Compact Correlated Hylleraas Wave Functions for the Lithium Isoelectronic Sequence: Ground-State Energies and a Complex-Rotation Assessment

Abstract

The nonrelativistic ground-state energy of the (1s 2 2s) 2 S term of atomic lithium and five members of its isoelectronic sequence (Be + , B 2 + , C 3 + , N 4 + , O 5 + ; Z = 3–8) is computed with a correlated Hylleraas-type trial function combined with the complex-rotation (complex-scaling) transformation of the radial coordinates, implemented symbolically and numerically in the computer-algebra system Maxima. Two variational basis sizes, Ω = 9 and Ω = 12, are compared for neutral lithium as a sensitivity test of the complex-scaled stabilization procedure; Ω = 9 gives the closer benchmark agreement and is used as the working basis for the ionic members of the sequence. The resulting energies agree with the multiple-basis-set Hylleraas benchmark of Yan, Tambasco and Drake with relative deviations below 6.1 × 10 -3 % over Z = 3–8, and with several independent Hylleraas, full-core-plus-correlation, and screening-constant calculations reported in the literature. The evolution of the optimized non-linear parameters with nuclear charge is examined and interpreted in terms of the progressive contraction of the 1s 2 core relative to the comparatively stable 2s valence orbital. Because the (1s 2 2s) 2 S term lies below the first ionization threshold rather than embedded in the continuum, the small imaginary parts produced by the complex-rotation procedure cannot be interpreted as a physical autoionization width; this limitation of applying a resonance-oriented technique to a genuine bound state is discussed explicitly. The present implementation is placed in the context of an earlier complex-rotation study of the same states by Diop et al. (2020), to which it is methodologically related but numerically independent.