Energy calculations of the (2P2 1D); (3D2 1G) and (4F2 1I) doubly excited states of helium isoelectronic sequence (z ≤ 20) via the modified atomic orbital theory

We report in this paper the total energies of the 2p2 1D, 3d2 1G, 4f2 1I doubly excited states of Helium isoelectronic sequence with nuclear charge Z ≤ 20. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) [1;2] 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 [3] combining with Hylleraas-type wave function [4]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This 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 each 2p2 1D, 3d2 1G, 4f 2 1I Doubly Excited States (DES) in the He-like systems. The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2 ) systems.