Author(s)

Malick Sow^1*, Ibrahima Sakho², Boubacar Sow¹, Abdou Diouf¹, Youssou Gning¹, Babou Diop¹, Matabara Dieng³, Abdourahmane Diallo⁴, Mamadou Diouldé Ba⁴, Jean Kouhissoré Badiane⁴, Mamadi Biaye⁵, Ahmadou Wagué¹

¹Department of Physics, Atoms Lasers Laboratory, Faculty of Sciences and Technologies, University Cheikh Anta Diop, Dakar, Senegal.
²Department of Physics, UFR Sciences et Technologies, University of Thiès, Thiès, Senegal.
³UFR SATIC, University Alioune DIOP de Bambey, Bambey, Senegal.
⁴Department of Physics, UFR of Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal.
⁵Department of Physics and Chemistry, Faculty of Sciences and Technologies of Training and Education, University Cheikh Anta Diop, Dakar, Senegal.

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}D, 4f^{2 1}I 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 2s^{2 1}S ground state and each doubly 2p^{2 1}D, 3d^{2 1}D, 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 (nl²) systems.

Modified Atomic Orbital Theory, Variational Calculations, Correlated Wavefunction, Energies, Ground-State, Doubly Excited States, Helium Isoelectronic Sequence, Atoms and Ions

Sow, M. , Sakho, I. , Sow, B. , Diouf, A. , Gning, Y. , Diop, B. , Dieng, M. , Diallo, A. , Ba, M. , Badiane, J. , Biaye, M. and Wagué, A. (2020) Modified Atomic Orbital Calculations of Energy of the (2s^{2 1}S) Ground-State, the (2p^{2 1}D); (3d^{2 1}D) and (4f^{2 1}I) Doubly Excited States of Helium Isoelectronic Sequence from H^- to Ca¹⁸⁺. Journal of Applied Mathematics and Physics, 8, 85-99. doi: 10.4236/jamp.2020.81007.