Single-double SD equations for lithium-like ions

Single-Double (SD) Equations for Lithium-like Ions 

The relativistic SD equations for hthium-like ions have been discussed at length in [54] so we will give only a brief reprise of the equations here. In the SD approach, the wave function of an atomic system with one valence electron is represented as  

The coefficients pma and pmnab are amplitudes for single and double excitations from the core, respectively Pmv is the amplitude for a single excitation of the valence electron, 

As before, antisymmetrized excitation amplitudes are designated by pijki = Pijki — Pijik-The correlation correction to the core energy is given in terms of the core excitation amplitudes by 

To solve Eqs. (176-181), an angular momentum decomposition is first carried out and the equations are then reduced to coupled equations involving single-body radial wave functions only. The radial wave functions for states v, m, n, a, b, are taken from a B-spline basis set [36] and the resulting coupled radial equations are solved iteratively. The core equations (176-177) are solved first and the valence equations (179-181) are then solved for valence states of interest using the converged core amplitudes. 

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