Calculation of the energy levels and charge radius of 24Mg and 32S isotopes in the cluster model

2020 ◽  
Vol 98 (2) ◽  
pp. 148-152
Author(s):  
Sahar Aslanzadeh ◽  
Mohammad Reza Shojaei ◽  
Ali Asghar Mowlavi
Keyword(s):  
Experimental Data ◽  
Excited State ◽  
Cluster Model ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Alpha Particles ◽  
Wave Functions ◽  
S Isotopes ◽  
Klein Gordon ◽  
Nu Method

In this work, the 24Mg and 32S isotopes are considered in the cluster model by solving the Schrödinger and Klein–Gordon equations using the Nikiforov–Uvarov (NU) method. The configuration of the alpha particles for the second excited state for 24Mg isotope is 12C + 12C. A local potential is used for these two equations that is compatible to the modified Hulthen plus quadratic Yukawa potential. By substituting this potential in the Schrödinger and Klein–Gordon equations, the energy levels and wave functions are obtained. The calculated results from the Schrödinger and Klein–Gordon equations, i.e., nonrelativity and relativity, respectively, are close to the results from experimental data.

Spinless Particles Subject to Unequal Scalar-Vector Nuclear Woods– Saxon Potentials in Arbitrary Dimensions

2013 ◽  
Vol 68 (12) ◽  
pp. 759-765 ◽  
Author(s):  
Majid Hamzavi ◽  
Sameer M. Ikhdair ◽  
Ali Akbar Rajabi
Keyword(s):  
Approximation Scheme ◽  
Energy Levels ◽  
Bound State ◽  
Wave Functions ◽  
Potential Term ◽  
Energy Eigenvalues ◽  
Spatial Dimensions ◽  
Klein Gordon ◽  
Arbitrary Dimensions ◽  
Nu Method

We present analytical bound state solutions of the spin-zero particles in the Klein-Gordon (KG) equation in presence of an unequal mixture of scalar and vector Woods-Saxon potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a parametric Nikiforov-Uvarov (NU) method. Our numerical energy eigenvalues demonstrate the existence of inter-dimensional degeneracy amongst energy states of the KG-Woods-Saxon problem. The dependence of the energy levels on the dimension D is numerically discussed for spatial dimensions D = 2 - 6.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

12C isotope in relativistic cluster model

2019 ◽  
Vol 34 (20) ◽  
pp. 1950158 ◽  
Author(s):  
N. Roshanbakht ◽  
M. R. Shojaei
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Cluster Model ◽  
Center Of Mass ◽  
Mass Motion ◽  
Body System ◽  
Central Potential ◽  
Relative Coordinates ◽  
Klein Gordon ◽  
Good Coincidence

12C isotope composing 3[Formula: see text] cluster was investigated in this study. Therefore, 12C can be considered as a 3-body system. For studying the interactions in 3[Formula: see text] clusters, a central potential was applied. Jacobi relative coordinates were also employed and center of mass motion was removed. In this paper, the Klein–Gordon (K–G) equation was solved using Nikiforov–Uvarov potential. At the end, the energy spectrum and wave function of isotope 12C were determined and the results were compared with the experimental data which showed good coincidence reflecting the success of our model in prediction.

scholarly journals EXCITED PIONS, ρ- AND ω-MESONS AND THEIR DECAYS IN A CHIRAL SU(2) × SU(2) LAGRANGIAN

1998 ◽  
Vol 13 (32) ◽  
pp. 5443-5457 ◽  
Author(s):  
M. K. VOLKOV ◽  
D. EBERT ◽  
M. NAGY
Keyword(s):  
Experimental Data ◽  
Excited State ◽  
Decay Constant ◽  
Three Dimensional ◽  
Form Factors ◽  
Weak Decay ◽  
Wave Functions ◽  
Spontaneous Breaking ◽  
Gap Equation ◽  
Decay Widths

A chiral SU(2) × SU(2) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the Nambu–Jona-Lasinio (NJL) quark model with separable nonlocal interactions, with form factors corresponding to three-dimensional ground and excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pions, ρ-and ω-mesons are described with the help of two form factors. The weak decay constant Fπ′ is calculated. The values for the decay widths of the processes ρ→2π, π′→ρπ, ρ′→2π, ρ′→ωπ and ω′→ρπ are obtained in agreement with the experimental data.

scholarly journals Spin averaged mass spectrum of heavy quarkonium via asymptotic iteration method

2019 ◽  
Vol 97 (12) ◽  
pp. 1342-1348
Author(s):  
Halil Mutuk
Keyword(s):  
Experimental Data ◽  
Mass Spectrum ◽  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Asymptotic Iteration Method ◽  
Heavy Quarkonium ◽  
Theoretical Studies

In this paper we solved Schrödinger equation with Song–Lin potential by using asymptotic iteration method (AIM). We obtained spin-averaged energy levels and wave functions of charmonium and bottomonium via AIM. Obtained results agree well with available experimental data and other theoretical studies.

About the Calculation of Electronic Transitions in the Original CNDO/2 Treatment

1973 ◽  
Vol 28 (2) ◽  
pp. 280-283 ◽  
Author(s):  
Gloria Finkelstein ◽  
Myriam Segre de Giambiagi ◽  
Mario Giambiagi
Keyword(s):  
Excited State ◽  
Electronic Transition ◽  
Energy Levels ◽  
Open Shell ◽  
Wave Functions ◽  
Electronic Transitions ◽  
Virtual Orbital ◽  
Orbital Approximation

The original CNDO/2 method is adapted to the open shell case in order to calculate the first singlettriplet electronic transition. The molecular wave functions are optimized, minimizing the fundamental and excited state energies. Some linear hydrocarbons and monocyclic azines are calculated. The results are improved compared with those obtained by means of the virtual orbital approximation. The modifications in the energy levels are discussed.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Calculating Fundamental Vibrational Frequencies of Rutile by Combining Ab Initio Method with GF Matrix Method

1994 ◽  
Vol 05 (02) ◽  
pp. 299-301
Author(s):  
Lin Libin ◽  
Zheng Xiangyin
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Matrix Method ◽  
Cluster Model ◽  
Normal Modes ◽  
Vibrational Frequencies ◽  
Ab Initio Method ◽  
Environment Factor ◽  
Factor Α ◽  
Good Agreement

Based on cluster model, we have calculated the fundamental vibrational frequencies of rutile by combining ab initio method and Wilson’s GF-matrix method. In the calculation, we have introduced the concept of environment factor α to correct the force field of the cluster model. The results of calculation are in good agreement to the experimental data and the normal modes give us clear physical picture of the crystal vibration.

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