Energy Positions of the &amp;lt;sup&amp;gt;1,3&amp;lt;/sup&amp;gt;D&amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt; Rydberg Series of the He-Like Ions Up to the &amp;lt;i&amp;gt;N&amp;lt;/i&amp;gt; = 9 Threshold

Matabara Dieng,Babou Diop,Mamadi Biaye,Ababacar Sadikhe Ndao,Malick Sow,Ahmadou Wagué,Youssou Gning

doi:10.4236/jamp.2020.88119

Abstract

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

Highlights

The double photoionization of helium has known a considerable importance because of the central role played by the electron-electron correlation in the ejection of two electrons by the absorption of a single photon
( ) ΦNlnl′ r1, r2 represent, the trial non-orthogonal wave functions that we have considered for the description of the inter-shell singlet and triplet doubly excited states of the helium-like ions
The screening constant by unit nuclear charge (SCUNC) formalism is used in this work to calculate the energy resonances of the helium-isoelectronic sequence converging to the N = 2 - 9 hydrogenic thresholds

Summary

Introduction

The double photoionization of helium has known a considerable importance because of the central role played by the electron-electron correlation in the ejection of two electrons by the absorption of a single photon. ( ) ΦNlnl′ r1, r2 represent, the trial non-orthogonal wave functions that we have considered for the description of the inter-shell singlet and triplet doubly excited states of the helium-like ions. The inter-shell singlet and triplet doubly excited wave functions were found in the basis containing the configurations with the following condition for the Hylleraas parameters j + k + m ≤ 3, corresponding to the basis dimension D = 13 or 7. The eigenvalues E obtained in the present calculations follow the Hylleraas-Undheim theorem [9] and do not include the Feshbach shifts because of the incomplete basis sets These calculations have been carried out in the framework of the variational method using interaction basis states with a real Hamiltonian.

General Formalism of the SCUNC Method

Results and Discussion

Summary