In this study,single-particle energy was examined using the finite difference method by taking 208Pb as an example.If the first derivative term in the spherical Dirac equation is discretized using a three-point formul...In this study,single-particle energy was examined using the finite difference method by taking 208Pb as an example.If the first derivative term in the spherical Dirac equation is discretized using a three-point formula,a one-to-one correspondence occurs between the physical and spurious states.Although these energies are exactly the same,the wave functions of the spurious states exhibit a much faster staggering than those of the physical states.Such spurious states can be eliminated when applying the finite difference method by introducing an extra Wilson term into the Hamiltonian.Furthermore,it was also found that the number of spurious states can be reduced if we improve the accuracy of the numerical differential formula.The Dirac equation is then solved in a momentum space in which there is no differential operator,and we found that the spurious states can be completely avoided in the momentum space,even without an extra Wilson term.展开更多
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
The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states...The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states.In this paper,we solve the RHB equation with the Woods-Saxon-type mean-field and Delta-type pairing-field potentials by using the finite-difference method(FDM).We inevitably obtain spurious states when using the common symmetric central difference formula(CDF)to construct the Hamiltonian matrix,which is similar to the problem resulting from solving the Dirac equation with the same method.This problem is solved by using the asymmetric difference formula(ADF).In addition,we show that a large enough box is necessary to describe the continuum quasi-particle states.The canonical states obtained by diagonalizing the density matrix constructed by the quasi-particle states are not particularly sensitive to the box size.Part of the asymptotic wave functions can be improved by applying the ADF in the FDM compared to the shooting method with the same box boundary condition.展开更多
基金partly supported by the National Natural Science Foundation of China(No.11875070)the Natural Science Foundation of Anhui Province(No.1908085MA16)
文摘In this study,single-particle energy was examined using the finite difference method by taking 208Pb as an example.If the first derivative term in the spherical Dirac equation is discretized using a three-point formula,a one-to-one correspondence occurs between the physical and spurious states.Although these energies are exactly the same,the wave functions of the spurious states exhibit a much faster staggering than those of the physical states.Such spurious states can be eliminated when applying the finite difference method by introducing an extra Wilson term into the Hamiltonian.Furthermore,it was also found that the number of spurious states can be reduced if we improve the accuracy of the numerical differential formula.The Dirac equation is then solved in a momentum space in which there is no differential operator,and we found that the spurious states can be completely avoided in the momentum space,even without an extra Wilson term.
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.
基金Supported by the National Natural Science Foundation of China(11775119,2175109)the Natural Science Foundation of Tianjin,China(19JCYBJC30800)。
文摘The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip lines.The key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle states.In this paper,we solve the RHB equation with the Woods-Saxon-type mean-field and Delta-type pairing-field potentials by using the finite-difference method(FDM).We inevitably obtain spurious states when using the common symmetric central difference formula(CDF)to construct the Hamiltonian matrix,which is similar to the problem resulting from solving the Dirac equation with the same method.This problem is solved by using the asymmetric difference formula(ADF).In addition,we show that a large enough box is necessary to describe the continuum quasi-particle states.The canonical states obtained by diagonalizing the density matrix constructed by the quasi-particle states are not particularly sensitive to the box size.Part of the asymptotic wave functions can be improved by applying the ADF in the FDM compared to the shooting method with the same box boundary condition.
