Abstract
The present work deals with an ab initio calculation of total energies of the doubly excited np2, nd2 and nf2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np2, nd2 and nf2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.
Highlights
Over the last two decades, various methods have been performed to understand electron -electron correlation effects in doubly excited states of He-like systems
In contrast with these ab initio methods applied in the analysis of two atomic systems spectra, the Screening constant by unit nuclear charge (SCUNC) formalism has the advantages to provide accurate energy position within a simple semi-empirical procedure as well as for the doubly (Nlnl’ 2S+1L) [12, 13] excited state than in the mixed configurations based on the classification scheme designated by the notation N (K,T )nA 2S +1 Lπ [14,15,16,17]
In the framework of the Screening constant by unit Nuclear charge formalism, total energies of the doubly ( Nl, nl ') 2S +1 L π excited states are expressed in the form
Summary
Over the last two decades, various methods have been performed to understand electron -electron correlation effects in doubly (nl2) excited states of He-like systems. Energy of the doubly (nl2) excited states of He-like systems cannot be expressed analytically from various ab initio methods such as the complex rotation method [1,2,3], the variationnal method of Hylleraas [4], the double sums over the total hydrogen spectrum formalism [5], the density functional theory [6], the formalism of the Feshbach projection operators [7, 8], the discretization technique [9], the truncated diagonalization method [10], the time-dependent variation perturbation theory [11], to name a few In contrast with these ab initio methods applied in the analysis of two atomic systems spectra, the Screening constant by unit nuclear charge (SCUNC) formalism has the advantages to provide accurate energy position within a simple semi-empirical procedure as well as for the doubly (Nlnl’ 2S+1L) [12, 13] excited state than in the mixed configurations based on the classification scheme designated by the notation N (K ,T )nA 2S +1 Lπ [14,15,16,17].
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