Eigenvalues and eigenfunctions of woods saxon potential in. Woodssaxon and squarewell potentials for nuclear shell model. Dkp equation is also solved analytically by means of nu method a vector deformed woods saxon potential 18. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a pdf plugin installed and enabled in your browser. How to superimpose woodsaxon and coulomb potential. Woods saxon since the nuclear interaction is short range, a natural improvement would be to adopt a central potential mimicking the empirical density distribution this is basically a square well with soft edges, as described by the woods saxon potential. Parameterization of the woodssaxon potential for shellmodel calculations n. Diffuseness parameters of woodssaxon potential for heavy. Ydrefors2 1university of jyvaskyla, department of physics, p. A comparison of woodssaxon and doublefolding potentials. Volya florida state university, physics department, tallahassee, fl 32306 dated. The woods saxonpotential or any other onebody potential cannot be used. Research article generalized nuclear woodssaxon potential.
Boundstate solution of swave kleingordon equation for. Ayse berkdemir a, cuneyt berkdemir a and ramazan sever b a department of physics, faculty of arts and sciences, erciyes university, kayseri, turkey. The sfr potentials considered are the standard cutoff woods saxon cws potentials and two potentials approaching zero smoothly. But the modified woods saxon potential has no exact or approximate solutions. 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. Woodssaxon potential in closed form for the 5dimensional bohr. Solutions of the central woodssaxon potential in 6 0. Potential energy of a heavy nuclear system in fusion. In order to probe the shape of the charge distribution. Calculation of rootmean square for some closed shell nuclei. Saxon the form of the potential, in terms of the distance r from the center of.
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 effect of woods saxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum j. Spinorbit interaction with woods saxon potential for nuclear states. The present fortran program is the third version triaxial 2014 of the same code. The result should look something like this picture. February 11, 20 the drastically expanded use of the woods saxon potential. 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.
I, the holder of this work, hereby release it into the public domain. Single particle calculations for a woodssaxon potential with triaxial. Now im thinking about improving the simple model to a more complex one. Using a quadrupole deformed generalized woodssaxon plus.
Single particle calculations for a woodssaxon cartesian. 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. Pdf parameterization of the woodssaxon potential for shell. In this work, we take specifically into account triaxial i. The squarewell potential is defined by for and for, where is the radius of the well the woods saxon potential is given by, where is the well depth. A second version of this code triaxial 2007 has been given in cpc 176 2007 634635. Microscopic calculation of the wobbling excitations. Pdf woodssaxon equivalent to a double folding potential. Solutions of ddimensional schrodinger equation for woods. A mathematica code has been written to check the mathematical algorithm for the method by finding the eigenvalues of the harmonic oscillator potential. In references 2, 3, and 7, the optical potential operator is v taj opt aj where t.
The woods saxon potential has fixed geometry and was applied as a. A woods saxon equivalent to a double folding potential in the surface region is obtained for the heavyion scattering potential. The twocomponent approach to the onedimensional dirac equation is applied to the woods saxon potential. Alexbrown nationalsuperconductingcyclotronlaboratory. Department of applied physics, faculty of engineering. Pdf the effect of woodssaxon potential on envelope. The coulomb plus woods saxon potentials are well known as modified woods saxon potential that plays a great role in nuclear physics. That is, the potential at xarises from the electrostatic attraction of the elemental charges in dx, integrated over all space. Study of restricted three body problem in classical mechanics. The type of a nuclear potential spherically symmetric. Generalized nuclear woodssaxon potential under relativistic spin. Therefore, a mean field potential is always empirical and its an example can be given as the woods. It provides a model for the properties of boundstate and continuum singleparticle wavefunctions. Woods saxon potential in the presence of a cosmic string 87 3.
Gonul university of gaziantep, department of engineering physics, 27310 gaziantepturkey abstract more recently, comprehensive application results of approximate analytical solutions of the woods saxon potential in closed form for the 5dimensional bohr hamiltonian have been. Eigenvalues and eigenfunctions of woods saxon potential in pt symmetric quantum mechanics. Motion of charged particle motion in electric and magnetic fieldsbu using matlab. More recently, comprehensive application results of approximate analytical solutions of the. 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. Analytical solution for sstates with the woodssaxon potentials. Parameterization of the woodssaxon potential for shell model calculations. For small deformations, the shape of the axially symmetric nucleus is usually given by 1 where. My idea is to superimpose the wood saxon potential with the coulomb potential. The woodssaxon potential is a mean field potential for the nucleons protons and neutrons inside the atomic nucleus, which is used to describe approximately the forces applied on each nucleon, in the nuclear shell model for the structure of the nucleus. Pdf corrected analytical solution of the generalized.
Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s. A convenient parametric form of the nuclear density was psoposed by woods and saxon ca. This potential follows a similar form as the experimental nuclear density distribution. The single particle energies and the single particle wave functions are calculated from onebody hamiltonian including a central field of woods saxon type, a spinorbit interaction, and the coulomb potential for the protons. Pdf solutions for a generalized woodssaxon potential.
By using the pekeris approximation, we present solutions of the dirac equation with the generalized woodssaxon potential with arbitrary. Fusion barriers for a large number of fusion reactions from light to heavy systems can be described well with this potential 3740. Theory and fortran program of the first version of this code triaxial have already been described in detail in computer physics comm. However, scientist have solved the woods saxon potential for s states l 0, exactly and also by some approximation they have also found the solutions for any l states. A woods saxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. Triaxially deformed woods saxon potential the triaxially deformed woods saxon potential considered in this work is a microscopic calculation of. Single particle calculations for a woodssaxon potential. You should get similar results using the 3d square well with the levels at the extreme left. Any lstate solutions of the woods saxon potential in arbitrary dimensions 3945 wave equation 8 with the ws potential is an exactly solvable problem for l 0 swave,3,4 15 however, it cannot be solved analytically for 6 0 because of the orbital coupling term r 2. Any lstate solutions of the woods saxon potential in.
Damping the tail of the woodssaxon potential request pdf. The dirac equation solutions of the generalized symmetric woods saxon potential energy in one spatial dimension 61 the boundstate solutions of the kleingordon equation with a. Chapter 10 nuclear properties university of michigan. In this study, we assume that the nuclear potential has a woods saxon form. The single particle energies and the single particle wave functions are calculated from onebody hamiltonian including a central. In this simulation, i approximate the potential of the nucleus by a simple square well. But there are some exceptions, for instance in the case of woodssaxon. Calculation of the eigenvalues for woodsaxons potential.
The parametric nikiforovuvarov nu method is used in calculations. Parameterization of the woodssaxon potential for shell. Townsend langley research center hampton, virginia. Use of a generalized woods saxon potential to describe unpolarized and polarized interactions outline of the presentation 1 motivation for this study. The deformation is specified by the usual bohr parameters. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata. The scattering and bound state solutions are derived. Phenomenological potentials in simple calculations, the potential energy of two separated nuclei is usually parameterized in terms of some function, i. Conclusion in this study, we have obtained the whole spectrum of woods saxon potential for swave kg equation by using. We present a computer program which solves the schrodinger equation of the stationary states for an average nuclear potential of woods saxon type. The woodssaxon potential is a mean field potential for the nucleons protons and neutrons.
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