Analytical Expressions to Energy Eigenvalues of the Hydrogenic Atoms and the Heavy Light Mesons in the Framework of 3D-NCPS Symmetries Using the Generalized Bopp's Shift Method

doi:10.55318/bgjp.2022.49.3.239

Cited by 8 publications

(4 citation statements)

References 68 publications

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“…One of the most important applications in the extended model of pNRQCD is to calculate the modified mass spectra of the heavy quarkonium systems (the mass of the quarkonium bound state), such as charmonium and bottomonium mesons, which have the quark and antiquark flavor in the symmetries of NCQM under improved internal energy potential at finite temperature. To achieve this goal, we generalize the traditional formula [84][85][86][87][88][89][90][91], 𝑀 = 2𝑚 + 𝐸 which defines the total mass of the different quarkonium states (resonance masses), to the new form:…”

Section: Resultsmentioning

confidence: 99%

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

Maireche

2023

East Eur. J. Phys.

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In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at ﬁnite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.

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Section: Resultsmentioning

confidence: 99%

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

Maireche

2023

East Eur. J. Phys.

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“…and E nr−yk nc−nl are the new energy eigenvalues that correspond (j = l + 1, s = 1), (j = l, s = 1), (j = l − 1, s = 1) and (j = l, s = 0) under improved modified Yukawa-Kratzer potential model interactions in 3D-NRNCQM symmetries. We generalized the original formula [106][107][108]:…”

Section: Spin-averaged Mass Spectra Of Hlm Under Imkscp Models In 3d-...mentioning

confidence: 99%

New Eigensolution of the Klein--Gordon and Shrödinger equations for improved modified Yukawa-Kratzer potential and its applications using Boop's Shift method and standard perturbation theory in the 3D-ERQM and 3D-ENRQM symmetries

Maireche

2023

Rev. Mex. Fís.

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The deformed Klein-Gordonequation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the improved modified Yukawa-Kratzer potential (IMYKP) model under the influence of the deformation space-space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp’s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H2) molecules under the IMYKP model it was shown to be sensitive to the atomic quantum numbers (j, l, s, m), mixed potential depths (V0, De, re), the screening parameter’s inverse α and noncommutativity parameters (Θ,τ ,χ). In addition, we analyzed the nonrelativistic energy values by applying the well-known transmission rules known in the literature. In addition, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the improved modified Kratzer potential, the improved generalized Kratzer potential, the improved Kratzer potential, the improved modified Kratzer plus screened Coulomb potential, the improved Hellmann potential, the improved Yukawa potential, and improved inversely square Yukawa potential. We noticed that these particular results are identical to our previous work and other known works in the literature. The study is further extended to calculate the mass spectra of mesons of charmonium (cc) and bottomonium (bb) within the framework of the IMYKP model in three-dimensional extended non-relativistic quantum mechanics (3D-ENRQM) symmetries.

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“…The SE played a vital role to obtain not only the energy spectrum of the diatomic and polyatomic molecule but also the spectrum of the heavy quarkonium system. The solution of the SE for the different potentials, as found in [60][61][62][63], has been obtained using generalized Boopp's shift method and standard perturbation theory. In the present work, medium-modified potential [64] has been used to investigate the properties of the heavy quarkonia.…”

Section: Quark-antiquark Potential In the Anisotropic Mediummentioning

confidence: 99%

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

Lal

Solanki

Sharma

et al. 2023

Advances in High Energy Physics

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We studied the effect of momentum space anisotropy on heavy quarkonium states using an extended magnetized effective fugacity quasiparticle model (EQPM). Both the real and imaginary part of the potential has been modified through the dielectric function by including the anisotropic parameter ξ . The real part of the medium-modified potential becomes more attractive in the presence of the anisotropy and constant magnetic field. The binding energy of the 1S, 2S, and 1P quarkonium states including anisotropy effects for both the oblate and the isotropic case were studied. We find that the binding energy of Q Q ¯ states becomes stronger in the presence of anisotropy. However, the magnetic field is found to reduce the binding energy. The thermal width of the charmonium and bottomonium 1 S states has been studied at constant magnetic field e B = 0.3 G e V 2 for isotropic and prolate cases. The effect of magnetic field on the mass spectra of the 1P state for the oblate case was also examined. The dissociation temperature for the 1S, 2S, and 1P states of charmonium and bottomonium has been determined to be higher for the oblate case with respect to the isotropic case.

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Analytical Expressions to Energy Eigenvalues of the Hydrogenic Atoms and the Heavy Light Mesons in the Framework of 3D-NCPS Symmetries Using the Generalized Bopp's Shift Method

Cited by 8 publications

References 68 publications

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

New Eigensolution of the Klein--Gordon and Shrödinger equations for improved modified Yukawa-Kratzer potential and its applications using Boop's Shift method and standard perturbation theory in the 3D-ERQM and 3D-ENRQM symmetries

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

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