In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the...In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms.Some numerical results are given too.展开更多
A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r...A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.展开更多
We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employ...We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.展开更多
The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of...The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.展开更多
Exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the Laplace transform approach and the Nikiforov–Uvarov(NU)method.The normalized eigenfunctions are...Exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the Laplace transform approach and the Nikiforov–Uvarov(NU)method.The normalized eigenfunctions are expressed in terms of hyper-geometric series and use the NU and Laplace methods to obtain the eigenvalues equations.The obtained result of the eigenvalue equation is compared.At the end,one can find with a simple transformation the lower spinor component of the Dirac equation.展开更多
Purpose Ionizing radiation protection is one of the most fundamental research and application fields in reducing the absorbed dose of sensitive internal organs.The presence of lead as the first radiation shield with a...Purpose Ionizing radiation protection is one of the most fundamental research and application fields in reducing the absorbed dose of sensitive internal organs.The presence of lead as the first radiation shield with a series of good features,such as high density and having some flexibility,and a series of features such as toxicity,low physical and chemical stability and high weight has been thinking about replacing it for a long time.Therefore,in this research,we have investigated features of the ionizing radiation shielding of composite compounds without lead in the photon energy range of 15 keV to 15 MeV.Methods To extract such features,it is necessary to use a computational method.In this research,we have done all our calculations based on the Geant4 tool based on the Monte Carlo method.This tool is a multi-purpose tool that can be used for particle transport calculations such as electrons,protons,neutrons,heavy charged particles and photons in different environments such as human tissues.Results We have calculated mass attenuation coefficient(MAC)by using the Monte Carlo simulations such as Geant4 tool,XMuDat and XCOM codes.In the continuation of the investigation of the protection feature,four laboratory energies have been selected and investigated.In fact,the performance of shields against 60 keV,662 keV and 1.2 MeV sources has been investigated.In this case,we have obtained the passing flux of photons,half-value layer(HVL),tenth-value layer(TVL)and mean free path(MFP).Then,the image of the passing photon flux of ^(241)Am(60 keV),^(137)Cs(662 keV)and^(60)Co(1.2 MeV)sources for a shielding sample is showed.Since the aim is to examine the overall protection characteristics of the samples,we have considered the source as a neutron-gamma mixture and made of 252Cf.In this case,the passing fux of photons and the ratio of neutrons passing through the shields are shown.In the continuation of the work,MIRD phantom has been used to check the performance of the shields in the amount of dose reached to the body and organs.In this case,for example,we have shown the received dose to the body and some organs as the ratio of the received dose in the presence of shields to the received dose in the absence of shields for the^(137)Cs source.Conclusions Quantitative results show that the selected compound is a suitable suggested compound for shielding ionizing rays in the range of diagnostic and therapeutic energies.展开更多
The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the ...The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.展开更多
In this paper, we have investigated the prospects of exploiting the rich world thorium reserves using Canada Deuterium Uranium （CANDU） reactors. The analysis is performed using the Monte Carlo MCNP code in order to ...In this paper, we have investigated the prospects of exploiting the rich world thorium reserves using Canada Deuterium Uranium （CANDU） reactors. The analysis is performed using the Monte Carlo MCNP code in order to understand how much time the reactor is in criticality conduction. Four different fuel compositions have been selected for analysis. We have obtained the infinite multiplication factor, k∞, under full power operation of the reactor over 8 years. The neutronic flux distribution in the full core reactor has already been investigated.展开更多
文摘In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms.Some numerical results are given too.
文摘A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.
文摘We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.
基金Project supported by the Scientific and Technical Research Council of Turkey
文摘The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.
文摘Exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the Laplace transform approach and the Nikiforov–Uvarov(NU)method.The normalized eigenfunctions are expressed in terms of hyper-geometric series and use the NU and Laplace methods to obtain the eigenvalues equations.The obtained result of the eigenvalue equation is compared.At the end,one can find with a simple transformation the lower spinor component of the Dirac equation.
文摘Purpose Ionizing radiation protection is one of the most fundamental research and application fields in reducing the absorbed dose of sensitive internal organs.The presence of lead as the first radiation shield with a series of good features,such as high density and having some flexibility,and a series of features such as toxicity,low physical and chemical stability and high weight has been thinking about replacing it for a long time.Therefore,in this research,we have investigated features of the ionizing radiation shielding of composite compounds without lead in the photon energy range of 15 keV to 15 MeV.Methods To extract such features,it is necessary to use a computational method.In this research,we have done all our calculations based on the Geant4 tool based on the Monte Carlo method.This tool is a multi-purpose tool that can be used for particle transport calculations such as electrons,protons,neutrons,heavy charged particles and photons in different environments such as human tissues.Results We have calculated mass attenuation coefficient(MAC)by using the Monte Carlo simulations such as Geant4 tool,XMuDat and XCOM codes.In the continuation of the investigation of the protection feature,four laboratory energies have been selected and investigated.In fact,the performance of shields against 60 keV,662 keV and 1.2 MeV sources has been investigated.In this case,we have obtained the passing flux of photons,half-value layer(HVL),tenth-value layer(TVL)and mean free path(MFP).Then,the image of the passing photon flux of ^(241)Am(60 keV),^(137)Cs(662 keV)and^(60)Co(1.2 MeV)sources for a shielding sample is showed.Since the aim is to examine the overall protection characteristics of the samples,we have considered the source as a neutron-gamma mixture and made of 252Cf.In this case,the passing fux of photons and the ratio of neutrons passing through the shields are shown.In the continuation of the work,MIRD phantom has been used to check the performance of the shields in the amount of dose reached to the body and organs.In this case,for example,we have shown the received dose to the body and some organs as the ratio of the received dose in the presence of shields to the received dose in the absence of shields for the^(137)Cs source.Conclusions Quantitative results show that the selected compound is a suitable suggested compound for shielding ionizing rays in the range of diagnostic and therapeutic energies.
文摘The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.
文摘In this paper, we have investigated the prospects of exploiting the rich world thorium reserves using Canada Deuterium Uranium （CANDU） reactors. The analysis is performed using the Monte Carlo MCNP code in order to understand how much time the reactor is in criticality conduction. Four different fuel compositions have been selected for analysis. We have obtained the infinite multiplication factor, k∞, under full power operation of the reactor over 8 years. The neutronic flux distribution in the full core reactor has already been investigated.
