon the resonance parameters and its variation with progressively heavier alkaline-earth atoms. We also establish the feasibility of accounting for important correlation effects through the use of multiconfiguration approximations, though we have not attempted an accurate calculation in this work. Our Be, Mg, and Ca results agree well with previously published single-configuration dilated basis-set calculations, but no such calculations have been carried out for Sr or Ba. Finally, we investigate the dilational stability of the numerical method since this has been an important consideration in basis-set calculations. A simple exercise based on Cauchy's theorem shows that analyticity of the Hartree-Fock radial wave functions implies that the energy and other physical quantities are independent of the dilation parameter, and a high degree of such independence is demonstrated in our numerical results.
Within the framework of the close-coupling method, ab initio calculations of parameters of multichannel quantum-defect theory have been carried out for several Rydberg series of Ca, Sr, and Ba. A local-density approximation, commonly used in solid-state calculations, including self-consistent, self-energy corrections, was made to the exchange-correlation potential. Good agreement with experimental values of multichannel quantum-defect theory parameters is obtained, permitting accurate prediction of highly excited-state binding energies.
Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.
Conditional probability distributions for the valence electrons of alkaline-earth atoms in their ground and valence excited states are constructed using large-basis Sturmlan configuration-interaction wave functions for two electrons in frozen, effective-core potentials. The distributions indicate that the ground states of Be, Mg, Ca, Sr, and Ba, and the valence excited states of Be, are much more like linear triatomic molecules, akin to doubly excited He, than like independent-particle systems such as the ground states of He and He-like ions.
Nonadiabatic effects on the structure of Rydberg states of alkaline-earth atoms are examined and found to be large in many cases. Calculations for the quantum defects of the singlet
F and
G series in calcium, including dynamical contributions, are shown to be in good agreement with recent experimental data. This is in contrast to predictions based on the adiabatic core-polarization model, which significantly overestimates the quantum defects. Values for quantum defects of Ca for $l\ensuremath{\ge}4$ are presented.
In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.