We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significa...We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.展开更多
The complex-scaled Green's function(CGF)method is employed to explore the single-proton resonance in 15F.Special attention is paid to the first excited resonant state 5/2+,which has been widely studied in both the...The complex-scaled Green's function(CGF)method is employed to explore the single-proton resonance in 15F.Special attention is paid to the first excited resonant state 5/2+,which has been widely studied in both theory and experiments.However,past studies generally overestimated the width of the 5/2+state.The predicted energy and width of the first excited resonant state 5/2+by the CGF method are both in good agreement with the experimental value and close to Fortune's new estimation.Furthermore,the influence of the potential parameters and quadruple deformation effects on the resonant states are investigated in detail,which is helpful to the study of the shell structure evolution.展开更多
The Schrodinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics.We demonstrate how simple transformations of the Schrodinger equation leads to a coupled linear...The Schrodinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics.We demonstrate how simple transformations of the Schrodinger equation leads to a coupled linear system,whereby each diagonal block is a high frequency Helmholtz problem.Based on this model,we derive indefinite Helmholtz model problems with strongly varying wavenumbers.We employ the iterative approach for their solution.In particular,we develop a preconditioner that has its spectrum restricted to a quadrant(of the complex plane)thereby making it easily invertible by multigrid methods with standard components.This multigrid preconditioner is used in conjunction with suitable Krylov-subspace methods for solving the indefinite Helmholtz model problems.The aim of this study is to report the feasibility of this preconditioner for the model problems.We compare this idea with the other prevalent preconditioning ideas,and discuss its merits.Results of numerical experiments are presented,which complement the proposed ideas,and show that this preconditioner may be used in an automatic setting.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12174147)the Chinese Scholarship Council(Grant Nos.202108210152 and 202006175016).
文摘We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.
基金Supported by the National Natural Science Foundation of China(11975167,11935001,11535004,11761161001)the National Key R&D Program of China(2018YFA0404403)the Science and Technology Development Fund of Macao(008/2017/AFJ)。
文摘The complex-scaled Green's function(CGF)method is employed to explore the single-proton resonance in 15F.Special attention is paid to the first excited resonant state 5/2+,which has been widely studied in both theory and experiments.However,past studies generally overestimated the width of the 5/2+state.The predicted energy and width of the first excited resonant state 5/2+by the CGF method are both in good agreement with the experimental value and close to Fortune's new estimation.Furthermore,the influence of the potential parameters and quadruple deformation effects on the resonant states are investigated in detail,which is helpful to the study of the shell structure evolution.
基金funded partially by Fonds voor Wetenschappelijk Onderzoek(FWO Bel-gium)projects G.0174.08 and 1.5.145.10,by the University of Antwerp,Belgium,and by the Institute of Business Administration,Karachi,Pakistan.We wish to thank the sponsors sincerely for their support.
文摘The Schrodinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics.We demonstrate how simple transformations of the Schrodinger equation leads to a coupled linear system,whereby each diagonal block is a high frequency Helmholtz problem.Based on this model,we derive indefinite Helmholtz model problems with strongly varying wavenumbers.We employ the iterative approach for their solution.In particular,we develop a preconditioner that has its spectrum restricted to a quadrant(of the complex plane)thereby making it easily invertible by multigrid methods with standard components.This multigrid preconditioner is used in conjunction with suitable Krylov-subspace methods for solving the indefinite Helmholtz model problems.The aim of this study is to report the feasibility of this preconditioner for the model problems.We compare this idea with the other prevalent preconditioning ideas,and discuss its merits.Results of numerical experiments are presented,which complement the proposed ideas,and show that this preconditioner may be used in an automatic setting.
