Exponentially correlated Hylleraas-Configuration Interaction studies of atomic systems. III Upper and Lower Bounds to He-Sequence Oscillator Strengths for the Resonance singlet S to singlet P Transition
James S. Sims, Bholanath Padhy, Maria Ruiz
A generalization of the Hylleraas-Configuration Interaction method (Hy-CI) first proposed by Wang et al., the Exponentially Correlated Hylleraas-Configuration Interaction method (E-Hy-CI) in which the single rij of an Hy-CI wave function is generalized to a form of the generic type rij^n_ij e−ωij rij , is explored. This type of correlation, suggested by Hirschfelder in 1960, has the right behavior both in the vicinity of the rij cusp as rij goes to 0 and as rij goes to infinity; this work continues the exploration, begun in the first two papers in this series (on the helium atom and on ground and excited S states of Li II), of whether wave functions containing both linear and exponential rij factors converge more rapidly than either one alone. In the present study we examine not only 1s2 1S states but 1s2p 1P states as well for the He I, Li II, Be III, C V and O VII members of the He isoelectronic sequence. All 1P energies except He I are better than previous results. The wave functions obtained are used to calculate oscillator strengths, including upper and lower bounds, for the He-sequence lowest (resonance) 1S → 1P transition. Interpolation techniques are used to make a graphical study of the oscillator strength behavior along the isoelectronic sequence. Comparisons are made with previous experimental and theoretical results. The results of this study are oscillator strengths for the 1s2 1S → 1s2p1P He isoelectronic sequence with rigorous non-relativistic quantum mechanical upper and lower bounds of (0.001-0.003) % and probable precision ≤ 0.0000003.
, Padhy, B.
and Ruiz, M.
Exponentially correlated Hylleraas-Configuration Interaction studies of atomic systems. III Upper and Lower Bounds to He-Sequence Oscillator Strengths for the Resonance singlet S to singlet P Transition, Atoms, [online], https://doi.org/10.3390/atoms11070107, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=936795
(Accessed September 22, 2023)