scholarly journals Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
E. S. William ◽  
J. A. Obu ◽  
I. O. Akpan ◽  
E. A. Thompson ◽  
E. P. Inyang
Keyword(s):  
Energy Spectrum ◽  
Coulomb Interaction ◽  
Jacobi Polynomials ◽  
Yukawa Potential ◽  
Analytical Investigation ◽  
Particle Energy ◽  
Spin Orbit ◽  
Centrifugal Barrier ◽  
Interaction Terms ◽  
Uvarov Method

The analytical solutions of the radial D-dimensional Schrödinger equation for the Yukawa potential plus spin-orbit and Coulomb interaction terms are presented within the framework of the Nikiforov-Uvarov method by using the Greene-Aldrich approximation scheme to the centrifugal barrier. The energy eigenvalues obtained are employed to calculate the single-energy spectrum of ⁵⁶Ni and ¹¹⁶Sn for distinct quantum states. We have also obtained corresponding normalized wave functions for the magic nuclei manifested in terms of Jacobi polynomials. However, the energy spectrum without Spin-orbit and Coulomb interaction terms precisely matches the quantum mechanical system of the Yukawa potential field at any arbitrary state.

scholarly journals Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 193
Author(s):  
E. P. Inyang ◽  
E. S. William ◽  
J. A. Obu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Hulthén Potential ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Special Cases ◽  
Uvarov Method

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

scholarly journals Interplay of spin–orbit coupling and Coulomb interaction in ZnO-based electron system

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
D. Maryenko ◽  
M. Kawamura ◽  
A. Ernst ◽  
V. K. Dugaev ◽  
E. Ya. Sherman ◽  
...  
Keyword(s):  
Coulomb Interaction ◽  
High Mobility ◽  
Electron System ◽  
Orbit Coupling ◽  
Electron Interaction ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Strong Electron ◽  
Strongly Coupled ◽  
Dimensional Electron System

AbstractSpin–orbit coupling (SOC) is pivotal for various fundamental spin-dependent phenomena in solids and their technological applications. In semiconductors, these phenomena have been so far studied in relatively weak electron–electron interaction regimes, where the single electron picture holds. However, SOC can profoundly compete against Coulomb interaction, which could lead to the emergence of unconventional electronic phases. Since SOC depends on the electric field in the crystal including contributions of itinerant electrons, electron–electron interactions can modify this coupling. Here we demonstrate the emergence of the SOC effect in a high-mobility two-dimensional electron system in a simple band structure MgZnO/ZnO semiconductor. This electron system also features strong electron–electron interaction effects. By changing the carrier density with Mg-content, we tune the SOC strength and achieve its interplay with electron–electron interaction. These systems pave a way to emergent spintronic phenomena in strong electron correlation regimes and to the formation of quasiparticles with the electron spin strongly coupled to the density.

On the single-particle-energy spectrum of a Λ particle in nuclear matter

1970 ◽  
Vol 48 (23) ◽  
pp. 2804-2808 ◽  
Author(s):  
K. F. Chong ◽  
Y. Nogami ◽  
E. Satoh
Keyword(s):  
Energy Spectrum ◽  
Nuclear Matter ◽  
Single Particle ◽  
Short Range ◽  
Particle Energy ◽  
Pair Approximation ◽  
Single Particle Energy ◽  
Short Range Repulsion ◽  
Separable Potentials ◽  
Independent Pair

The single-particle-energy spectrum of a Λ particle in nuclear matter is examined in the independent-pair approximation, by assuming nonlocal separable potentials for the ΛN interaction. Effects of short-range repulsion in the ΛN interaction on the Λ binding are also examined in terms of separable potentials of rank two.

Spin–orbit-coupled BEC in a double-well potential: Quantum energy spectrum and flat band

2015 ◽  
Vol 379 (30-31) ◽  
pp. 1762-1765 ◽  
Author(s):  
Wen-Yuan Wang ◽  
Hui Cao ◽  
Jie Liu ◽  
Li-Bin Fu
Keyword(s):  
Energy Spectrum ◽  
Flat Band ◽  
Spin Orbit ◽  
Quantum Energy ◽  
Double Well Potential

Trapped particle energy spectrum in shuttle middeck

1996 ◽  
Vol 18 (12) ◽  
pp. 149-157
Author(s):  
Gautam D Badhwar ◽  
Jagdish U Patel ◽  
Anderi Konradi ◽  
Francis A Cucinotta ◽  
John W Kern
Keyword(s):  
Energy Spectrum ◽  
Particle Energy
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