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In this present work, we have calculated the energies positions of the 2s22p2(1D)nd2P, 2s22p2(1D)nd2S, 2s22p2(1D)ns 2D, 2s22p2(1S)nd2D and 2s2p3(3P)np2D Rydberg series in the photoionization spectra from the 2P° metastable state of the O+ ion. Calculations were performed up to n = 40 applyingthe Screening Constant by Unit Nuclear Charge (SCUNC) via its semi empirical formalism. The quantum defect and the effective charge are also calculated.The results agree within 98% to Aguilars experimental data, and with Sows theoretical results to within 99%. These data can be a useful guideline for future experimental and theoretical studies.

We report in this paper energy positions of Rydberg series from metastable state of Ca3+ ion.. Calculations are performed up to n = 20 using the Screening Constant by Unit Nuclear Charge (SCUNC). The present results compared wellwith the experimental data of Ghassan A Alna’washi which are the only available values.The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

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.

In this paper, resonance energies and excitation energies of doubly 2sns 1,3Se, 2snp 1,3P0, 2pnp 1,3De, 2pnd 1,3F0 and 2pnf 1,3Ge excited states of the helium isoelectronic sequence with Z ≤ 10 are calculated. Calculations are carried out in the framework of the variational procedure of the formalism of the Screening Constant per Unit Nuclear Charge (SCUNC). New correlated wave function of Hylleraas type is used. Precise resonance and excitation energies are tabulated and good agreement is obtained when a comparison is made with available literature values.

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.

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.

In this present work, we have calculated the energies positions of the 2s22p2(1D)nd2P, 2s22p2(1D)nd2S, 2s22p2(1D)ns2D, 2s22p2(1S)nd2D and 2s2p3(3P)np2D Rydberg series in the photoionization spectra from the2P° metastable state of the O+ion. Calculations were performed up ton= 40 applyingthe Screening Constant by Unit Nuclear Charge (SCUNC) via its semi empirical formalism. The quantum defect and the effective charge are also calculated.The results agree within 98% to Aguilars experimental data, and with Sows theoretical results to within 99%. These data can be a useful guideline for future experimental and theoretical studies. &nbsp

We report in this paper energy positions of Rydberg series from metastable state of Ca3+ ion.. Calculations are performed up to n = 20 using the Screening Constant by Unit Nuclear Charge (SCUNC). The present results compared wellwith the experimental data of Ghassan A Alna’washi which are the only available values.The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies. &nbsp

In this paper, we report the energies and resonant widths of the [(2s3s1Seand 2s3s3Se) (2s4s1Seand 2s4s3Se) (2s3p1P0and 2s3p3P0) (2s4p1P0and 2s4p3P0) (2p3p1Deand 2p3p3De) (2p4p1Deand 2p4p3De) (3s4s1Seand 3s4s3Se) (3s4p1P0and 3s4p3P0) (3p4p1Deand 3p4p3De) (3d4d1Geand 3d4d1Ge)] 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. &nbsp

In this paper, we have applied the complex rotation method to the calculations energies of the ground state (1s22s) 2S and the low-lying excited (1s2ns)2S states with n = 3, 4 and 5; of lithium and its isoelectronic series. For the ground state, the calculations were made up to Z = 20 and for the low-lying excited states up to Z = 10. These energies calculations were made using new special forms of Hylleraas-type wave functions designed by combining incomplete radial hydrogenic wave functions and Hylleraas-type wave functions. Using a numerical calculation program, the values of the resonance energies are calculated. Our results are compared with the results of ab-initio calculations using Hylleraas type wave functions and with semi-empirical results by Screening Constant by Unit Nuclear Charge (SCUNC) formalism. Analysis of the present results is achieved by calculating the ratio and the difference between our values and those of other authors. The results obtained are in good agreement with those of the theoretical methods available in the literature. This agreement shows the adequacy of our wave function with small bases to satisfactorily describe the ground state and the low-lying excited states of the three-electron atomic systems.