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Öğe Calculation of electric field gradient in spherical quantum dots(Taylor & Francis, 2020) Çakır, Bekir; Yakar, Yusuf; Özmen, AyhanWe have calculated the ground and excited energy states of the quantum dot as a function of the depth of confining potential well and radius R. Based on the calculated energies and wave functions, the electric field gradient induced by the non-spherical charge at impurity is investigated as a function of dot radius and the confining potential. For Deuterium dot with spherical confining potential, the expectation value of the quadrupole moment operator is carried out. The calculations show that the dot radius, the confining potential and the impurity charge have a great influence on the electric field gradient and the quadrupole moment. It is found that as the confining potential increases, the peak position of the electric field gradient shifts toward smaller dot radii and its amplitude increases with the increase of confining potential.Öğe Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree-Fock-Roothaan method(World Scientific Publ Co Pte Ltd, 5 Toh Tuck Link, Singapore, 2008) Çakır, Bekir; Özmen, Ayhan; Atav, Ülfet; Yüksel, Hüseyin; Yakar, YusufThe electronic structure of Quantum Dot (QD), GaAs/AlxGa1-xAs, has been investigated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. One-electron system with an on-center impurity is considered by assuming a spherically symmetric confining potential of finite depth. The ground and excited state energies of one-electron QD were calculated depending on the dot radius and stoichiometric ratio. Expectation values of energy were determined by using the HFR method along with Slater-Type Orbitals (STOs) and QGA was used for the wave-functions optimization. In addition, the effect of the size of the basis set on the energy of QD was investigated. We also calculated the binding energy for a dot with finite confining potential. We found that the impurity binding energy increases for the finite potential well when the dot radius decreases. For the finite potential well, the binding energy reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. Whereas in previous study, in Ref. 40, for the infinite potential well, we found that the impurity binding energy increases as the dot radius decreases.Öğe Calculation of hyperfine interaction in spherical quantum dot(Academic Press, 2015) Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanIn this study, we have calculated the unperturbed wavefunctions and energy eigenvalues of the ground and excited states of a spherical quantum dot, GaAs/AlxGa1-xAs, by using quantum genetic algorithm and Hartree-Fock Roothaan method. Hyperfine coupling constant and hyperfine energy of is, 2p, 3d and 4f levels are carried out as a function of dot radius. The results show that the hyperfine constant and hyperfine energy varies rapidly in the strong and medium confining regions as dot radius decreases. It is worth pointing out that dot radius, impurity charge and angular momentum have a strong influence on the hyperfine energy. It is also found that hyperfine energy and hyperfine splitting vary with aluminium concentration ratio x.Öğe Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential(Elsevier Science Bv, 2010) Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanIn the effective mass approximation, we calculated the binding energy and wave function for the 1s-, 1p-, 1d- and 1f-states of a spherical quantum dot (QD) with parabolic potential by using a combination of quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. In addition, we also investigated the linear and the third-order nonlinear optical absorption coefficients as a function of the incident photon energy for the 1s-1p, 1p-1d and 1d-1f transitions. Our results are shown that the existence of impurity has great influence on optical absorption coefficients. Moreover, the optical absorption coefficients are strongly affected by the incident optical intensity, relaxation time, parabolic potential and dot radius.Öğe Calculation of oscillator strength and the effects of electric field on energy states, static and dynamic polarizabilities of the confined hydrogen atom(2013) Çakır, Bekir; Yakar, Yusuf; Özmen, AyhanIn this study, we investigate the effect of an electric field on energy states of a spherical quantum dot with infinite confining potential using the perturbation method. We also perform the static dipole and dynamic dipole polarizabilities. In addition, the oscillator strengths have been calculated for the dipole transitions between higher unperturbed states. The results show that impurity and dot radius have an important effect on the Stark shift, and the effect of electric field is insensitive in small dot radii. For the excited states the Stark shift from the first-order increases linearly with the increase of electric field strength. On the other hand, the Stark shift from the first-order decreases with increasing of the magnetic quantum number. A very important future is that, for dot radius region 1.8aB?R?7 aB, the static dipole polarizabilities change very quickly. In addition, it is found that as the dot radius increases, the photon energy corresponding to the singularity of dynamic dipole polarizability decreases. © 2013 Elsevier B.V.Öğe Calculation of Zeeman splitting and Zeeman transition energies of spherical quantum dot in uniform magnetic field(Elsevier Science Bv, 2016) Çakır, Bekir; Atav, Ülfet; Yakar, Yusuf; Özmen, AyhanIn this study we report a detailed theoretical investigation of the effect of an external magnetic field on the 1s-, 2p-, 3d- and 4f-energy states of a spherical quantum dot. We treat the contribution of the diamagnetic term as a perturbation and discuss the effect of the diamagnetic term on the 1s-, 2p-, 3d- and 4f-energy states. We also have calculated the Zeeman transition energies between 2p -> 1s and 3d -> 2p states with m = 0, +/- 1 and 0, +/- 1, +/- 2 as a function of dot radius and the magnetic field strength. The results show that the magnetic field, impurity charge and dot radius have a strong influence on the energy states and the Zeeman transitions. It is found that the energies of the electronic states with m < 0 addition of the diamagnetic term firstly decrease toward a minimum, and then increase with the increasing magnetic field strength. We have seen that as magnetic field intensity is adjusted, frequency of the emitted light can be changed for Zeeman transitions.Öğe Computation of energy states of hydrogenic quantum dot with two-electrons(American Institute Physics, 2016) Yakar, Yusuf; Özmen, Ayhan; Çakır, Bora OrçunIn this study we have investigated the electronic structure of the hydrogenic quantum dot with two electrons inside an impenetrable potential surface. The energy eigenvalues and wavefunctions of the ground and excited states of spherical quantum dot have been calculated by using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method, and the energies are investigated as a function of dot radius. The results show that as dot radius increases, the energy of quantum dot decreases. © 2016 AIP Publishing LLC.Öğe Computation of hyperfine energies of hydrogen, deuterium and tritium quantum dots(Elsevier Science, 2016) Çakır, Bekir; Özmen, Ayhan; Yakar, YusufThe hyperfine energies and hyperfine constants of the ground and excited states of hydrogen, deuterium and tritium quantum dots(QDs) are calculated. Quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) methods are employed to calculate the unperturbed wave functions and energy eigenvalues. The results show that in the medium and strong confinement regions the hyperfine energy and hyperfine constant are strongly affected by dot radius, impurity charge, electron spin orientation, impurity spin and impurity magnetic moment. Besides, in all dot radii, the hyperfine splitting and hyperfine constant of the confined hydrogen and tritium atoms are approximately equivalent to each other and they are greater than the confined deuterium atom.Öğe Computation of ionization and various excited state energies ofhelium and helium-like quantum dots(Wiley-Blackwell, 2011) Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanIn the effective mass approximation, we calculated the wave functions and some energy states of helium and helium-like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree-Fock Roothaan (HFR). The results are in a good agreement with literature results.Öğe Computation of relativistic terms in a spherical quantum dot(Elsevier Science, 2013) Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanWe studied a hydrogenic impurity located at the center of a spherical quantum dot with an infinite spherical confining potential and calculated energy levels and wavefunctions using Quantum Genetic Algorithm(QGA) and Hartree-Fock Roothaan (HFR) method. In addition, we investigated the first-order relativistic terms such as the relativistic correction to the kinetic energy, Darwin and spin-orbit interaction term. These terms were calculated using the first-order perturbation theory. The electronic charge density for the Darwin term was carried out from a global operator defined by Hiller, Sucher and Feinberg. The results revealed that the relativistic corrections are important in small dot radii and they should not be neglected to improve the accuracy of calculations. Crown CopyrightÖğe Computation of rotation matrices making lined?up to the local cartesian coordinates(Wiley Online Lİbrary, 2007) Yakar, Yusuf; Özmen, Ayhan; Çakır, Bekir; Yüksel, HüseyinRotation matrices were expressed in terms of Gaunt coefficients and complex spherical harmonics. The rotation matrices were calculated using two different ways. In the first, Gaunt coefficients and normalized complex spherical harmonics were directly calculated using binomial coefficients; in the second, Gaunt coefficients and complex spherical harmonics were recursively calculated. The methods were compared with respect to accuracy and computation time (CPU) for low and very high quantum numbers.Öğe Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot(Elsevier Science, 2009) Özmen, Ayhan; Yakar, Yusuf; Çakır, Bekir; Atav, ÜlfetThe electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s-1p, 1p-1d and id-If transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.Öğe Coulomb, exchange, kinetic, nuclear attraction and ionization energies of two-electron quantum dot with finite confinement potential(Elsevier B.V., 2023) Yakar, Yusuf; Çakır, Bekir; Demir, Celalettin; Özmen, AyhanWe have calculated Coulomb, exchange and configuration-average ionization energies for the ground and excited configurations in helium atom confined by a spherical cavity of finite barrier height. In addition, we have carried out kinetic energies, nuclear attraction energies, confining potential energies and probabilities of finding the electrons that occupy different subshells. In the strong and intermediate confinement regions, the results show that the barrier height of potential well and dot size have a strong influence on the energies and probabilities. The kinetic energies of electrons in 1s and nl orbitals increase as the height of the potential barrier increases, but in nuclear attraction energies the opposite behavior occurs. It is found that Coulomb and exchange energies rapidly decrease after the critical confinement radii, in which the electron in nl orbital escapes out of the well. The configuration-ionization confinement radius depends strongly on the potential barrier height.Öğe Dipole and quadrupole polarizabilities and oscillator strengths of spherical quantum dot(Elsevıer Science Bv, 2018) Yakar, Yusuf; Çakırr, Bekir; Özmen, AyhanIn this study, the energy eigenvalues and eigenfunctions of the ground and excited states of a spherical quantum dot are calculated by using the Quantum Genetic algorithm (QGA) and Hartree-Eock Roothaan (HFR) method. Based on the calculated energies and wave functions, the static and dynamic dipole polarizabilities, the quadrupole polarizability, dipole and quadrupole oscillator strengths of spherical quantum dot are carried out as a function of dot size and the confining potential as perturbative. The results show that dot size and confining potential have a great influence on the polarizability and oscillator strength. It is found that the polarizability increases due to the spatial confinement effect in the strong confinement region. In the weak confinement region, the polarizability increases again until it reaches the saturation value. In addition, the peak positions of the dipole and quadrupole oscillator strengths shift toward smaller dot radii with the increases of the potential well depth.Öğe Electronic structure and binding energy of spherical quantum dot(Aksaray Üniversitesi, 2017) Yılmazer, Fatma; Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanIn this study, we have calculated the energy states and the wavefunctions of the spherical quantum dot with finite and infinite confining potential. In addition, we have investigated the binding energies of the ground and excited states of the spherical quantum dot as a function of dot radius. In order to calculate the energy eigenvalues and the wavefunctions Quantum Genetic Algorithm and Hartre-Fock Roothaan method have been employed. The results show that dot radius and confinement potential has a great effect on the energy states and binding energies. In large dot radii, the effect of confinement potential on energy states is disappeared and energy states go to the energy values of hydrogen atom.Öğe Electronic structure and relativistic terms of one-electron spherical quantum dot(Elsevier, 2013) Özmen, Ayhan; Çakır, Bekir; Yakar, YusufWe calculated the energy eigenvalues and eigenfunctions of the ground and excited states of a hydrogenic impurity located at the center of a spherical quantum dot using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method. In addition, we carried out the relativistic effects such as the relativistic correction to the kinetic energy, spin-orbit and Darwin terms by using the perturbation method. The electronic charge density for the Darwin term is computed from the Hiller, Sucher and Feinberg formulation instead of the traditional delta function operator. The results show that impurity, dot radius and confining potential have a great influence on the relativistic effects. In addition, as the absolute value of confining potential increases, the peak values of relativistic corrections increase and move toward lower dot radii. (C) 2013 Elsevier B.V. All rights reserved.Öğe Electronic structure of two-electron quantum dot with parabolic potential(Taylor & Francis Ltd, 2015) Yakar, Yusuf; Çakır, Bekir; Özmen, AyhanIn this study, we investigate the parabolic potential effects on the ground and excited energy states of two-electron quantum dot with impurity inside an infinite spherical confining potential well. The wave function and energy eigenvalues were calculated using a modified variational optimization procedure based mainly on quantum genetic algorithm and Hartree-Fock-Roothaan method. The results show that the parabolic potential and impurity charge have a strong effect on the energy states and ionization energies. It is worth pointing out that as impurity charge increases, the ionization energy rises, but the ionization dot radius decreases. On the other hand, as parabolic potential increases, the ionization energy decreases, but the ionization dot radius increases.Öğe Energies of the ground and excited states of confined two-electron atom in finite potential well(Elsevier B.V., 2023) Demir, Celalettin; Çakır, Bekir; Yakar, Yusuf; Özmen, AyhanFor the ground and excited configurations, we have carried out the energy eigenvalues and corresponding wavefunctions of two-electron atom enclosed by finite confining potential by using Quantum Genetic Algorithm (QGA) procedure and Hartree-Fock Roothaan (HFR) method. Besides, we have analysed in detail orbital energies and probabilities of finding electron for the configurations 1S (1s2), 3S (1s2s), 3P (1s2p), 3D (1s3d) and 3F (1s4f). The results reveal that the potential barrier height plays a significant role on average energies, state energies, orbital energies and probabilities of finding electrons in orbitals. As dot size is extremely small and extremely large, the energies for 1snl configurations are getting close to each other, but between these two extreme situations they are separating from each other. While going to higher excited states, singlet and triplet states are almost the same due to the weakening of the exchange energy.Öğe Energy states, oscillator strengths and polarizabilities of many electron atoms confined by an impenetrable spherical cavity(Wiley, 2021) Yakar, Yusuf; Çakır, Bekir; Demir, Celalettin; Özmen, AyhanWe have calculated the ground and excited state energies and the orbital energies of three-electron atoms inside impenetrable spherical cavity. Energy eigenvalues and wavefunctions are calculated from the variational approximation method which is a combination of quantum genetic algorithm procedure and Hartree-Fock Roothaan method. In addition, the important parameters such as static and dynamic polarizability, oscillator strength and pressure have been investigated as perturbative. The results reveal that cavity radius and impurity charge have played an important role on the polarizability, the oscillator strength and pressure of the system. In addition, it is seen that when cavity radius is extremely large, all energies and the other physical parameters approach the values of a free space atom. As the dot radius decreases, the polarizability of system decreases due to the strong spatial confinement, but the pressure exerting on the system as the cavity radius R is shrunk increases. In addition, as the impurity charge increases, the oscillator strength decreases.Öğe Evaluation of orbital? and ground state energies of some open? and closed?shell atoms over integer and noninteger slater type orbitals(Wiley Online Library, 2007) Yakar, YusufAb initio calculations of the orbital and the ground state energies of some open? and closed?shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two?electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.
