This brief comparative study confirms the reliability o f present results in a concrete manner. Popescu2, ramona anton3, liana sandru4 1national institute for lasers, plasma and radiation physics, bucharest, romania, email. Boundstate solution of swave kleingordon equation for. Grothouse saxon wood counters, bar tops and butcher blocks. It is assumed that two protons and two neutron occupy a 1s level with the same energies. The woodssaxonpotential or any other onebody potential cannot be used. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the nikiforov. This potential follows a similar form as the experimental nuclear density distribution. February 11, 20 the drastically expanded use of the woods saxon potential in modern day nuclear physics and the.
We also show how overcritical effects depend on the shape of the short range potential. Eigenvalues and eigenfunctions of woods saxon potential in. Some thoughts on the quenching of spectroscopic factor march 31, 2020. Saxon wood is the first of a series of specially curated woods, hand selected and sourced by paul grothouse. Pdf solutions for a generalized woodssaxon potential. The hf variational calculation is carried out for five nuclei in the 2sld. Single particle calculations for a woodssaxon potential.
In the present study, the theoretical calculations are performed by. Single particle calculations for a woodssaxon potential with triaxial deformations, and large cartesian oscillator basis new version code. Eudml solutions of the central woodssaxon potential in. In this simulation, i approximate the potential of the nucleus by a simple square well. The positions of the l 0 smatrix poles are calculated in generalized woodssaxon gws potential and in cutoff generalized woodssaxon cgws potential. The model is based on two spherical woodsaxon potentials and the potential separable expansion method. In this report are presented the results of a considerably restricted version of such a program. The boundstate solution of kg equation for woodssaxon potential has been of a great interest in the last decades with different methods 17 21. The solutions of the radial equations are calculated numerically for the cgws potential and analytically for gws using the formalism of gy. A mathematica code has been written to check the mathematical algorithm for the method by finding the eigenvalues of the harmonic oscillator potential. Alpha elastic scattering of pnuclei were studied for calculating optical potentials. The result should look something like this picture. Pdf the effect of woodssaxon potential on envelope. Solutions of ddimensional schrodinger equation for woods.
Parameterization of the woodssaxon potential for shellmodel calculations n. Any lstate solutions of the woodssaxon 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. Energy level diagram for woodssaxon potential with spinorbit force. Applied sciences py 2009 pb university politehnica of bucharest, department of mathematics and physics, bucharest. 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 show that the antiparticle bound states arise also for the woodssaxon potential, which is a smoothed out form of the square well potential. The static properties and form factors of the deuteron. The woodssaxon potential is generally given as a function of the radial variable, so after a separation of variables, the multipole expansion is no different than what one would obtain for any other sphericallysymmetric potential, like a harmonic oscillator or coulomb potential. Pdf scattering of woodssaxon potential in schrodinger. Now im thinking about improving the simple model to a more complex one.
From equation 7, the proton charge form factor is p hence, equations 6, 8, and 10 yield a. Parameterization of the woods saxon potential for shellmodel calculations n. Saxon the form of the potential, in terms of the distance r from the center of. Spectroscopic factor and the sumrule april 5, 2020. In addition, one can add residual interactions and correlations to produce.
How to superimpose woodsaxon and coulomb potential. Research article generalized nuclear woodssaxon potential. Woodsaxon potential the potential of a nucleon inside a nucleus is often approximated as a spherical potential well with soft walls, 1erra with a r. Hartreefock calculations with woodsaxon basis functions. The spherical woodsaxon potential that was used as a major part of nuclear shell model, has received a lot of attention in nuclear mean field model, and plays an essential role in microscopic physics 16. Woodssaxon potential in the presence of a cosmic string 87 3. Fusion barriers for a large number of fusion reactions from light to heavy systems can be described well with this potential. Use of a generalized woodssaxon potential to describe unpolarized and polarized interactions outline of the presentation 1 motivation for this study. 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. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india. We calculate the total energy of he 4 nuclei using the ws potential. Extended woodsaxon potential for determination of fission crosssection of 232 th with neutron energy range 1200 mev. The effect of woodssaxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer ali khaledinasab, m. Saxon wood counters, bar tops, and butcher blocks are exclusively available at grothouse.
Parameterization of the woodssaxon potential for shell. Saxon wood has been chosen for its stunning visual appeal and unique appearance. My idea is to superimpose the woodsaxon potential with the coulombpotential. The woodsaxon potential is a reasonable potential for nuclear shell model and hence attracts lots of attention in nuclear physics. A woodsaxon potential form factor is used for both real and imaginary part. Diffuseness parameters of woodssaxon potential for heavy. In figure 1, we illustrated the shape of the woodssaxon potential and its generalized form in. 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. The kleingordon equation the onedimensional kleingordon equation to solve. The nuclear shape was parametrized in terms of the cassinian ovaloids. Energy dependent woodssaxon potential model edwsp model the nucleusnucleus potential is the fundamental characteristic of heavy ion fusion reactions. Volya florida state university, physics department, tallahassee, fl 32306 dated. Ti solutions of the central woodssaxon potential in case using mathematical modification method. Coulomb energy for a sorbital under woodssaxon potential april 7, 2020.
A fortran90 code for solving the twocenter nuclear shell model problem is presented. It provides a model for the properties of boundstate and continuum singleparticle wavefunctions. 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. Although the potential is different from mean field theory, it gives the better result than ripl2. Distributions of the smatrix poles in woodssaxon and cut. The type of a nuclear potential spherically symmetric. A parametrization of the spinorbit part of the potential was obtained in the region corresponding to large deformations second minimum, depending only on. Alexbrown nationalsuperconductingcyclotronlaboratory. Chapter 10 nuclear properties university of michigan. In this study, we assume that the nuclear potential has a woodssaxon form.
The woods saxon 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. R a2 where r0 r0a 1 3 is the radius of the corresponding nuclei with r0 as a constant. Therefore, a mean field potential is always empirical and its an example can be given as the woods. Calculation of energy dependent level density parameter. A new version of the twocenter model, namely the superasymmetric two.
The potential parameters extracted in the present study exhibit a satisfactory result with respect to existing global potential parameters. The structure of singleparticle levels in the second minima of 237,239,241pu was analyzed with the help of an axiallydeformed woodssaxon potential. The effect of woodssaxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer. The kleingordon equation with the woodssaxon potential well. That is, the potential at xarises from the electrostatic attraction of the elemental charges in dx, integrated over all space. Woodssaxon and squarewell potentials for nuclear shell model. The form of the generalized woodssaxon potential is as follows 41, 42. Calculation of the eigenvalues for woodsaxons potential. Pdf extended woodsaxon potential for determination of.
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. Introduction over the past couple of decades, new algoritms have improved the accuracy. February 11, 20 the drastically expanded use of the woodssaxon potential in modern day nuclear physics and the. Solutions of the central woodssaxon potential in 6 0. Solaimani 0 1 0 department of physics, faculty of science, qom university of technology, qom, iran 1 physics faculty, shahrood university, p.
Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s. In order to probe the shape of the charge distribution. Woodssaxon potential is a short range nuclear potential and it is important in all branches of physics. Solutions of woodssaxon potential with spinorbit and centrifugal terms through nikiforovuvarov method mr pahlavani, sa alavi communications in theoretical physics 58 5, 739, 2012.
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