Formulation of Strutinsky's method for atomic systems in the extended Kohn–Sham scheme

Abstract

Strutinsky's standard averaging method is formulated in the framework of the extended Kohn-Sham scheme and a two-step procedure permitting the application of the method is proposed. A Taylor-series expansion of the groundstate energy-function of the occupation numbers is derived, which involves the averaged energy as the leading term and shell corrections as smaller terms. Numerical applications for atoms and ions from Be through Ar are presented and discussed.

Strutinsky's shell‐correction method in the extended Kohn–Sham scheme for the investigation of binding energies of atoms and cations in the ground state

“…Now we have shown in recent work [41] that *In Ref. [20] the first-order term is obtained through formal application of Eq. (44), including the virtual levels with negative occupancy.…”

“…[20] we formulated a procedure, recalled here in Section 3, for splitting the ground-state energy of a multifermionic system into averaged and shell-correction parts in the framework of the extended Kohn-Sham scheme. The single-particle spectrum, obtained as self-consistent solutions of the KS equations, is smoothed using Strutinsky's technique and yields averaged occupation numbers {ñ i }.…”

“…In Ref. [20] we used a non-SC (non-iterative) procedure as a first step of the full optimization of the oscillating part of the energy. Here we compare the self-consistent (SC) and non-SC procedures for the ground-state energies of atoms from Be through Ca.…”

“…In a previous article [20] we proposed a formulation of Strutinsky's SCM in the frame of the extended Kohn-Sham (EKS) scheme. Using Strutinsky's averaging technique, we split the ground-state energy, E 0 , into an averaged part, Ẽ , and a shell-correction expansion of the oscillating part, ␦E ϭ ¥ i ␦ i E. The leading term in this series, ␦ 1 E, has been expressed using the KS orbital energies, i , around the Fermi level.…”

“…We include this section in our article because the numerically tested HF form of SCM is the basis of our formulation of SCM in the EKS scheme. In Section 3 we recall the two-step procedure allowing the application of the method [20] and introduce novel "transition state" numbers in the Taylor series expansion of the ground-state energy function, yielding elimination of the second-order shell-correction term. Section 4 is devoted to the presentation and discussion of shell effects obtained for the ground-state energy function of a series of atoms and cations from Be through Ca, and to the assessment of the relevance and reliability of this approach.…”