scholarly journals Arbitrary Solution of the Schrödinger Equation Interacting with the Superposition of Hulthen with Spin-orbit Plus Adjusted Coulomb Potential Model

2021 ◽  
Vol 3 (6) ◽  
pp. 76-83
Author(s):  
E. A. Thompson ◽  
I. O. Akpan ◽  
C. A. Thompson
Keyword(s):  
Coulomb Potential ◽  
Single Particle ◽  
Potential Model ◽  
Particle Energy ◽  
Spin Orbit ◽  
Nuclear System ◽  
Radial Part ◽  
Nuclear Core ◽  
Special Cases ◽  
Nu Method

In this study, we solve the non-relativistic radial part of the Schrödinger wave equation for the superposition of the Hulthen with spin-orbit plus adjusted Coulomb potential (SHSC) potential using the Nikiforov-Uvarov (NU) method for arbitrary states. The Hulthen with spin-orbit plus adjusted Coulomb (SHSC) potential is the simplest potential field for a nuclear system and has been used to obtain the single particle energy spectrum for both nucleon species orbiting a closed nuclear core. We also obtained in this study the corresponding single particle normalized wave function expressed in terms of the Jacobi polynomial. Besides, we obtained two special cases of the energy spectra for the SHSC potential.

STUDY OF NUCLEAR BOUND STATES USING MEAN-FIELD WOODS–SAXON AND SPIN-ORBIT POTENTIALS

2012 ◽  
Vol 27 (29) ◽  
pp. 1250167 ◽  
Author(s):  
M. R. PAHLAVANI ◽  
S. A. ALAVI
Keyword(s):  
Differential Equation ◽  
Single Particle ◽  
Bound States ◽  
Numerical Solutions ◽  
Mean Field ◽  
Particle Energy ◽  
Nuclear Potential ◽  
Spin Orbit ◽  
Energy Eigenvalues ◽  
Special Cases

The neutron single-particle bound states as solutions of radial Schrödinger equation for the central Woods–Saxon potential together with spin-orbit interaction and centrifugal terms have been obtained analytically. By introducing new variable and using Taylor expansion, the differential equation has been transformed to solvable hypergeometric type. This differential equation has also been solved using Nikiforov–Uvarov (NU) method. Neutron single-particle states have been derived as self-adjoint form of hypergeometric series. By means of boundary conditions, which implies eigenvalue condition as complicated relation between energy eigenvalues and parameters of nuclear potential, the neutron single-particle energy eigenvalues have been derived using graphical method. To examine method, numerical results in special cases of S states are evaluated. Results obtained using this method are in satisfactory agreements with available numerical solutions.

scholarly journals The First Excited State of 9B

1987 ◽  
Vol 40 (3) ◽  
pp. 307 ◽  
Author(s):  
FC Barker
Keyword(s):  
Excited State ◽  
Single Particle ◽  
Potential Model ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
S Wave ◽  
Analogue State ◽  
First Excited State ◽  
Particle Potential ◽  
Single Particle Potential

The energy of the ! + first excited state of 9B is derived from the measured energy of the analogue state in 9Be together with calculated values of the Coulomb displacement energy. The latter include contributions from the internal Coulomb interaction, the electromagnetic spin-orbit interaction and the different external wavefunctions in 9Be and 9B. The ! + excitation energy is predicted to be greater in 9B than in 9Be,arising from an inverted Thomas-Ehrman shift, due to the 9Be state being above the 8 Be(g.s.) + s-wave neutron threshold. This result is in conflict with a recently published calculation (Sherr and Bertsch 1985), which was based on a single-particle potential model.

scholarly journals Effects of isovector scalar δ–meson on Λ–hypernuclei

2015 ◽  
Vol 24 (03) ◽  
pp. 1550019
Author(s):  
M. Ikram ◽  
S. K. Singh ◽  
S. K. Biswal ◽  
S. K. Patra
Keyword(s):  
Binding Energy ◽  
Single Particle ◽  
Energy Levels ◽  
Mean Field Theory ◽  
Mean Field ◽  
Particle Energy ◽  
Spin Orbit ◽  
Single Particle Energy ◽  
Relativistic Mean Field ◽  
Meson Coupling

We analyze the effects of δ–meson on hypernuclei within the framework of relativistic mean field theory. The δ–meson is included into the Lagrangian for hypernuclei. The extra nucleon–meson coupling (gδ) affects every piece of physical observables, like binding energy, radii and single-particle energies of hypernuclei. Magnitude of effects in hypernuclei is found to be relatively less than their normal nuclei because of the presence of Λ hyperon. Flipping of single-particle energy levels are observed with the strength of gδ in the considered hypernuclei as well as normal nuclei. The spin-orbit potentials are observed for considered hypernuclei and the effect of gδ on spin-orbit potentials is also analyzed. The calculated Λ binding energy (BΛ) are quite agreeable with experimental data. The sensitivity of BΛ for s- and p- orbitals with the strength of gδ is also analyzed. Lambda mean potential is investigated which is found to be consistent with other predictions.

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.

Shell-Tunneling Spectroscopy of the Single-Particle Energy Levels of Insulating Quantum Dots

Nano Letters ◽  
2001 ◽  
Vol 1 (10) ◽  
pp. 551-556 ◽  
Author(s):  
E. P. A. M. Bakkers ◽  
Z. Hens ◽  
A. Zunger ◽  
A. Franceschetti ◽  
L. P. Kouwenhoven ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Single Particle ◽  
Energy Levels ◽  
Tunneling Spectroscopy ◽  
Particle Energy ◽  
Single Particle Energy

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.

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