Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used ...Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.展开更多
Colloid-colloid interactions in charge-stabilized dispersions can to The crystallization process and polymorph selection of hard-core some extent be represented by the hard-core Yukawa model. Yukawa model are studied ...Colloid-colloid interactions in charge-stabilized dispersions can to The crystallization process and polymorph selection of hard-core some extent be represented by the hard-core Yukawa model. Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic （fcc） phase. The contact value of bard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed （hcp） structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic （bcc）. The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald＇s step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.展开更多
Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type a...Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.展开更多
We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr)...We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.展开更多
A recently developed expansion method for analytically solving the ground states of strongly coupling Schroedinger equations by Friedberg, Lee, and Zhao is extended to excited states and applied to power-law central f...A recently developed expansion method for analytically solving the ground states of strongly coupling Schroedinger equations by Friedberg, Lee, and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed. As examples for application of the extended method, the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.展开更多
文摘Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.
基金the National Natural Science Foundation of China (11172302, 11302226, 10972217)the Opening Fund of State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, China (LNM201503)
文摘Colloid-colloid interactions in charge-stabilized dispersions can to The crystallization process and polymorph selection of hard-core some extent be represented by the hard-core Yukawa model. Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic （fcc） phase. The contact value of bard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed （hcp） structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic （bcc）. The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald＇s step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.
文摘Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.
文摘We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.
文摘A recently developed expansion method for analytically solving the ground states of strongly coupling Schroedinger equations by Friedberg, Lee, and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed. As examples for application of the extended method, the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.
