Variational Calculations for Quartet States of Three-Electron Atomic Systems

Abstract

The conventional Rayleigh-Ritz variational method in which one uses pure Slater-type orbitals and correlated factors r""* in the basis functions has been applied to obtain the eigenvalues of the five lowest lying states with symmetries 4 P°, 4 j? e , and 4 5 e for three-electron atomic systems. To find the absolute minimum which is attainable for each eigenvalue, the nonlinear parameters (exponential parameters) have been varied freely in submatrices up to order 30 with 20 noncorrelated and 10 correlated basis functions. This variation has been carried through separately to find the five lowest eigenvalues of each symmetry in Li and for only the lowest one in He"~. For the other members of the isoelectronic sequence up to Z=10, the absolute minima of the three lowest lying eigenvalues are found approximately by using the correlated subset of order 30 with common fixed exponential parameters for each symmetry and by freely varying the scale parameter. The lowest 4 P° state is found to be bound in He~ with a binding energy > 0.033 eV. No sign of binding is indicated for the lowest 4 S« state, but the lowest i P e state is also found to be bound by >0.20 eV. The results for Li indicate as certain that the transitions 4 S«(1)-4 P°(1) and 4 P«(1)-4 P°(1) are responsible for the two observed multiplets present at 2934 and 3714 A, respectively in the optical spectrum. These lines cannot be classified in the normal singly excited spectrum of the atom or ion. The results for Li are compared in detail with those obtained by recent electron-impact experiments and by other theoretical calculations.

Perturbation treatment of the Hartree–Fock equations of 1s2p3s4Pθ state of the lithium isoelectronic sequence

“…We compare our results with experiment and those of Holerien and Geltman [4] and Junker and Bardsley [5] in Table I1 for the ions lithium to neon. We see TABLE 11.…”

“…These states have evoked considerable theoretical interest because of the problem of identification and classification and assignment of lines due to radiative transitions between them. HolGien and Geltman [4] have calculated, by a variation method using explicitly correlated basis sets, the energies of nine metastable states for members of the lithium isoelectronic sequence up to neon. Their results have been used generally to assign these states.…”

Inner-shell excitation of open-shell atoms: a spin-dependent localized Hartree–Fock density-functional approach

“…Both experimental [27,28,29,30,31,32,33,34,35] and theoretical data [36,37,38,39,40,41,42,43,44,45,46,47,48,49] are abundant. In TABLE I to TABLE III we present the total and excitation energies of our calculations with PW and LYP correlation potentials and energy functionals for inner-shell excited states 1s2sns 2,4 S (n = 2 ∼ 8), 1s2snp 2,4 P (n = 2 ∼ 8), and 1s2p 2 2 S, 2,4 P , and 2 D, respectively.…”

“…In TABLE I to TABLE III we present the total and excitation energies of our calculations with PW and LYP correlation potentials and energy functionals for inner-shell excited states 1s2sns 2,4 S (n = 2 ∼ 8), 1s2snp 2,4 P (n = 2 ∼ 8), and 1s2p 2 2 S, 2,4 P , and 2 D, respectively. For comparison we also list in these tables representative experimental data [29,31,34] as well as theoretical results obtained from calculations using density work-functional formalism (WF) [36], saddlepoint complex-rotation (SPCR) [37,38,39,40], extensive configuration-interaction calculation (ECI) [43,44,45,46], and Rayleigh-Ritz variational method (RRV) [49].…”

High‐lying core‐excited quartet states in Li‐like N4+ and F6+ ions

“…Using Rayleigh-Ritz method, Holøien and Geltman [14] first studied the quartet states of Li-like ions (Z ¼ 2-10). Cheng et al [11] explored the fine structure and transition wavelengths of the 1s2s2p 4 …”