在解Bohr Hamiltonian的过程中出现了很多种方法,且有很多在最后都是用不同的势来得到不同的解析解,典型的有Coulomb-like和Kratzer-like势、Linear势、Davidson势.除此之外,还有Bohr sHarmonic-Oscillator解法、Wilets and Jean解法、E...在解Bohr Hamiltonian的过程中出现了很多种方法,且有很多在最后都是用不同的势来得到不同的解析解,典型的有Coulomb-like和Kratzer-like势、Linear势、Davidson势.除此之外,还有Bohr sHarmonic-Oscillator解法、Wilets and Jean解法、Elliott-Evans-Park s解法等.这些解法都给出了与实验室比较接近的光谱,但其中有一个普遍现象:很多最后的解析能谱都比实验能谱低.在该文中用Hulthen势来作出它的修正能谱,以更好地与实验值接近.最后,用240U和240Pu作为例子来进行比较.展开更多
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordi...Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.展开更多
We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the ext...We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm （AB） flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.展开更多
We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions t...We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional NikiforovUvarov method. The normalization constant for the Hulthen potential is also computed.展开更多
Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigen...Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.展开更多
The objective of this work is to calculate and compare the energy eigenvalue of Hulthen Potential using the NU method and AIM method. Using these two methods the energy eigenvalue calculated from the NU method is less...The objective of this work is to calculate and compare the energy eigenvalue of Hulthen Potential using the NU method and AIM method. Using these two methods the energy eigenvalue calculated from the NU method is less than AIM method. Moreover, the energy eigenvalue calculated from both methods is charge independent and only depends upon the quantum numbers and screening parameters, while the third term of energy eigenvalue calculated using the NU method is only dependent on screening parameters.展开更多
This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifuga...This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.展开更多
The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenv...The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.展开更多
Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary ...Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.展开更多
We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable...We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.展开更多
The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal te...The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.展开更多
In this study,a phenomenological model is proposed based on Wentzel-Kramers-Brillouin(WKB)theory and applied to investigate the two-proton(2p)radioactive half-lives of nuclei near or beyond the proton drip line.The to...In this study,a phenomenological model is proposed based on Wentzel-Kramers-Brillouin(WKB)theory and applied to investigate the two-proton(2p)radioactive half-lives of nuclei near or beyond the proton drip line.The total diproton-daughter nucleus interaction potential is composed of the Hulthen-type electrostatic term and the centrifugal term.The calculated 2p radioactive half-lives can accurately reproduce the existing 10 experimental datasets of five true 2p radioactive nuclei withσ=0.736.In addition,we extend this model to predict the half-lives of possible 2p radioactive nuclei whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.The predicted results are in agreement with those obtained using the Gamow-like model,generalized liquid drop model,Sreeja formula,and Liu formula.展开更多
In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scatt...In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELb -- 100 MeV for the a-a system and ELab = 15 MeV for a-3He and a-3H systems. The S-wave phase shift 5o for the system tends to 2n and 53/2_ for thea-3He system tends to n, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2- states of a-3He and a-3H systems, With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2- states. We have also compared our results with the convenient Born approximations.展开更多
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
文摘Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.
文摘We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm （AB） flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.
文摘We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional NikiforovUvarov method. The normalization constant for the Hulthen potential is also computed.
文摘Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.
文摘The objective of this work is to calculate and compare the energy eigenvalue of Hulthen Potential using the NU method and AIM method. Using these two methods the energy eigenvalue calculated from the NU method is less than AIM method. Moreover, the energy eigenvalue calculated from both methods is charge independent and only depends upon the quantum numbers and screening parameters, while the third term of energy eigenvalue calculated using the NU method is only dependent on screening parameters.
文摘This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.
文摘The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.
基金supported by the Scientific and Technological Research Council of Turkey
文摘Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.
文摘We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.
基金Supported by the Algerian Ministry of Higher Education and Scientific Research(MESRS)
文摘The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.
基金Supported in part by the National Natural Science Foundation of China(11205083,11505100,11705055)the Construct Program of the Key Discipline in Hunan Province,the Research Foundation of Education Bureau of Hunan Province,China(18A237)+3 种基金the Natural Science Foundation of Hunan Province,China(2018JJ3324)the Innovation Group of Nuclear and Particle Physics in USC,the Shandong Province Natural Science Foundation,China(ZR2015AQ007)the National Innovation Training Foundation of China(201910555161)the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment,University of South China(2019KFZ10)。
文摘In this study,a phenomenological model is proposed based on Wentzel-Kramers-Brillouin(WKB)theory and applied to investigate the two-proton(2p)radioactive half-lives of nuclei near or beyond the proton drip line.The total diproton-daughter nucleus interaction potential is composed of the Hulthen-type electrostatic term and the centrifugal term.The calculated 2p radioactive half-lives can accurately reproduce the existing 10 experimental datasets of five true 2p radioactive nuclei withσ=0.736.In addition,we extend this model to predict the half-lives of possible 2p radioactive nuclei whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.The predicted results are in agreement with those obtained using the Gamow-like model,generalized liquid drop model,Sreeja formula,and Liu formula.
文摘In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthdn type inter- action is considered to describe the a-a, t-a He and t=3 H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELb -- 100 MeV for the a-a system and ELab = 15 MeV for a-3He and a-3H systems. The S-wave phase shift 5o for the system tends to 2n and 53/2_ for thea-3He system tends to n, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2- states of a-3He and a-3H systems, With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2- states. We have also compared our results with the convenient Born approximations.
