Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india received 26 march 2009. Solutions of ddimensional schrodinger equation for woods. Parameterization of the woodssaxon potential for shellmodel. Different from the traditional bistable sr system, we realize the sr based on the joint of woods saxon potential wsp and gaussian potential gp instead of a reflectionsymmetric quartic potential. R a2 where r0 r0a 1 3 is the radius of the corresponding nuclei with r0 as a constant. The woodssaxon potential is probably the most studied and widely used short range potential in all of nuclear physics. Download limit exceeded you have exceeded your daily download allowance. Parameterization of the woodssaxon potential for shellmodel calculations n. Bound states of the dirac equation for the generalized woods. Eigen spectra for woodssaxon plus rosenmorse potential.
February 11, 20 the drastically expanded use of the woods saxon potential in modern day nuclear physics and the. The nuclear shape was parametrized in terms of the cassinian ovaloids. Nuclear potential of the woodssaxon form, which is described by the potential depth v 0, the radius parameter, and the diffuseness parameter, is widely used in the a analyses of nuclear collisions. Jan 22, 2016 woodssaxon potential the woodssaxon potential is a mean field potential for the nucleons protons and neutrons inside the atomic nucleus, which is used to approximately describe the forces.
Bound state solutions of the dirac equation for the generalized woodssaxon potential are examined for arbitrary. The model is based on two spherical woodsaxon potentials and the potential separable expansion method. J theor appl phys solutions of ddimensional schrodinger equation for woods saxon potential with spinorbit, coulomb and centrifugal terms through a new hybrid numerical fitting nikiforovuvarov method a. Potential representation method for woodssaxon potential 45 are presented like analytical solution 7 by expanding in the power series the interaction potential vr. The structure of singleparticle levels in the second minima of 237,239,241pu was analyzed with the help of an axiallydeformed woods saxon potential. This work aims for a new stochastic resonance sr model which performs well in bearing fault diagnosis. Calculation of the eigenvalues for woodsaxons potential. Pdf canonical scalar field inflation with a woodssaxon.
Pdf 559 k pdf plus 608 k surface interaction effects to a kleingordon particle embedded in a woodssaxon potential well in terms of thermodynamic functions 1, 2. A variety of woods saxon and skyrme hartreefock potentials have been tried and from this experience the following procedure was found to be the most successful in reproducing the charge form factors. A detailed study of the scattering and boundstates problems for these models is presented. It describes the singleparticle motion in lowenergy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures. Download fulltext pdf parameterization of the woodssaxon potential for shellmodel calculations article pdf available october 2007 with 1,057 reads. Pdf parameterization of the woodssaxon potential for. A 338 2005 90, physics letters a on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Woodssaxon potential parametrization at large deformations for. Solutions of the central woodssaxon potential in 6 0 case. A woods saxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. Each level is characterized by the quantum numbers n number of vibrational quanta and l angular momentum. How to superimpose woodsaxon and coulomb potential. Dkp equation is also solved analytically by means of nu method a vector deformed woodssaxon potential 18. Woodssaxon potential for a 50, relative to v 0 with a 0.
Boudjedaa solved the dkp equation in the presence of woodssaxon potential for spin 1 and spin 0 and they also deduced the transmission and reflection coefficients 17. Generalized nuclear woodssaxon potential under relativistic spin. Single particle calculations for a woodssaxon potential. With this potential model, all the parameters in the woodssaxon and gaussian sr wsgsr. Scattering of the woodssaxon potential in the schrodinger.
Single particle calculations for a woodssaxon potential with triaxial deformations, and large cartesian oscillator basis new version code. Microscopic calculation of the wobbling excitations. Triaxially deformed woodssaxon potential the triaxially deformed woodssaxon potential considered in this work is a microscopic calculation of wobbling excitations standard one widely used in the study of highspin states. Parameterization of the woodssaxon potential for shell. The ws potential is a continuous function that has two adjustable parameters. The pt and non pt symmetric solutions for this potential are also presented.
In this context, for the first time, the molecular potential has been applied to obtain nuclear potential within the optical model. In table 1 we give the woodssaxon potential parameters of 240pu used in the present calculations. The woodssaxon potential with point interactions sciencedirect. These parameters, as we will show, allow one to treat different systems and to simulate smooth model potentials and in. Analysis of molecular, woodssaxon and squared woodssaxon. A fortran90 code for solving the twocenter nuclear shell model problem is presented. Now im thinking about improving the simple model to a more complex one. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india. A parametrization of the spinorbit part of the potential was obtained in the region corresponding to large deformations second minimum, depending only on. However, scientist have solved the woodssaxon potential for sstates l 0, exactly and also by some approximation they have also. Woodssaxon potential parametrization at large deformations for plutonium odd isotopes. Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s.
Canadian journal of physics canadian science publishing. The single particle energies and the single particle wave functions are calculated from onebody hamiltonian including a central field of woodssaxon type, a spinorbit interaction, and the coulomb potential for the protons. Saxon potentials are well known as modified woods saxon potential that plays a great role in nuclear physics. Stochastic resonance with woodssaxon potential for. Solutions of woodssaxon potential with spinorbit and. In addition, the exhaustive analysis of the results reveals the fact that the usual woodssaxon potential cannot be solved analytically within the. We obtain the wavefunction in terms of heuns function and then we find transmission. The woodssaxonpotential or any other onebody potential cannot be used. In this simulation, i approximate the potential of the nucleus by a simple square well. The result should look something like this picture. We have investigated bound states of the schrodinger equation for the woodssaxon potential decorated with a finite number of the dirac.
Volya florida state university, physics department, tallahassee, fl 32306 dated. Single particle calculations for a woodssaxon potential with triaxial. Mar 17, 2016 we consider the onedimensional dirac equation with the woodssaxon potential in the framework of position dependent mass and pseudoscalar interaction. Solaimani 0 1 0 department of physics, faculty of science, qom university of technology, qom, iran 1 physics faculty, shahrood university, p. We demonstrate that the potential provides a good description of the nuclear mean field leading to quality singleparticle spectra, nuclear radii, prediction of driplines, shell closures and other properties. Single particle calculations for a woodssaxon potential with. The structure of singleparticle levels in the second minima of 237,239,241pu was analyzed with the help of an axiallydeformed woodssaxon potential. Solutions 4 and 8 satisfy the standard boundary conditions 9 of the schrodinger equation and, represent the wave functions by the interaction potential. Calculation of the eigenvalues for woodsaxons potential by. A woodssaxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. Bound states of the dirac equation for the generalized.
My idea is to superimpose the woodsaxon potential with the coulombpotential. Single particle calculations for a woodssaxon potential with triaxial deformations, and large. The twocomponent approach to the onedimensional dirac equation is applied to the woods saxon potential. In figure 1, we illustrated the shape of the woods saxon potential and its generalized form in. The scattering and bound state solutions are derived. Thus presented woodssaxon fit provides adequate singleparticle basis for shell model calculations bridging over into the continuum. A 338 2005 90, physics letters a on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at.
Diffuseness parameters of woodssaxon potential for heavy. A comparison of woodssaxon and doublefolding potentials. In this study, we assume that the nuclear potential has a woods saxon form. Woodssaxon potential parametrization at large deformations. The form of the generalized woods saxon potential is as follows 41, 42. The twocomponent approach to the onedimensional dirac equation is applied to the woodssaxon potential. Generalized nuclear woodssaxon potential under relativistic. A variety of woodssaxon and skyrme hartreefock potentials have been tried and from this experience the following procedure was found to be the most successful in reproducing the charge form factors. By imposing appropriate constraints on the mass function and the pseudoscalar term new exact solvable models are obtained. Effective mass and pseudoscalar interaction in the dirac. University of gaziantep, department of engineering physics, 27310 gaziantepturkey. In this work, woodsaxon potential have been considered to calculate the eigenvalues by using numerov method for a sturmliouville problem defined with the boundary values r0 r12 0.
It provides a model for the properties of boundstate and continuum singleparticle wavefunctions. In figure 1, we illustrated the shape of the woodssaxon potential and its generalized form in. Pdf solutions for a generalized woodssaxon potential. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india received 26 march 2009 abstract. In order to find the best fitted value of the diffuseness parameter in comparison with the experimental data, the chi square method 2 is used. Analytical solutions of the schrodinger equation with the. The form of the generalized woodssaxon potential is as follows 41, 42. In this work, wood saxon potential have been considered to calculate the eigenvalues by using numerov method for a sturmliouville problem defined with the boundary values r0 r12 0. Using the nikiforovuvarov method which is based on solving the secondorder differential equations, we firstly analyzed the energy spectra and eigenfunctions of the woodssaxon potential. Eigenvalues and eigenfunctions of woods saxon potential in. Alexbrown nationalsuperconductingcyclotronlaboratory.
Pdf remarks on the woodssaxon potential researchgate. Stochastic resonance with woods saxon potential for rolling element bearing fault diagnosis. Therefore, a mean field potential is always empirical and its an example can be given as the woods. Gordon equation of the symmetric generalized woods. Eigenvalues and eigenfunctions of woods saxon potential in pt.
Solutions of woodssaxon potential with spinorbit and centrifugal terms through nikiforovuvarov method. Author links open overlay panel siliang lu qingbo he fanrang kong. Diffuseness parameters of woodssaxon potential for heavyion. In this study, we assume that the nuclear potential has a woodssaxon form.
A particular solution of heun equation for hulthen and woods. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. Woods saxon potential in closed form for the 5dimensional bohr. A comparison of woodssaxon and doublefolding potentials for. The nuclear potential is assumed to have a woodssaxon form, which is characterized by the surface diffuseness parameter, the potential depth, and the radius parameter.
We utilize, as additional potential, the woodssaxon ws potential function 27. Department of physics, akdeniz university, 07058 antalya, turkey. It is found that the nonlocality, introduced in the woodssaxon potential through an energyindependent effective mass. The woods saxonpotential or any other onebody potential cannot be used. Solutions of the central woodssaxon potential in 6 0. With this potential model, all the parameters in the woods saxon and gaussian sr wsgsr. One to one correspondence isomorphism of the aforesaid equation with the radial schrodinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions hulthen and woods.
My idea is to superimpose the wood saxon potential with the coulomb potential. The squarewell potential is defined by for and for, where is the radius of the well the woodssaxon potential is given by, where is the well depth. We consider the onedimensional dirac equation with the woodssaxon potential in the framework of position dependent mass and pseudoscalar interaction. I, the holder of this work, hereby release it into the public domain. A parametrization of the spinorbit part of the potential was obtained in the region corresponding to large deformations second minimum, depending only on the nuclear. A particular solution of heun equation for hulthen and. Nuclear potential of the woods saxon form, which is described by the potential depth v 0, the radius parameter, and the diffuseness parameter, is widely used in the a analyses of nuclear collisions. Stochastic resonance with a joint woodssaxon and gaussian.
This paper focuses on the realization of an inflationary model from a canonical scalar field theory with a woods saxon potential, in the slowroll approximation. Schrodinger equation, woodssaxon potential, rosenmorse potential. Different from the traditional bistable sr system, we realize the sr based on the joint of woodssaxon potential wsp and gaussian potential gp instead of a reflectionsymmetric quartic potential. Then, the theoretical calculations have been repeated by using the woodssaxon and squared woodssaxon potentials. The effectivemass schrodinger equation could be transformed into heuns equation which is a fuchsiantype equation with four singularities by using a coordinate transformation. In the framework of the ptsymmetric quantum mechanics, we secondly solved the timeindependent schrodinger equation for the pt and nonptsymmetric. A mathematica code has been written to check the mathematical algorithm for the method by finding the eigenvalues of the harmonic oscillator potential. But there are some exceptions, for instance in the case of woodssaxon. The angular distributions of elastic scattering of 7 be projectile from 10 b, 14 n, and 208 pb have been reanalyzed. Nuclear radii from a nonlocal woodssaxon potential springerlink. A study of confined quantum systems using the woodssaxon.
Woodssaxon potential the woodssaxon potential is a mean field potential for the nucleons protons and neutrons inside the atomic nucleus, which is. Department of engineering physics, university of gaziantep, 27310. Thus presented woods saxon fit provides adequate singleparticle basis for shell model calculations bridging over into the continuum. Woodssaxon and squarewell potentials for nuclear shell model. Gaining confidence from this work, exact solvability of the woodssaxon type potentials in lower dimensions for the bound states having zero. Solution of the dirac equation for the woodssaxon potential with spin and pseudospin symmetry phys. The exact energy eigenvalues and wavefunctions are derived analytically by using the nikiforov and uvarov method.
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