scholarly journals Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

2015 ◽  
Vol 24 (11) ◽  
pp. 1550089 ◽  
Author(s):  
M. Chabab ◽  
A. Lahbas ◽  
M. Oulne
Keyword(s):  
Potential Model ◽  
Heavy Nuclei ◽  
Axially Symmetric ◽  
Eigenvalues And Eigenfunctions ◽  
Unstable Nuclei ◽  
Unstable Case ◽  
Two Parameters ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Good Agreement

In the present paper, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning–Rosen potential for [Formula: see text]unstable nuclei as well as exactly separable rotational ones with [Formula: see text]. Some heavy nuclei with known [Formula: see text] and [Formula: see text] bandheads have been fitted by using two parameters in the [Formula: see text]unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.

PHENOMENOLOGICAL POTENTIAL, MODEL WAVEFUNCTION AND DIFFRACTIVE INTERACTION OF THREE-NUCLEON-NUCLEI WITH HEAVY NUCLEI

2000 ◽  
Vol 09 (06) ◽  
pp. 449-458
Author(s):  
V. YU. KORDA
Keyword(s):  
Relative Motion ◽  
Cross Sections ◽  
Ground State ◽  
Potential Model ◽  
Heavy Nuclei ◽  
Interaction Processes ◽  
Phenomenological Potential ◽  
Three Body ◽  
Analytical Expressions

On the basis of the simple strict three-body analysis the hyperspherical phenomenological potential and model wavefunction of the three-nucleon ground-state relative motion are built to be permutationally invariant. The analytical expressions for the integrated cross-sections of different three-nucleon-nuclei–nuclei diffraction interaction processes are derived with the new wavefunction presented.

scholarly journals A long sought result: Closed analytical solutions of the Bohr Hamiltonian with the Morse potential

2019 ◽  
Vol 17 ◽  
pp. 15
Author(s):  
D. Bonatsos ◽  
I. Boztosun ◽  
I. Inci
Keyword(s):  
Analytical Solutions ◽  
Morse Potential ◽  
Asymptotic Iteration Method ◽  
Heavy Nuclei ◽  
Energy Eigenvalues ◽  
Angular Momenta ◽  
Medium Mass ◽  
Unstable Case ◽  
Analytical Expressions ◽  
Two Parameter

Closed analytical solutions of the Morse potential for nonzero angular momenta has been an open problem for decades, solved recently by the Asymptotic Iteration Method (AIM) for solving differential equations. Closed analytical expressions have been obtained for the energy eigenvalues and B(E2) rates of the Bohr Hamiltonian in the γ-unstable case, as well as in an exactly separable rotational case with γ ≈ 0, called the exactly separable Morse (ES-M) solution. All medium mass and heavy nuclei with known β1 and γ1 bandheads have been fitted by using the two-parameter γ-unstable solution for transitional nuclei and the three-parameter ES-M for rotational ones. It is shown that bandheads and energy spacings within the bands are well reproduced for more than 50 nuclei in each case. Comparisons to the fits provided by the Davidson and Kratzer potentials, also soluble by the AIM, are made.

scholarly journals The Stationary Concentrated Vortex Model

Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  
Keyword(s):  
Vortex Structure ◽  
Radial Direction ◽  
Symmetry Axis ◽  
Outer Part ◽  
Vertical Direction ◽  
Axially Symmetric ◽  
New Model ◽  
Vortex Model ◽  
Axis Of Symmetry ◽  
Good Agreement

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

ALPHA-DECAY STUDIES ON 130-153Eu NUCLEI

2013 ◽  
Vol 22 (11) ◽  
pp. 1350081 ◽  
Author(s):  
K. P. SANTHOSH ◽  
B. PRIYANKA
Keyword(s):  
Experimental Data ◽  
Potential Model ◽  
Alpha Decay ◽  
Shell Closure ◽  
Proximity Potential ◽  
Deformed Nuclei ◽  
Neutron Shell ◽  
Good Agreement ◽  
Neutron Shell Closure

The alpha-decay half-lives of the 24 isotopes of Eu (Z = 63) nuclei in the region 130≤A≤153, have been studied systematically within the Coulomb and proximity potential model (CPPM). We have modified the assault frequency and re-determined the half-lives and they show a better agreement with the experimental value. We have also done calculations on the half-lives within the recently proposed Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed half-lives are compared with the experimental data and they are in good agreement. Using our model, we could also demonstrate the influence of the neutron shell closure at N = 82, in both parent and daughter nuclei, on the alpha-decay half-lives.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

Linear bounded potential model for semiconductor band bending

2022 ◽  
Author(s):  
Facundo Villavicencio ◽  
Jorge Mario Ferreyra ◽  
German Bridoux ◽  
Manuel Villafuerte
Keyword(s):  
Potential Model ◽  
Simple Expression ◽  
Linear Potential ◽  
Charge Balance ◽  
Band Bending ◽  
Mass Approximation ◽  
Hole Confinement ◽  
Dimensional Electron Gas ◽  
Analytical Expressions ◽  
Franz Keldysh Effect

Abstract We propose a simple but unexplored model for the semiconductor band bending with the aim to obtain a relatively simple expression to calculate the energy spectrum for the confined levels and the analytical expressions for wave-functions. This model consists of a linear potential but it is bounded or trimmed in energy unlike the well known wedge potential model. We present exact solutions for this potential in the frame of the effective mass approximation and they are valid for electron or hole confinement potential. This model provides a more adequate physical scenario than the wedge potential since it takes into account the charge balance involved in the band bending potential. These results allow to treat confined potential problems as in the case of a two-dimensional electron gas (2DEG) in a simplified way. We discuss the application of this approximation to the recombination time of electrons an holes and for the Franz-Keldysh effect.

An analytical model of an I-cored coil located above a conductive material with a hole

2018 ◽  
Vol 82 (2) ◽  
pp. 21001
Author(s):  
Grzegorz Tytko ◽  
Leszek Dziczkowski
Keyword(s):  
Test Object ◽  
Middle Layer ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Cylindrical Coordinate ◽  
Air Space ◽  
Through Hole ◽  
Tree Method ◽  
Good Agreement ◽  
Made In

The paper examines the problem of an axially symmetric I-cored coil located above a three-layered plate with a hole in the middle layer. A cylindrical coordinate system was applied, wherein the solution domain was truncated in the radial direction. The employment of the truncated region eigenfunction expansion (TREE) method resulted in deriving the final formulas for the change of the coil impedance with regard to the air space, and also pertaining to the test object without a flaw. Formulas for various configurations of the test object, among others for a surface hole, a subsurface hole and a through hole, have been presented. For the purpose of defectoscopy, the influence of the hole in the plate on the impedance components was investigated. The calculations were made in Matlab for frequencies from 100 Hz to 50 kHz. The obtained results were verified using the finite element method (FEM) in Comsol Multiphysics package. A very good agreement was observed in the case of both the resistance and reactance.

RELATIVISTIC OPTICAL MODEL FOR PROTON-NUCLEUS ELASTIC SCATTERING

2002 ◽  
Vol 11 (05) ◽  
pp. 425-436 ◽  
Author(s):  
M. Y. H. FARAG ◽  
M. Y. M. HASSAN
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Optical Potential ◽  
Optical Model ◽  
Potential Model ◽  
Optical Potential Model ◽  
Relativistic Description ◽  
Good Agreement

The relativistic description of the proton-nucleus elastic scattering can be considered within the framework of a relativistic optical potential model. The elastic scattering of proton with the nuclei 12 C , 16 O , 20 Ne , and 24 Mg at 800 MeV and 1.04 GeV are studied for relativistic and nonrelativistic treatments. The real optical potentials and the differential cross sections of these reactions are calculated. The obtained results are compared with the corresponding results obtained from the calculation depending on the Woods–Saxon optical potential which were adjusted to fit the experimental data. The present results are in good agreement with the experimental data.

scholarly journals Comparison of GPM Core Observatory and Ground-Based Radar Retrieval of Mass-Weighted Mean Raindrop Diameter at Midlatitude

2018 ◽  
Vol 19 (10) ◽  
pp. 1583-1598 ◽  
Author(s):  
Leo Pio D’Adderio ◽  
Gianfranco Vulpiani ◽  
Federico Porcù ◽  
Ali Tokay ◽  
Robert Meneghini
Keyword(s):  
High Sensitivity ◽  
Sensitivity Study ◽  
Three Dimensions ◽  
Convective Precipitation ◽  
Precipitation Pattern ◽  
Dual Frequency ◽  
Weighted Mean ◽  
Raindrop Size Distribution ◽  
Two Parameters ◽  
Good Agreement

Abstract One of the main goals of the National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM) mission is to retrieve parameters of the raindrop size distribution (DSD) globally. As a standard product of the Dual-Frequency Precipitation Radar (DPR) on board the GPM Core Observatory satellite, the mass-weighted mean diameter Dm and the normalized intercept parameter Nw are estimated in three dimensions at the resolution of the radar. These are two parameters of the three-parameter gamma model DSD adopted by the GPM algorithms. This study investigates the accuracy of the Dm retrieval through a comparative study of C-band ground radars (GRs) and GPM products over Italy. The reliability of the ground reference is tested by using two different approaches to estimate Dm. The results show good agreement between the ground-based and spaceborne-derived Dm, with an absolute bias being generally lower than 0.5 mm over land in stratiform precipitation for the DPR algorithm and the combined DPR–GMI algorithm. For the DPR–GMI algorithm, the good agreement extends to convective precipitation as well. Estimates of Dm from the DPR high-sensitivity (HS) Ka-band data show slightly worse results. A sensitivity study indicates that the accuracy of the Dm estimation is independent of the height above surface (not shown) and the distance from the ground radar. On the other hand, a nonuniform precipitation pattern (interpreted both as high variability and as a patchy spatial distribution) within the DPR footprint is usually associated with a significant error in the DPR-derived estimate of Dm.

Sign in / Sign up

Export Citation Format

Share Document