Mirror nuclei of 9B and 9Be in the shell model and cluster model

In this paper, we study the 9B and 9Be mirror nuclei with shell and cluster models. The modified Eckart plus Coulomb repulsive potentials are selected to describe the interaction between particles. By solving the Schrödinger equation, the exact solution of this equation is obtained by the parametric Nikiforov–Uvarov (PNU) method. The eigenvalues and wave function are calculated for 9B and 9Be. Our results are compared with experimental results, as well as results from other papers, and are in good agreement.

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Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potentials

Journal of Scientific Research ◽

10.3329/jsr.v3i1.5310 ◽

2010 ◽

Vol 3 (1) ◽

pp. 25 ◽

Cited By ~ 9

Author(s):

A. N. Ikot ◽

L. E. Akpabio ◽

E. B. Umoren

Keyword(s):

Exact Solution ◽

Wave Function ◽

Energy Spectrum ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Negative Energy ◽

Dinger Equation ◽

Radial Schrödinger Equation ◽

Rosen Potential

We have analytically solved the radial Schrödinger equation with inverted Woods-Saxon and Manning-Rosen Potentials. With the ansatz for the wave function, we obtain the generalized wave function and the negative energy spectrum for the system.Keywords: Inverted Woods-Saxon Potentials; Manning-Rosen Potential; Schrödinger Equation.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i1.5310 J. Sci. Res. 3 (1), 25-33 (2011)

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Calculation of the Electric Quadrupole Moment of 6Li and 7Li in Shell Model and Cluster Model

Jordan Journal of Physics ◽

10.47011/14.4.7 ◽

2021 ◽

Vol 14 (4) ◽

pp. 333-338

Keyword(s):

Wave Function ◽

Shell Model ◽

Quadrupole Moment ◽

Cluster Model ◽

Particle System ◽

Cluster Structure ◽

Electric Quadrupole ◽

Experimental Results ◽

Electric Quadrupole Moment ◽

Model Calculations

Abstract: In this paper, we have investigated electric quadrupole moment of (_^6)Li and (_^7)Li in both shell model and cluster model. In shell model, the nuclei (_^6)Li and (_^7)Li can be modeled as one core plus nucleons. Nucleons outside the closed shell can be considered as a two- and three-particle system. In cluster structure, we have selected alpha clusters and triton or deuteron in interaction with alpha cluster ((_^7)Li and (_^6)Li involving α+(_^3)H and α+(_^2)H, respectively). By solving Schrödinger equation and using suitable potential for interaction between particles by applying Nikiforov-Uvarov method, potential coefficients have been computed. Then, we have calculated the energy and wave function for nuclei(_^6)Li and (_^7)Li and compared the results obtained with experimental results. By having the wave function, we can obtain the quadrupole moment. These values are compared with predictions from shell-model and cluster-model calculations. Although the difference between them is small, the electric quadrupole moment results in the cluster model are in good agreement with experimental results. Keywords: Electric quadrupole moment, Shell-model, Cluster-model, Li isotopes, Non-relativistic equation.

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Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

Risalah Fisika ◽

10.35895/rf.v2i2.117 ◽

2018 ◽

Vol 2 (2) ◽

pp. 43-47

Author(s):

A. Suparmi, C. Cari, Ina Nurhidayati

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Schrödinger Equation ◽

Coulomb Potential ◽

Schrodinger Equation ◽

Minimal Length ◽

Energy Spectra ◽

Atomic Particle ◽

Approximate Analytical Solutions ◽

Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

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