Abstract
We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1D, 4f2 1I of the Helium isoelectronic sequence from H- to Ca18+. 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 2s2 1S ground state and each doubly 2p2 1D, 3d2 1D, 4f2 1I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2) systems.
Highlights
The resolution of the Schrödinger equation gives for the ground-state of the Helium atom the value E = 108.8 eV
We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1G, 4f2 1I of the Helium isoelectronic sequence from H− to Ca18+
The experimental result being equal to E0 = −79.0 eV, one conceives that one takes into account the electronic correlation term, overestimating, numerous studies provided evidence of the importance of the electronic correlation in the ground-state and in the doubly excited state of
Summary
Combining the perturbation theory [9] to the Ritz variational method [10], Sakho et al, [11] set in motion a technic of analytical calculation of the ground state energy E (1S0), the first ionization energy J (1S0) and the radial correlation expectation value r1−21 (1S0) for the Helium-like ions from. The general expression of the energy resonances is given by the formula [24] presented previously (in Rydberg units): In this equation m and q (m < q) denote the principal quantum numbers of the (2S+1LJ)nl-Rydberg series of the considered atomic system used in the empirical determination of the σi(2S+1LJ)-screening constants, s represents the spin of the nl-electron (s = 1/2), E∞ is the energy value of the series limit generally determined from the NIST atomic database, En denotes the corresponding energy resonance, and Z represents the nuclear charge of the considered element. LJ: denote the considered quantum state (S, P, D, F, ...)
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