Calculations of the energy levels of atoms and ions with Z ≤ 10 are carried out in this paper using the variational method. New wave function with two terms including correlation was performed to calculate excited (ns 2 ) 1 S e , (np 2 ) 1 D e , (nd 2 ) 1 G e , (nf 2 ) 1 I e , (nh 2 ) 1 M e and (ng 2 ) 1 K e states with (n ≤ 7). The results obtained show quantitatively the great significance of electron correlation effects in the doubly excited states. These results are in compliance with some experimental and theoretical data.
We report in this paper the ground-state energy 2s 2 1 S and total energies of doubly excited states 2p 2 1 D, 3d 2 1 G, 4f 2 1 I of the Helium isoelectronic sequence from H − to Ca 18+. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [1] combining with Hylleraas-type wave function [2]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This first proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for the 2s 2 1 S ground state and each doubly 2p 2 1 D, 3d 2 1 G, 4f 2 1 I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl 2) systems.
In this paper, we report the energies and resonant widths of the [(2s3s 1Se and 2s3s 3Se) (2s4s 1Se and 2s4s 3Se) (2s3p 1P0 and 2s3p 3P0) (2s4p 1P0 and 2s4p 3P0) (2p3p 1De and 2p3p 3De) (2p4p 1De and 2p4p 3De) (3s4s 1Se and 3s4s 3Se) (3s4p 1P0 and 3s4p 3P0) (3p4p 1De and 3p4p 3De) (3d4d 1Ge and 3d4d 1Ge)] Doubly Excited States of Helium isoelectronic series with nuclear charge Z (2 ≤ Z ≤ 10).Calculations are performedusing the Complex Rotation Method (CRM) in the framework of a variational procedure. The purpose of this study required a new correlated hydrogenic radial wave function combined with a Hylleraas wave function. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed variational procedure, leads to accurate results in good agreement with available other theoretical results.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (Nℓ Nℓ) 2S+1Lᴨsystems.
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