scholarly journals A PERTURBATIVE TREATMENT FOR THE ENERGY LEVELS OF NEUTRAL ATOMS

2006 ◽  
Vol 21 (31) ◽  
pp. 6465-6476 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Entire Range ◽  
Potential Model ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Binding Energies ◽  
Neutral Atoms ◽  
Large N ◽  
Perturbative Method ◽  
Screening Parameter ◽  
Perturbative Treatment

Energy levels of neutral atoms have been reexamined by applying an alternative perturbative scheme in solving the Schrödinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

scholarly journals Approximate κ-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Open Physics ◽  
2012 ◽  
Vol 10 (2) ◽  
Author(s):  
Sameer Ikhdair
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Relativistic Limit ◽  
Special Cases ◽  
Wide Range ◽  
Screening Parameter

AbstractUsing an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.

Shifted large-N expansion for the energy levels of neutral atoms

1986 ◽  
Vol 2 (3) ◽  
pp. 207-210 ◽  
Author(s):  
R. Dutt ◽  
Y. P. Varshni
Keyword(s):  
Energy Levels ◽  
Neutral Atoms ◽  
Large N ◽  
Large N Expansion

Nonrelativistic treatment of hydrogen-like and neutral atoms subjected to the generalized perturbed Yukawa potential with centrifugal barrier in the symmetries of noncommutative quantum mechanics

2020 ◽  
Vol 17 (05) ◽  
pp. 2050067
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Potential Model ◽  
Yukawa Potential ◽  
Hamiltonian Operator ◽  
Real Space ◽  
Neutral Atoms ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Generalized Gamma Function

We have obtained the approximate analytical solutions of the nonrelativistic Hydrogen-like atoms such as [Formula: see text] and [Formula: see text] and neutral atoms such as ([Formula: see text] and [Formula: see text]) atoms with a newly proposed generalized perturbed Yukawa potential with centrifugal barrier (GPYPCB) model using the generalized Bopp’s shift method and standard perturbation theory in the symmetries of noncommutative three-dimensional real space phase (NC: 3D-RSP). By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and generalized Hamiltonian operator for all orbital quantum numbers [Formula: see text] in the symmetries of NC: 3D-RSP. The potential is a superposition of the perturbed Yukawa potential and new terms proportional with [Formula: see text]) appear as a result of the effects of noncommutativity properties of space and phase on the perturbed Yukawa potential model. The obtained energy eigenvalues appear as functions of the generalized Gamma function, the discreet atomic quantum numbers [Formula: see text], two infinitesimal parameters [Formula: see text], which are induced by (position–position and phase–phase). In addition, the dimensional parameters [Formula: see text] of perturbed Yukawa potential with centrifugal barrier model in NC: 3D-RSP. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of perturbed Yukawa potential model and the two operators are modified spin–orbit interaction and the modified Zeeman operator for the previous Hydrogenic and neutral atoms.

Two Approximate Analytic Eigensolutions of the Hellmann Potential with any Arbitrary Angular Momentum

2013 ◽  
Vol 68 (10-11) ◽  
pp. 701-708 ◽  
Author(s):  
Sameer M. Ikhdair ◽  
Babatunde J. Falaye
Keyword(s):  
Yukawa Potential ◽  
Energy Levels ◽  
Numerical Data ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Special Cases ◽  
Wide Range ◽  
Pure Coulomb ◽  
Screening Parameter ◽  
Hellmann Potential

The parametric Nikiforov-Uvarov (pNU) and asymptotic iteration method (AIM) are applied tostudy the approximate analytic bound state eigensolutions (energy levels and wave functions) of theradial Schr¨odinger equation (SE) for the Hellmann potential which represents the superposition ofthe attractive Coulomb potential (-a/r) and the Yukawa potential bexp(-δ/r)/r of arbitrary strengthb and screening parameter d in closed form. The analytical expressions to the energy eigenvalues Enlyield quite accurate results for a wide range of n; l in the limit of very weak screening but the resultsbecome gradually worse as the strength b and the screening coefficient d increase. The calculatedbound state energies have been compared with available numerical data. Special cases of our solutionlike pure Coulomb and Yukawa potentials are also investigated.

Approximate Analytical Solutions of the Perturbed Yukawa Potential with Centrifugal Barrier

2013 ◽  
Vol 68 (6-7) ◽  
pp. 454-460 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Analytical Solutions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Type Potential ◽  
Coulomb Potentials

By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation for a perturbed Yukawa potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and compared with the standard Yukawa potential. Further, we found the energy levels of the familiar Mie-type potential when the screening parameter of the perturbed Yukawa potential goes to zero, and finally, standard Yukawa and Coulomb potentials are discussed.

scholarly journals A New Piano-Stool Ruthenium(II) P-Cymene-Based Complex: Crystallographic, Hirshfeld Surface, DFT, and Luminescent Studies

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 13
Author(s):  
Mohd. Muddassir ◽  
Abdullah Alarifi ◽  
Mohd. Afzal
Keyword(s):  
Density Functional ◽  
Weak Interactions ◽  
Energy Levels ◽  
Hirshfeld Surface ◽  
Binding Energies ◽  
Orbital Energy ◽  
Aminosalicylic Acid ◽  
Full Characterization

A new complex (Ru(η6-p-cymene)(5-ASA)Cl2) (1) where 5-ASA is 5-aminosalicylic acid has been prepared by reacting the ruthenium arene precursors ((η6-arene)Ru(μ-Cl)Cl)2, with the 5-ASA ligands in a 1:1 ratio. Full characterization of complex 1 was accomplished by elemental analysis, IR, and TGA following the structure obtained from a single-crystal X-ray pattern. The structural analysis revealed that complex 1 shows a “piano-stool” geometry with Ru-C (2.160(5)- 2.208(5)Å), Ru-N (2.159(4) Å) distances, which is similar to equivalents sister complex. Density functional theory (DFT) was used to calculate the significant molecular orbital energy levels, binding energies, bond angles, bond lengths, and spectral data (FTIR, NMR, and UV–VIS) of complex 1, consistent with the experimental results. The IR and UV–VIS spectra of complex 1 were computed using all of the methods and choose the most appropriate way to discuss. Hirshfeld surface analysis was also executed to understand the role of weak interactions such as H⋯H, C⋯H, C-H⋯π, and vdW interactions, which play a significant role in the crystal environment’s stability. Moreover, the luminescence results at room temperature show that complex 1 gives a more intense emission band positioned at 465 nm upon excitation at 330 nm makes it a suitable candidate for the building of photoluminescent material.

scholarly journals Opacities in Strong Magnetic Helds

1995 ◽  
Vol 10 ◽  
pp. 588-590
Author(s):  
Dayal T. Wickramasinghe
Keyword(s):  
Entire Range ◽  
White Dwarfs ◽  
Specific Problem ◽  
Transition Probabilities ◽  
Strong Field ◽  
Energy Levels ◽  
Dipolar Field ◽  
Origin And Evolution ◽  
End Products ◽  
Hydrogen Lines

White dwarfs are one of the most readily studied end products of stellarevolution. Their observed properties have provided and continue to provide important constraints for the theory of stellar evolution. Likewise, a study of magnetism in white dwarfs provides unique insights into the origin and evolution of magnetic fields in stars.Spectacular progress has been made on the specific problem of the structure of the hydrogen atom in strong fields. Energy levels and transition probabilities are now known for all low lying states of hydrogen for the entire range of field strengths appropriate to white dwarfs and neutron stars (104-1013G) (Rosner et al 1984, Forster et al 1984 and Henry and O’Connell 1984). These calculations resulted in the identification of spectral features in the magnetic white dwarf Grw+70°8247 which had remained unidentified for over 50 years (Minkowski 1938), with Zeeman shifted hydrogen lines in a magnetic field of 100 -320 MG ((eg Wickamasinghe and Ferrano 1989). Several other strong field magnetic white dwarfs have since been discovered through hydrogen Zeeman spectroscopy. The data presently at hand show that most hydrogen rich magnetic white dwarfs have complex non-dipolar field structures with strong evidence for higher order multipole components.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

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