In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials ar...In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials are obtained via this method. The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed. The PT-symmetry and Hermiticity for these potentials are also discussed.展开更多
The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quan...The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials and or the generalized hypergeometric functions have been obtained. A short-cut of the Nikiforov-Uvarov (NU) method is used in the solution. A unified treatment of the Eckart, Rosen-Morse, Hulthén and Woods-Saxon potential models can be easily derived from our general solution. The present calculations are found to be identical with those ones appearing in the literature. Further, based on the PT-symmetry, the bound state solutions of the trigonometric Rosen-Morse potential can be easily obtained.展开更多
An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts...An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts of the equation are solved by the Nikiforov-Uvarov method. The general results obtained in this work can be reduced to the standard forms already present in the literature.展开更多
The present article highlights the inconsistency of static Woods Saxon potential and the applicability of energy dependent Woods Saxon potential to explore the fusion dynamics of ^(48)_(22)Ti+^(58,60,64)_(28)Ni,^(46)_...The present article highlights the inconsistency of static Woods Saxon potential and the applicability of energy dependent Woods Saxon potential to explore the fusion dynamics of ^(48)_(22)Ti+^(58,60,64)_(28)Ni,^(46)_(22)Ti+^(64)_(28)Ti+^(50)_(22)Ti+^(60)_(28)Ni,and^(19)_9F+^(93)_(41)Nb reactions leading to formation of different Sn-isotopes via different entrance channels.Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations.However,the predictions of onedimensional Wong formula based upon energy dependent Woods Saxon potential model(EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy.Therefore,the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.展开更多
The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barri...The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barrier. Energy eigenvalues and the corresponding eigenfunctions are computed for various values of quantum numbers n, I.展开更多
By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction pote...By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.展开更多
The exact analytical solution of the Klein–Gordon equation for the spin-0 particles in the generalized Woods–Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obta...The exact analytical solution of the Klein–Gordon equation for the spin-0 particles in the generalized Woods–Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0particles.展开更多
A Woods–Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods–Saxon potential on sin...A Woods–Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods–Saxon potential on single particle orbits around the Fermi surface are investigated in66Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness.展开更多
Systematic total Routhian surface calculations for even–even N = 104 midshell isotones with 66≤Z≤82 have been carried out based on a more realistic diffuse-surface deformed Woods–Saxon nuclear potential in (β_2, ...Systematic total Routhian surface calculations for even–even N = 104 midshell isotones with 66≤Z≤82 have been carried out based on a more realistic diffuse-surface deformed Woods–Saxon nuclear potential in (β_2, γ, β_4) deformation space, focusing on the rotation-induced shapecoexisting phenomena. As an example and basic test, the oblate property at the ground state in ^(184)Hg is well reproduced and the microscopic origin is analyzed from the single-particle structure. The present calculated results are compared with available experimental information, showing a good agreement. It is systematically found that in this isotonic chain several bands with different shapes(e.g., prolate, oblate and superdeformed prolate bands, seven non-collective band) may show a strong competition and coexisting phenomenon at a certain domain of the rotational frequency.展开更多
文摘In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials are obtained via this method. The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed. The PT-symmetry and Hermiticity for these potentials are also discussed.
文摘The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials and or the generalized hypergeometric functions have been obtained. A short-cut of the Nikiforov-Uvarov (NU) method is used in the solution. A unified treatment of the Eckart, Rosen-Morse, Hulthén and Woods-Saxon potential models can be easily derived from our general solution. The present calculations are found to be identical with those ones appearing in the literature. Further, based on the PT-symmetry, the bound state solutions of the trigonometric Rosen-Morse potential can be easily obtained.
文摘An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts of the equation are solved by the Nikiforov-Uvarov method. The general results obtained in this work can be reduced to the standard forms already present in the literature.
基金Supported by Dr.D.S.Kothari Post-Doctoral Fellowship Scheme sponsored by University Grants Commission(UGC)New DelhiIndia
文摘The present article highlights the inconsistency of static Woods Saxon potential and the applicability of energy dependent Woods Saxon potential to explore the fusion dynamics of ^(48)_(22)Ti+^(58,60,64)_(28)Ni,^(46)_(22)Ti+^(64)_(28)Ti+^(50)_(22)Ti+^(60)_(28)Ni,and^(19)_9F+^(93)_(41)Nb reactions leading to formation of different Sn-isotopes via different entrance channels.Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations.However,the predictions of onedimensional Wong formula based upon energy dependent Woods Saxon potential model(EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy.Therefore,the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.
文摘The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barrier. Energy eigenvalues and the corresponding eigenfunctions are computed for various values of quantum numbers n, I.
文摘By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.
基金supported by the Turkish Science and Research Council (TüBITAK) and Akdeniz University
文摘The exact analytical solution of the Klein–Gordon equation for the spin-0 particles in the generalized Woods–Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0particles.
基金Supported by Chinese University Scientific Fund under Grant No.2011JS050
文摘A Woods–Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods–Saxon potential on single particle orbits around the Fermi surface are investigated in66Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness.
基金supported by the Natural Science Foundation of China(Nos.11675148 and 11505157)the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province(No.2017GGJS008)+2 种基金the Foundation and Advanced Technology Research Program of Henan Province(No.162300410222)the Outstanding Young Talent Research Fund of Zhengzhou University(No.1521317002)the Physics Research and Development Program of Zhengzhou University(No.32410017)
文摘Systematic total Routhian surface calculations for even–even N = 104 midshell isotones with 66≤Z≤82 have been carried out based on a more realistic diffuse-surface deformed Woods–Saxon nuclear potential in (β_2, γ, β_4) deformation space, focusing on the rotation-induced shapecoexisting phenomena. As an example and basic test, the oblate property at the ground state in ^(184)Hg is well reproduced and the microscopic origin is analyzed from the single-particle structure. The present calculated results are compared with available experimental information, showing a good agreement. It is systematically found that in this isotonic chain several bands with different shapes(e.g., prolate, oblate and superdeformed prolate bands, seven non-collective band) may show a strong competition and coexisting phenomenon at a certain domain of the rotational frequency.
