This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis...This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000 is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.展开更多
A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave...A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave function on harmonic oscillator (HO) functions with different sizes in the Jacobi coordinates instead of only one unique size parameter in the traditional approach. The method presented obeys the principles of antisymmetry and translational invariance. The theoretical formulation has been illustrated by evaluation of ground state energies of a number of Coulomb three-body systems with two identical particles for zero HO excitation energy. The analytical solution of this problem in case of only one size parameter has been derived. The obtained results show significant advantage of the base with different sizes over the traditional approach for investigation of the bound state problem of quantum systems.展开更多
采用反射不对称相对论平均场(Reflection Asymmetric Relativistic Mean Field,RAS-RMF)理论研究了226Th和216Th原子核的基态性质.通过改变RAS-RMF理论计算中双中心谐振子基的不对称系数δ3、形变参数δ2以及基大小参数N,探讨了基参数...采用反射不对称相对论平均场(Reflection Asymmetric Relativistic Mean Field,RAS-RMF)理论研究了226Th和216Th原子核的基态性质.通过改变RAS-RMF理论计算中双中心谐振子基的不对称系数δ3、形变参数δ2以及基大小参数N,探讨了基参数的变化对计算结果的影响.结果表明:双中心谐振子基参数的改变对RAS-RMF计算结果都存在稳定的区间,在这个稳定区间里,RAS-RMF计算结果与实验数据以及有限力程小液滴模型(FRDM)计算结果一致.尤其是反射不对称自由度的引入,改进了相对论平均场的理论计算,给出了与实验更加符合的结果,表明RAS-RMF理论对描述具有反射不对称形变的原子核更具优越性.展开更多
Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and ...Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the（l2）N term in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asvmmetric ootential is obtained and discussed bv the above two numerical methods, and their consistencv is shown in the obtained single-particle energies with the differences smaller than 10-4[hω0]展开更多
Ⅰ. RADIAL EQUATIONFor the nuclear motion of a diatomic molecule, the radial equation, after separating the translational motion of the mass center and the angular part, can be written
文摘This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000 is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.
文摘A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave function on harmonic oscillator (HO) functions with different sizes in the Jacobi coordinates instead of only one unique size parameter in the traditional approach. The method presented obeys the principles of antisymmetry and translational invariance. The theoretical formulation has been illustrated by evaluation of ground state energies of a number of Coulomb three-body systems with two identical particles for zero HO excitation energy. The analytical solution of this problem in case of only one size parameter has been derived. The obtained results show significant advantage of the base with different sizes over the traditional approach for investigation of the bound state problem of quantum systems.
文摘采用反射不对称相对论平均场(Reflection Asymmetric Relativistic Mean Field,RAS-RMF)理论研究了226Th和216Th原子核的基态性质.通过改变RAS-RMF理论计算中双中心谐振子基的不对称系数δ3、形变参数δ2以及基大小参数N,探讨了基参数的变化对计算结果的影响.结果表明:双中心谐振子基参数的改变对RAS-RMF计算结果都存在稳定的区间,在这个稳定区间里,RAS-RMF计算结果与实验数据以及有限力程小液滴模型(FRDM)计算结果一致.尤其是反射不对称自由度的引入,改进了相对论平均场的理论计算,给出了与实验更加符合的结果,表明RAS-RMF理论对描述具有反射不对称形变的原子核更具优越性.
基金supported by the National Basic Research Program of China (Grant No. 2013CB834400)the National Natural Science Foundation of China (Grants Nos. 11335002, 11375015, 11461141002, and 11621131001)
文摘Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the（l2）N term in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asvmmetric ootential is obtained and discussed bv the above two numerical methods, and their consistencv is shown in the obtained single-particle energies with the differences smaller than 10-4[hω0]
文摘Ⅰ. RADIAL EQUATIONFor the nuclear motion of a diatomic molecule, the radial equation, after separating the translational motion of the mass center and the angular part, can be written
