Exponentially Correlated Hylleraas–Configuration Interaction Studies of Atomic Systems. III. Upper and Lower Bounds to He-Sequence Oscillator Strengths for the Resonance 1S→1P Transition - James S. Sims; Bholanath Padhy; María Belén Ruiz Ruiz (Atoms, 2023)
The exponentially correlated Hylleraas–configuration interaction method (E-Hy-CI) is a generalization of the Hylleraas–configuration interaction method (Hy-CI) in which the single <semantics>rij</semantics> of an Hy-CI wave function is generalized to a form of the generic type <semantics><msubsup>rijνij</msubsup>e−ωijrij</semantics>. This work continues the exploration, begun in the first two papers in this series (on the helium atom and on ground and excited <semantics>S</semantics> states of Li II), of whether wave functions containing both linear and exponential <semantics>rij</semantics> factors converge more rapidly than either one alone. In the present study, we examined not only 1<semantics>s2</semantics> <semantics>1S</semantics> states but 1s2p <semantics>1P</semantics> states for the He I, Li II, Be III, C V and O VII members of the He isoelectronic sequence as well. All <semantics>1P</semantics> energies except He I are better than previous results. The wave functions obtained were used to calculate oscillator strengths, including upper and lower bounds, for the He-sequence lowest (resonance) <semantics>1S→</semantics><semantics>1P</semantics> transition. Interpolation techniques were used to make a graphical study of the oscillator strength behavior along the isoelectronic sequence. Comparisons were made with previous experimental and theoretical results. The results of this study are oscillator strengths for the 1<semantics>s2</semantics> <semantics>1S→</semantics> 1s2<semantics>p<mspace width="4pt"></mspace>1P</semantics> He isoelectronic sequence with rigorous non-relativistic quantum mechanical upper and lower bounds of (0.001–0.003)% and probable precision ≤ 0.0000003, and were obtained by extending the previously developed E-Hy-CI formalism to include the calculation of transition moments (oscillator strengths).