Theses supervised by Prof. Dr. Bülent Gönül
10 theses · Gaziantep University
Heavy-ion fusion reactions at extreme sub-barrier energies
Recent years have witnessed an increase in interest in the study of fusion reactions at extreme sub-barrier energies, despite the fact that it is challenging to measure them due to their extremely small cross sections. Such reactions are essential to understand the creation of heavy elements in varied settings. In the present thesis work, the status of the field is reviewed involving all the related theoretical and experimental works carried out so far. The unexpected behavior seen in the steep falloff of measured cross-sections at low incident energies is explained in detail using new physics concepts related to the fusion process of atomic nuclei. Besides that, the framework of the sudden and adiabatic approaches using different potential structures especially shallow and deep potentials is discussed through the supersymmetric phase equivalent potential concept in quantum theory.
A novel approach for heavy quarkonium spectra
In this work, we attempt to investigate heavy quark systems ( and ) in the non-relativistic framework using phenomenological inter-quark potentials. For this reason, we have developed a powerful and flexible theoretical formalism, within the frame of the Schrödinger equation, to use for the analysis of heavy quarkonium systems involving exactly solvable energy-dependent potentials, together with quasi-/conditionally-solvable and non-solvable interaction potentials. Our first application to exactly solvable systems has clarified that energy dependent term in the potential leads to saturation of the spectra and degree of saturation is governed by the magnitude of perturbation. Second application to quasi-exactly solvable potentials, which is the Coulomb plus linear potential with a quadratic term, has justified the success of the present formalism due to its wide range of applicability, considering the comparison of the findings obtained by the present approach with those of experimental results and the other theoretical predictions in the related literature. Finally, the application of this new technique to also non-solvable systems involving Cornell potential has shed some light on the questions concerning with the limitations of the traditional perturbation techniques.
Neutron halo and related structure in light nuclei
The works appeared recently dealing with exotic halo nuclei have displayed striking variations in nuclear shell structures and revealed the emergence of novel magic numbers unlike the stable nuclei. One of the significant reasons for these variations is the effect of tensor forces on nuclear structures, which has been reviewed in this report. Also, with the consideration of three-body nuclear forces, the known dramatic peculiarity over the oxygen isotopes has been debated to clarify why is the heaviest bound oxygen isotope. Finally, we focus at loosely bound neutron states within the frame of light halo nuclei to grasp why the weak binding plays a crucial role in observing the change in energies of lowest states. Keywords: Exotic nuclei, neutron-halo nuclei, , nuclear tensor force, three-body interaction force, binding energy
A simulation for detecting anti personnel landmines with 14 MeV neutron source
The present thesis work investigates the problem of detecting anti personnel landmines with practically applicable neutron back scattering method and suggests a new simulation technique based on Monte Carlo method for the purpose of landmine detection using 14 MeV-neutron as the radiation source. Different landmine scenarios simulated for different explosives, soil types and buried depths have been considered within the framework of the present study. A set of electronic equipment including data acquisition and software systems to employ in APL detector system has been suggested to use it with the new technology having silicon photo multipliers. Along this line, the simulation software source code we developed has been inserted into the text. The results obtained are carefully discussed.
Supersymmetric quantum mechanics and its applications in physics
Ill ABSTRACT SUPERSYMMETRIC QUANTUM MECHANICS AND ITS APPLICATIONS IN PHYSICS ÖZER, Okan Ph. D in Engineering Physics Supervisor: Prof. Dr Bülent GÖNÜL June 2003, 95 pages Theoretical formulation of the supersymmetric quantum mechanics is re viewed and its applications to some physical problems are studied. The super- symmetric quantum mechanics (SUSYQM) is based on the factorization of the Schrödinger equation, leading to generalized operators and partner potentials. The Hamiltonian hierarchy and the factorization in the method are briefly dis cussed. It is also combined with the perturbation theory which is used for the systems that are not exactly solvable. The method is applied to the Hulthen po tential and an expression for the energy levels which gives satisfactory values for the non-zero angular momentum states of the potential is obtained. It is shown that a very general connection can be established between a class of singular potentials in iV-dimensional space through the application of a suitable transfor mation by SUSYQM. Using this way, a connection between screened Coulomb and anharmonic oscillator potentials is obtained. A general mapping procedure is described for the transformation of a differential equation with a position- dependent mass to the Shrödinger equation with a constant mass under canoni cal transformations. In the frame of SUSYQM, it is shown that the Schrödinger equation in its new form may have solutions if the original potential is solvable and shape-invariant one. Finally, It is demonstrated how the SUSYQM method can also be employed for the construction of n-parameter family of potentials which possess localized positive energy state(s) in the continuum. Key words: Supersymmetric Quantum Mechanics, Shape invariant potentials, Hamiltonian hierarchy, Supersymmetric perturbation theory, Hulthen potential, iV-dimensional space, Position-dependent mass, Bound states in continuum.
Comprehensive treatments for Schrödinger equations involving constant and non-constant masses
The concept of the elegant work introduced by Lévai in Ref. [21] is extended for the solutions of the Schrödinger equation with more realistic other potentials used in different disciplines of physics within the constant mass consideration. The connection between the present model and the other alternative algebraic technique [32] in the literature is discussed in detail. Extending the point canonical transformation approach introduced in this thesis in a manner distinct from the previous ones, we also propose a unified approach of generating potentials of all classes having non-constant masses.
Applications of a new approach to bound-states
Recently developed approach for the treatment of Schrödinger equations isapplied to anharmonic oscillator and Yukawa type potentials to have reliableexpressions for their bound state energies and eigenfunctions. In addition, weshow that the present novel formalism is entirely equivalent to a well knownalternative model in the literature.Keywords: Anharmonic Oscillator, Yukawa Potential, Perturbation, Exactlysolvable potentials
Applications of a novel approach to relativistic and non-relativistic problems in physics
We have developed an algebraic approach for the treatment of time-independent Schrödinger equation with constant/non-constant masses within the frame of non-relativistic quantum theory. The model developed then has been successfully applied in various fields of physics involving exactly/approximately solvable potentials. The first part of the thesis work is devoted to the presentation of these applications, such as the application results for noncentral potentials, applicability of the scheme for scattering theory and careful analysis of the application results for quantum systems with position-dependent masses in arbitrary dimensions After gaining confidence from the successful applications of this novel formalism to non-relativistic systems, we have extended our investigations by studying the applicability of the model also for the relativistic considerations in the light of Klein-Gordon and Dirac equations involving only bound quantum states. These considerations require naturally the split of the relativistic equations into two parts, unlike the other models in the literature, which provide a clear visualization of the relativistic contributions, in an explicit manner, to the solution in the non-relativistic limit. Key words: Schrödinger Equation, Dirac Equation, Klein-Gordon Equation, Exactly-solvable Systems, Non-central Potentials, Position-dependent Mass.
Woods-saxon potansiyeli içeren bohr hamiltoniyeninin özel çözümleri
The recent influential studies on the nuclear structure have focused on the quantum shape phase transitions of atomic nuclei within the frame of the Collective Model, which have enabled many researchers to test the reliability of the models used. As the special solutions of the Bohr Hamiltonian dealing with collective behaviour of the nucleus in terms of collective variables beta and gama in five-dimension, E(5) and X(5) are the most important critical point symmetries, which describe the shape phase transition between vibrational and gama-unstable/axially symmetric prolate rotor, respectively. Hence, for the first time in the related literature, considering both E(5) and X(5) critical point symmetries, the Bohr Hamiltonian with the well-known Woods-Saxon potential involving the repulsive angular momentum barrier in the non-relativistic domain is solved analytically. We observe that the corresponding new solution well reproduces energy spacing within the ground state and gama bands for more than 100 even-even deformed nuclei, and gives an insight to the physically acceptable parameters that is required for reliable and accurate calculations.
An overview on the nuclear level density calculations
In this work, the basic knowledge on the level densities for nuclei is reviewed and the necessary fundamental relations are well described together with the required semi-empirical expressions currently employed in nuclear reaction codes. In addition, the drawbacks on the theoretical models used for analyzing level densities are carefully discussed.