The woodssaxon potential is a mean field potential for the nucleons protons and neutrons. Pdf the effect of woodssaxon potential on envelope. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum j. Now im thinking about improving the simple model to a more complex one. This potential follows a similar form as the experimental nuclear density distribution.
Parameterization of the woodssaxon potential for shell. Using a quadrupole deformed generalized woodssaxon plus. The sfr potentials considered are the standard cutoff woods saxon cws potentials and two potentials approaching zero smoothly. Pdf parameterization of the woodssaxon potential for shell. The single particle energies and the single particle wave functions are calculated from onebody hamiltonian including a central. Solutions of the central woodssaxon potential in 6 0. 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. The deformation is specified by the usual bohr parameters. By using the pekeris approximation, we present solutions of the dirac equation with the generalized woodssaxon potential with arbitrary.
Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s. 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. Department of applied physics, faculty of engineering. Dkp equation is also solved analytically by means of nu method a vector deformed woods saxon potential 18. Pdf solutions for a generalized woodssaxon potential. Parameterization of the woodssaxon potential for shellmodel calculations n. The type of a nuclear potential spherically symmetric. 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.
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. Townsend langley research center hampton, virginia. In this study, we assume that the nuclear potential has a woods saxon form. Calculation of the eigenvalues for woodsaxons potential. Microscopic calculation of the wobbling excitations. The coulomb plus woods saxon potentials are well known as modified woods saxon potential that plays a great role in nuclear physics. Generalized nuclear woodssaxon potential under relativistic spin. Eigenvalues and eigenfunctions of woods saxon potential in pt symmetric quantum mechanics. February 11, 20 the drastically expanded use of the woods saxon potential in modern day nuclear physics and the.
February 11, 20 the drastically expanded use of the woods saxon potential. 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. Alexbrown nationalsuperconductingcyclotronlaboratory. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata. More recently, comprehensive application results of approximate analytical solutions of the. Single particle calculations for a woodssaxon potential. In references 2, 3, and 7, the optical potential operator is v taj opt aj where t. A convenient parametric form of the nuclear density was psoposed by woods and saxon ca.
Parameterization of the woodssaxon potential for shell model calculations. Woodssaxon and squarewell potentials for nuclear shell model. Spinorbit interaction with woods saxon potential for nuclear states. Use of a generalized woods saxon potential to describe unpolarized and polarized interactions outline of the presentation 1 motivation for this study. 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. A woods saxon equivalent to a double folding potential in the surface region is obtained for the heavyion scattering potential. But the modified woods saxon potential has no exact or approximate solutions. For small deformations, the shape of the axially symmetric nucleus is usually given by 1 where. We present a computer program which solves the schrodinger equation of the stationary states for an average nuclear potential of woods saxon type. Theory and fortran program of the first version of this code triaxial have already been described in detail in computer physics comm. Pdf corrected analytical solution of the generalized. Single particle calculations for a woodssaxon potential with triaxial. In order to probe the shape of the charge distribution. 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. Any lstate solutions of the woods saxon potential in. The twocomponent approach to the onedimensional dirac equation is applied to the woods saxon potential. Potential energy of a heavy nuclear system in fusion. 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.
A woods saxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. Boundstate solution of swave kleingordon equation for. The scattering and bound state solutions are derived. Triaxially deformed woods saxon potential the triaxially deformed woods saxon potential considered in this work is a microscopic calculation of.
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. Research article generalized nuclear woodssaxon potential. The result should look something like this picture. 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. 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. The present fortran program is the third version triaxial 2014 of the same code. You should get similar results using the 3d square well with the levels at the extreme left. The woodssaxon potential is a mean field potential for the nucleons protons and neutrons inside the atomic nucleus, which is used to approximately describe. Solutions of ddimensional schrodinger equation for woods. Chapter 10 nuclear properties university of michigan. That is, the potential at xarises from the electrostatic attraction of the elemental charges in dx, integrated over all space. 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.
How to superimpose woodsaxon and coulomb potential. I, the holder of this work, hereby release it into the public domain. 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. A mathematica code has been written to check the mathematical algorithm for the method by finding the eigenvalues of the harmonic oscillator potential. Motion of charged particle motion in electric and magnetic fieldsbu using matlab. Ayse berkdemir a, cuneyt berkdemir a and ramazan sever b a department of physics, faculty of arts and sciences, erciyes university, kayseri, turkey. Pdf woodssaxon equivalent to a double folding potential.
The effect of woods saxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer. Damping the tail of the woodssaxon potential request pdf. Woodssaxon potential in closed form for the 5dimensional bohr. Diffuseness parameters of woodssaxon potential for heavy. Fusion barriers for a large number of fusion reactions from light to heavy systems can be described well with this potential 3740. It provides a model for the properties of boundstate and continuum singleparticle wavefunctions. Saxon the form of the potential, in terms of the distance r from the center of. Woods saxon potential in the presence of a cosmic string 87 3. Study of restricted three body problem in classical mechanics. Eigenvalues and eigenfunctions of woods saxon potential in. Calculation of rootmean square for some closed shell nuclei.
In this work, we take specifically into account triaxial i. My idea is to superimpose the wood saxon potential with the coulomb potential. Single particle calculations for a woodssaxon cartesian. A comparison of woodssaxon and doublefolding potentials. The woods saxon potential has fixed geometry and was applied as a.
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