Bound state solutions of the Dirac equation for the generalized Cornell potential model

Abu‐Shady, M.; Khokha, E. M.

doi:10.1142/s0217751x21501955

Cited by 15 publications

(14 citation statements)

References 67 publications

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“…One of the potential models that has significant contributions in the study of diverse systems in quantum chemistry and nuclear physics is the generalized Cornell potential (GCP) which is defined as [35–39].

U (r) = a r^{2} + br - \frac{d}{r} + \frac{f}{r^{2}} + V_{0},

where

a, b, d, f,

and

V_{0}

are the potential parameters.…”

Section: Introductionmentioning

confidence: 99%

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The influence of magnetic and Aharanov–Bohm fields on energy spectra of diatomic molecules in the framework of the Dirac equation with the generalized interaction potential

Khokha

Abu‐Shady

Abdel-Karim

2022

Int J of Quantum Chemistry

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In this study, we present the relativistic and non-relativistic solutions of the Dirac equation with the spin symmetry for the generalized Cornell potential (GCP) using the wave function ansatz method in the existence of external magnetic and Aharanov-Bohm (AB) flux fields. The relativistic energy eigenvalues and the corresponding eigenfunctions are found for varied vibrational and magnetic quantum numbers. By adapting the GCP parameters, we derive the relativistic and nonrelativistic energy eigenvalues with and without external fields for a set of potential models including the Killingbeck, harmonic oscillator, pseudoharmonic, anharmonic, Cornell, Coulomb, Kratzer, and modified Kratzer potentials. Additionally, the nonrelativistic energy spectra of the Kratzer and modified Kratzer potentials are reported with and without external magnetic and AB flux fields for several diatomic molecules (DMs). We discovered that in the existence of external magnetic and AB flux fields, the non-relativistic energy spectrum increases and degeneracy disappears. Furthermore, the AB flux field has a stronger impact on the energy spectrum than the magnetic field. To substantiate our findings, we calculate the energy levels of the Kratzer and modified Kratzer potentials for diverse DMs and find that they are perfectly consistent with previous studies.

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U (r) = a r^{2} + br - \frac{d}{r} + \frac{f}{r^{2}} + V_{0},

where

a, b, d, f,

and

V_{0}

are the potential parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Karayer [38] studied the solutions of the SE with the GCP in the presence of external magnetic and AB flux fields using the extended NU method. In Abu-Shady and Khokha [39], the solutions of the DE for the GCP were found using the NU method under the condition of spin symmetry. Moreover, the obtained results were applied to study some DMs and heavy mesons.…”

mentioning

confidence: 99%

The influence of magnetic and Aharanov–Bohm fields on energy spectra of diatomic molecules in the framework of the Dirac equation with the generalized interaction potential

Khokha

Abu‐Shady

Abdel-Karim

2022

Int J of Quantum Chemistry

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“…In recent decades, the advent of new and powerful calculation software has allowed relativistic chemistry to develop and refine theoretical predictions on the physicochemical properties of matter. We are not only talking about the relativistic effects that have had experimental confirmation, well documented and discussed in the works of Pyykkö [3,4,17,18], but also those that are emerging from the study of innovative topological materials where theoretical chemistry has found a new fertile ground to test its potential [55][56][57][58][59]. In this article, we revisit the pillars on which the relativistic computational methods of chemistry are based, hidden in the lines of code that often are not clear to those who use such software.…”

Section: Concluding Discussionmentioning

confidence: 99%

A discussion on the relativistic corrections of the electronic structures of multi‐electron atoms

Nanni

2023

Int J of Quantum Chemistry

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The theory of special relativity is a topic not addressed in theoretical chemistry courses. Einstein's theory of relativity is mainly applied to high‐energy phenomena governed by physical laws not used to describe the chemical bond. Nevertheless, the electrons of heavy elements orbit around the nucleus with relativistic velocities. Here it is, then, the laws that appeared so unusual for chemistry became fundamental tools for investigating the properties of these atoms. Studying the electronic structure of heavy elements is the best place for chemists to learn to tame the pitfalls of a little‐known subject, such as Einstein's theory, and become familiar with its elegant formalism. In this paper, the main relativistic approaches to quantum chemistry are revisited. The problem of the finite nuclear size, the approximation methods used to solve the relativistic equations for k‐shell electrons, and the problem of the negative energy continuum are investigated. Some ansatzes to solve divergence's problem of relativistic corrections near the nucleus are proposed. Finally, a possible connection between the self‐consistent field method and bondonic chemistry is also investigated.

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“…The finding of the equation was based on the MSA in the integral equation theory of simple fluids, however, other approaches can be used for finding similar equations of the specific bond volume of Morse potential. The method which was employed for deriving the formula of the specific bond volume of Morse potential can be applied for other potentials, for instance: the dispersion potentials [38], the screening potential [30], and the two powers potential such as Lennard-Jones (6-12 type) potential and other types of the similar potentials [39][40][41][42][43][44][45], however, this study focused on the Morse potential.…”

Section: The Method: the Specific Bond Volume Of Morse Potentialmentioning

confidence: 99%

Morse potential specific bond volume: a simple formula with applications to dimers and soft–hard slab slider

Al‐Raeei

2022

J. Phys.: Condens. Matter

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Morse potential interaction is an important type of the vibrational potentials, especially, in the quantum mechanics which is used for the describing of general vibrational cases rather than the harmonic one. Morse potential has three fitting parameters, the depth of the Morse interaction, the distance of equilibrium bond and the range parameter which determines the range of the well. The Morse interaction specific bond volume is a three dimensional image of the bond length in its molar case, and this specific volume is the generalisation in three dimensions. In this study, the integral equation theory of the simple fluids has been applied for deriving a novel formula of the specific bond volume for Morse potential based on one of the approaches in the theory and based on the boundary conditions. We find that the specific bond volume of Morse potential depends on the absolute temperature via logarithmic function and square root function, besides, the specific bond volume of Morse potential decreases when the temperature decreases for different values of the molar volume and for different values of the depth of Morse well. In addition to that, the specific bond volume of Morse potential increases when the depth of the well decreases for different temperature values. Also, it is found from the formula which we derive that the specific bond volume of Morse potential increases via linear function with the molar volume of the system for different values of temperatures. We apply the formula of the specific bond volume of Morse potential for finding this specific volume for two molecules of the hydrogen halogens, which are the hydrogen chloride, and hydrogen fluoride. We find that the specific bond volume of the hydrogen chloride is greater than the one of the hydrogen fluoride. Also, we apply the formula for the two simple molecules gases which are the hydrogen molecules, and the nitrogen molecules. Besides, we apply the formula for the slab–slider system in two cases: hard and soft materials, and we concluded that the changes of the specific bond volume of the soft materials is faster than the hard materials. We believe that the formula which is found of the specific bond volume of Morse potential is general and can be applied for multiple materials.

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Bound state solutions of the Dirac equation for the generalized Cornell potential model

Cited by 15 publications

References 67 publications

The influence of magnetic and Aharanov–Bohm fields on energy spectra of diatomic molecules in the framework of the Dirac equation with the generalized interaction potential

The influence of magnetic and Aharanov–Bohm fields on energy spectra of diatomic molecules in the framework of the Dirac equation with the generalized interaction potential

A discussion on the relativistic corrections of the electronic structures of multi‐electron atoms

Morse potential specific bond volume: a simple formula with applications to dimers and soft–hard slab slider

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