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. Generalized nuclear woodssaxon potential under relativistic. 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. In references 2, 3, and 7, the optical potential operator is v taj opt aj where t. Chapter 3 nuclear size and shape university of southampton. Although woods saxon distributions are adequate for many nuclei, a better representation for the charge distribution of light and medium weight nuclei three to eight protons is the harmonic well distribution refs. The woodssaxon potential and its modifications are used for various applications in. Pdf solutions for a generalized woodssaxon potential. A comparison of woodssaxon and doublefolding potentials for. The structure of singleparticle levels in the second minima of 237,239,241pu was analyzed with the help of an axiallydeformed woods saxon 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. In figure 1, we illustrated the shape of the woods saxon potential and its generalized form in. Single particle calculations for a woodssaxon potential with triaxial deformations, and large cartesian oscillator basis new version code.
The effect of woodssaxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer ali khaledinasab, m. Alphadecay quantumtunnelling calculations based on a. The central component of each potential is a fiveparameter refinement of the woodssaxon potential including two new parameters, of which one parameter governs the behavior at large distances. The form of static woodssaxon potential is defined as 0 0, 1 exp n v vr rr a. Generalized nuclear woodssaxon potential under relativistic spin. 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. We also show how overcritical effects depend on the shape of the short range potential. Schrodinger equation, woodssaxon potential, rosenmorse potential. Pdf the effect of woodssaxon potential on envelope.
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. In figure 1, we illustrated the shape of the woodssaxon potential and its generalized form in. Access full article top access to full text full pdf how to cite top. 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. The central component of each potential is a fiveparameter refinement of the woods saxon potential including two new parameters, of which one parameter governs the behavior at large distances. February 11, 20 the drastically expanded use of the woods saxon potential in modern day nuclear physics and the. In this study, we assume that the nuclear potential has a woodssaxon form. The woodssaxon potential and its modifications are used for various applications in different branches of physics 2325. 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. Research article generalized nuclear woodssaxon potential. Popescu2, ramona anton3, liana sandru4 1national institute for lasers, plasma and radiation physics, bucharest, romania, email. Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s.
The saxonwoods model is also useful for the analyses of these data and yields a nuclear radius for large a, given by r 1. The woodssaxon potential in the dirac equation arxiv vanity. Woodssaxon and squarewell potentials for nuclear shell model. The twocomponent approach to the onedimensional dirac equation is applied to the woods saxon potential. My idea is to superimpose the wood saxon potential with the coulomb potential.
Communications in theoretical physics nuclear physics. Pdf bound state solutions of the klein gordon equation. The effect of woods saxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer. Pdf remarks on the woodssaxon potential researchgate. The woodssaxon potential is a mean field potential for the nucleons protons and neutrons. Diffuseness parameters of woodssaxon potential for heavyion. We have investigated bound states of the schrodinger equation for the woodssaxon potential decorated with a finite number of the dirac delta functions and presented bound state wave functions for swave states. Eigenvalues and eigenfunctions of woods saxon potential in pt.
A parametrization of the spinorbit part of the potential was obtained in the region corresponding to large deformations second minimum, depending only on. The kleingordon equation with the woodssaxon potential well. The woodssaxon potential alone does not reproduce experimentally observed magic num. Saxon potentials are well known as modified woods saxon potential that plays a great role in nuclear physics. You should get similar results using the 3d square well with the levels at the extreme left. My idea is to superimpose the woodsaxon potential with the coulombpotential. The scattering and bound state solutions are derived and the conditions for a transmission resonance when the transmission coefficient is unity and supercriticality when the particle bound state is at e. Alexbrown nationalsuperconductingcyclotronlaboratory. 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. In this simulation, i approximate the potential of the nucleus by a simple square well. 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. Diffuseness parameters of woodssaxon potential for heavy. Communications in theoretical physics nuclear physics related.
The result should look something like this picture. Canadian journal of physics canadian science publishing. Solutions 4 and 8 satisfy the standard boundary conditions 9 of the schrodinger equation and, represent the wave functions by the interaction potential. Applied sciences py 2009 pb university politehnica of bucharest, department of mathematics and physics, bucharest. The twocomponent approach to the onedimensional dirac equation is applied to the woodssaxon potential.
But there are some exceptions, for instance in the case of woodssaxon. Calculation of the eigenvalues for woodsaxons potential. It provides a model for the properties of boundstate and continuum singleparticle wavefunctions. The nuclear shape was parametrized in terms of the cassinian ovaloids. We see that the strong force extends over approximately the same region as the nuclear charge, and that the volume of the nucleus is proportional to the number of nucleons. By applying transfer matrices, an eigenvalue equation is obtained. The onedimensional kleingordon kg equation has been solved for the ptsymmetric generalized woodssaxon ws potential. The structure of singleparticle levels in the second minima of 237,239,241pu was analyzed with the help of an axiallydeformed woodssaxon potential. Saxon and derivative woodssaxon potentials can be solved in analytical form for sstate neutrons. The woodssaxonpotential or any other onebody potential cannot be used.
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. Fusion barriers for a large number of fusion reactions from light to heavy systems can be described well with this potential. The woodssaxon potential plays an essential role in microscopic physics, since it can be used to describe the interaction of a nucleon with the heavy nucleus. Alphadecay quantumtunnelling calculations based on a folded.
A particular solution of heun equation for hulthen and. 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. Jassim, diffuseness parameters of woodssaxon potential for heavy ion systems through large angle quasi elastic scattering, international journal of science and research ijsr, 3, 9, 15141518 2014. We study the bound state solutions of the kleingordon equation with woods saxon plus attractive inversely quadratic potential using the parametric nikiforovuvarov method. 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 folded woodssaxon cluster potential has been successfully applied to the calculations of. A comparison of woodssaxon and doublefolding potentials. Calculation of the eigenvalues for woodsaxons potential by. The onedimensional kleingordon kg equation has been solved for the ptsymmetric generalized woods saxon ws potential. This potential follows a similar form as the experimental nuclear density distribution. Analytical solution for sstates with the woodssaxon potentials.
Woodssaxon potential for a 50, relative to v 0 with a 0. Using a quadrupole deformed generalized woodssaxon plus. The pt and non pt symmetric solutions for this potential are also presented. Use of a generalized woods saxon potential to describe unpolarized and polarized interactions motivation for this study the elastic di erential cross section is well explained, but all of its observables of polarization have not been properly described. Single particle calculations for a woodssaxon potential. Therefore, a mean field potential is always empirical and its an example can be given as the woods. The nikiforovuvarovnu method which is based on solving the secondorder linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. The effect of woodssaxon potential on envelope function, intersubband dispersion curves and group velocity of inasgaas quantum dots with wetting layer. Woodssaxon potential parametrization at large deformations. Parameterization of the woodssaxon potential for shell. Potential representation method for woodssaxon potential 45 are presented like analytical solution 7 by expanding in the power series the interaction potential vr. Jakimovski2 1departament of physics, faculty of natural sciences and mathematics, state university of tetovo, ilinden street nn,1200, macedonia 2institute of physics, faculty of natural sciences and mathematics, ss. Jan 22, 2016 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 applied on each nucleon. Eudml solutions of the central woodssaxon potential in.
Department of physics, akdeniz university, 07058 antalya, turkey. We show that the antiparticle bound states arise also for the woodssaxon potential, which is a smoothed out form of the square well potential. Saxon the form of the potential, in terms of the distance r from the center of. We calculate the total energy of he 4 nuclei using the ws potential. 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. Ra, 9 where u0 is the depth of potential, r is the radius of potential, and a is the width of surface diffuseness 22. Microscopic calculation of the wobbling excitations. 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. We study the bound state solutions of the kleingordon equation with woodssaxon plus attractive inversely quadratic potential using the parametric nikiforovuvarov method. We obtained the bound state energy eigenvalues and the corresponding. The quantity v 0 is depth and a is the diffuseness parameter of.
Use of a generalized woodssaxon potential to describe unpolarized and polarized interactions outline of the presentation 1 motivation for this study. A woodssaxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. Pdf bound state solutions of the klein gordon equation with. Solutions of the central woodssaxon potential in l 0 case using. Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india. Woodssaxon potential is a shortrange potential and is given by. The form of the generalized woods saxon potential is as follows 41, 42. Woodssaxon potential in the presence of a cosmic string 87 3. The woods saxonpotential or any other onebody potential cannot be used. A woods saxon shape was assumed with a different well depth for each orbit but with the same potential radius and diffuseness. It is assumed that two protons and two neutron occupy a 1s level with the same energies. 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 woodssaxon potential with spinorbit and centrifugal terms through nikiforovuvarov method mr pahlavani, sa alavi communications in theoretical physics 58 5, 739, 2012. Pdf more recently, comprehensive applications of approximate analytical solutions of the woodssaxon ws potential in closed form for the.
Parameterization of the woodssaxon potential for shellmodel calculations n. The woodssaxon potential with point interactions sciencedirect. How to superimpose woodsaxon and coulomb potential. This brief comparative study confirms the reliability o f present results in a concrete manner. Solaimani 0 1 0 department of physics, faculty of science, qom university of technology, qom, iran 1 physics faculty, shahrood university, p. The standard values of the woodssaxon parameters were used without any adjustment. In this study, we assume that the nuclear potential has a woods saxon form. R a2 where r0 r0a 1 3 is the radius of the corresponding nuclei with r0 as a constant. Now im thinking about improving the simple model to a more complex one. There exist many potentials, and combinations among them, proposed for this interaction.
The kleingordon equation the onedimensional kleingordon equation to solve. Townsend langley research center hampton, virginia. Solutions of the central woodssaxon potential in 6 0 case. The scattering and bound state solutions are derived. The type of a nuclear potential spherically symmetric.
Solutions of ddimensional schrodinger equation for woods. 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. Relativistic dynamics of a scalar boson confined by woods. Eigen spectra for woodssaxon plus rosenmorse potential. Ti solutions of the central woodssaxon potential in case using mathematical modification method. Solutions of the central woodssaxon potential in l. Parameterization of the woodssaxon potential for shellmodel. The form of the generalized woodssaxon potential is as follows 41, 42. Eigenvalues and eigenfunctions of woods saxon potential in. Woodssaxon potential in closed form for the 5dimensional bohr hamiltonian have been appeared 14 and its comparison to the data for many different nuclei.
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