The properties of exotic nuclei are the focus of the present research.Two-neutron halo structures of neutron-rich17,19B were experimentally confirmed.We studied the formation mechanism of halo phenomena in17,19B using...The properties of exotic nuclei are the focus of the present research.Two-neutron halo structures of neutron-rich17,19B were experimentally confirmed.We studied the formation mechanism of halo phenomena in17,19B using the complex momentum representation method applied to deformation and continuum coupling.By examining the evolution of the weakly bound and resonant levels near the Fermi surface,s–d orbital reversals and certain prolate deformations were observed.In addition,by analyzing the evolution of the occupation probabilities and density distributions occupied by valence neutrons,we found that the ground state of15B did not exhibit a halo and the ground states of17B and19B exhibited halos at 0.6≤β2≤0.7 and0.3≤β2≤0.7,respectively.The low-l components in the valence levels that are weakly bound or embedded in the continuous spectrum lead to halo formation.展开更多
The self-consistent quadruple potential is deduced within the relativistic mean-field(RMF)framework and substituted into the Hamiltonian,which is calculated using the complex momentum representation(CMR).Considering e...The self-consistent quadruple potential is deduced within the relativistic mean-field(RMF)framework and substituted into the Hamiltonian,which is calculated using the complex momentum representation(CMR).Considering even-even titanium isotopes as an example,this study investigated various properties,including the resonant states of neutron-rich nuclei in the RMF-CMR model,and used them to describe the binding energy.The abrupt decrease in the two-neutron separation energy(S_(2n))corresponds to the traditional magic number.The resonant and bound states are simultaneously exposed in the complex moment plane,where the continuum is along the integration contour.The four oblate neutron-rich nuclei^(72-78)Ti are weakly bound or resonant because their Fermi energies are approximately 0 MeV.The root-meansquare(RMS)radii of these nuclei increase suddenly compared with those of others(neutron number N<48).Moreover,^(78)Ti and^(76)Ti are determined as drip-line nucleons by the value of S_(2n) and the energy levels,respectively.Finally,the weak-bounded character can be represented by diffuse density probability distributions.展开更多
Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear theory.Accordingly,we explored the viability of the complex momentum representation...Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear theory.Accordingly,we explored the viability of the complex momentum representation(CMR)approach coupled with new potentials.We focus on predicting the energy of the low-lying 2p_(3∕2)resonance in 17 O,which is critical for s-process nucleosynthesis and missing in previous theoretical research.Using a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy,we successfully predicted the resonant energy of this level for the first time.Our predictions of the bound levels and 1d_(3∕2)resonance agree well with the measurement results.Additionally,we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in^(29,31)F.We found that the CMR-based predictions of the bound-level energies and unbound 1f7∕2 level agree well with the results obtained using the scattering phase shift method.Subsequently,we successfully found a solution for the 2p_(3∕2)resonance with energy just above the threshold,which is decisive for halo formation.展开更多
By combining the Skyrme-Hartree-Fock method with complex momentum representation(CMR),the resonant states of_(Λ)^(17)O,_(Λ)^(41)Ca,_(Λ)^(49)Ca,and_(Λ)^(57)Ni were investigated.The phase shifts for hyperon-nucleus ...By combining the Skyrme-Hartree-Fock method with complex momentum representation(CMR),the resonant states of_(Λ)^(17)O,_(Λ)^(41)Ca,_(Λ)^(49)Ca,and_(Λ)^(57)Ni were investigated.The phase shifts for hyperon-nucleus elastic scattering were determined with continuum level density(CLD),and the scattering length as well as the resonance energy were obtained by utilizing the effective range expansion.Our method,abbreviated as CMR-CLD,exhibits good consistency with traditional approaches and provides ground work for investigating scattering and resonance problems in deformed and multi-hyperon hypernuclei.展开更多
Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, ...Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.展开更多
This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-pa...This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-particle levels of bound and resonant states,and neutron density distributions and shapes.Simultaneously,special attention is paid to the distinctive physical phenomena associated with these isotopes.The deformed relativistic mean field theory in complex momentum representations with BCS pairings(DRMF-CMR-BCS)employed in our research provides resonant states with real physics,offering insights into deformed halo nuclei.Four effective interactions(NL3,NL3^(*),PK1,and NLSH)were considered to assess the influence of continuum and deformation effects on halo structures.Calculations for odd-even nuclei ^(35–43)Na revealed the dependence on the chosen effective interaction and number of considered resonant states.Neutron occupation patterns near the Fermi surface,particularly in orbitals 1/2^(−)_(3) and 3/2^(−)_(2),were determined to be crucial in halo formation.The study provided detailed insights into the density distributions,shape evolution,and structure of neutron-rich sodium isotopes,contributing valuably to the field of nuclear physics.展开更多
In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion mat...In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method.展开更多
To explore the properties of neutron-rich nuclei with approximately 40 protons,the density-dependent point coupling(DD-PC1)effective interaction parameter is adopted in the relativistic mean-field theory with the comp...To explore the properties of neutron-rich nuclei with approximately 40 protons,the density-dependent point coupling(DD-PC1)effective interaction parameter is adopted in the relativistic mean-field theory with the complex momentum representation(RMF-CMR).The calculated two-neutron separation energy(S_(2n))and root-mean-square(rms)radii support the halo structure that appear in Mo and Ru isotopic chains.Besides,the neutron skin structures appear in Kr and Sr isotopes.The conclusions drawn are also supported by the single-particle energy levels and their occupancy probability and density distribution.Particularly,the energy levels,which reduce to bound states or are approximately 0 MeV with a small orbital angular momentum,are suggested to provide the primary contribution to increasing the neutron radius.Moreover,the single-particle energy levels significantly reflect the shell structure.In addition,the neutron drip line nuclei for Kr,Sr,Mo,and Ru elements are proposed via the changes in S_(2n).展开更多
Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in wh...Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane.We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature,and the dependence on the contour of momentum integration.Satisfactory results are obtained.^17O is chosen as an example,and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.展开更多
The recently developed relativistic-mean-field in complex momentum representation with the functional NL3^(*)was used to explore the exotic properties of neutron-rich Pd,Cd,Te,and Xe isotopes.The results were compared...The recently developed relativistic-mean-field in complex momentum representation with the functional NL3^(*)was used to explore the exotic properties of neutron-rich Pd,Cd,Te,and Xe isotopes.The results were compared with those obtained using the relativistic Hartree-Bogoliubov(RHB)calculations and available experimental data.The single-particle levels were obtained for the bound and resonant states.The two neutron separation energies and root mean square(rms)radii agree with the experimental data.It is shown that there is a halo structure in extremely neutron-rich^(164-180)Te and^(164-182))Xe,,as well as a thick neutron skin in extremely neutron-rich Pd and Cd isotopes.From the numbers of neutrons(N_(λ))Te and(N_(0)),occupying the levels above the Fermi surface and zero-potential energy level,it was found that pairing correlations play an important role in the formation of halo phenomena.These findings are further supported by investigating S_(2n),rms radii,occupation probabilities,contributions of single-particle levels to the neutron rms radii,and density distributions.The neutron rms radii increased sharply,evidently deviating from the traditional rule r■N^(1/3),and the density distributions were very diffuse.Finally,the contributions of different single-particle levels to the total neutron density and wavefunction are discussed.It was found that the sudden increase in the neutron rms radii and diffuse density distributions mainly arise from the resonant levels with a lower orbital angular momentum near the continuum threshold.展开更多
基金the National Natural Science Foundation of China(Nos.12205001,11935001,and 12204001)the Scientific Research program of Anhui University of Finance and Economics(Nos.ACKYC22080 and ACKYC220801).
文摘The properties of exotic nuclei are the focus of the present research.Two-neutron halo structures of neutron-rich17,19B were experimentally confirmed.We studied the formation mechanism of halo phenomena in17,19B using the complex momentum representation method applied to deformation and continuum coupling.By examining the evolution of the weakly bound and resonant levels near the Fermi surface,s–d orbital reversals and certain prolate deformations were observed.In addition,by analyzing the evolution of the occupation probabilities and density distributions occupied by valence neutrons,we found that the ground state of15B did not exhibit a halo and the ground states of17B and19B exhibited halos at 0.6≤β2≤0.7 and0.3≤β2≤0.7,respectively.The low-l components in the valence levels that are weakly bound or embedded in the continuous spectrum lead to halo formation.
基金the National Natural Science Foundation of China(Nos.11935001 and 11875070)Natural Science Foundation of Anhui Province(No.1908085MA16).
文摘The self-consistent quadruple potential is deduced within the relativistic mean-field(RMF)framework and substituted into the Hamiltonian,which is calculated using the complex momentum representation(CMR).Considering even-even titanium isotopes as an example,this study investigated various properties,including the resonant states of neutron-rich nuclei in the RMF-CMR model,and used them to describe the binding energy.The abrupt decrease in the two-neutron separation energy(S_(2n))corresponds to the traditional magic number.The resonant and bound states are simultaneously exposed in the complex moment plane,where the continuum is along the integration contour.The four oblate neutron-rich nuclei^(72-78)Ti are weakly bound or resonant because their Fermi energies are approximately 0 MeV.The root-meansquare(RMS)radii of these nuclei increase suddenly compared with those of others(neutron number N<48).Moreover,^(78)Ti and^(76)Ti are determined as drip-line nucleons by the value of S_(2n) and the energy levels,respectively.Finally,the weak-bounded character can be represented by diffuse density probability distributions.
基金supported by the National Natural Science Foundation of China(Nos.12175010,11375022,11775014)Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB34010000)US Department of Energy Office of Science,Office of Nuclear Physics,under Award Number DE-AC05-00OR22725.
文摘Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear theory.Accordingly,we explored the viability of the complex momentum representation(CMR)approach coupled with new potentials.We focus on predicting the energy of the low-lying 2p_(3∕2)resonance in 17 O,which is critical for s-process nucleosynthesis and missing in previous theoretical research.Using a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy,we successfully predicted the resonant energy of this level for the first time.Our predictions of the bound levels and 1d_(3∕2)resonance agree well with the measurement results.Additionally,we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in^(29,31)F.We found that the CMR-based predictions of the bound-level energies and unbound 1f7∕2 level agree well with the results obtained using the scattering phase shift method.Subsequently,we successfully found a solution for the 2p_(3∕2)resonance with energy just above the threshold,which is decisive for halo formation.
基金Supported by the National Natural Science Foundation of China(12035011,11905103,11947211,11761161001,11961141003,12022517,12375122)the National Key R&D Program of China(2023YFA1606503)+1 种基金the Science and Technology Development Fund of Macao,China(0048/2020/A1,008/2017/AFJ)the Fundamental Research Funds for the Central Universities(22120210138,22120200101)。
文摘By combining the Skyrme-Hartree-Fock method with complex momentum representation(CMR),the resonant states of_(Λ)^(17)O,_(Λ)^(41)Ca,_(Λ)^(49)Ca,and_(Λ)^(57)Ni were investigated.The phase shifts for hyperon-nucleus elastic scattering were determined with continuum level density(CLD),and the scattering length as well as the resonance energy were obtained by utilizing the effective range expansion.Our method,abbreviated as CMR-CLD,exhibits good consistency with traditional approaches and provides ground work for investigating scattering and resonance problems in deformed and multi-hyperon hypernuclei.
文摘Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.
基金Partly supported by the National Natural Science Foundation of China (11935001, 11575001)the Natural Science Foundation of Anhui Province(2008085MA26)+2 种基金Anhui project (Z010118169)the Heavy Ion Research Facility in Lanzhou (HIRFL)(HIR2021PY007)the project of Key Laboratory of High Precision Nuclear Spectroscopy conducted in Chinese Academy of Sciences.
文摘This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-particle levels of bound and resonant states,and neutron density distributions and shapes.Simultaneously,special attention is paid to the distinctive physical phenomena associated with these isotopes.The deformed relativistic mean field theory in complex momentum representations with BCS pairings(DRMF-CMR-BCS)employed in our research provides resonant states with real physics,offering insights into deformed halo nuclei.Four effective interactions(NL3,NL3^(*),PK1,and NLSH)were considered to assess the influence of continuum and deformation effects on halo structures.Calculations for odd-even nuclei ^(35–43)Na revealed the dependence on the chosen effective interaction and number of considered resonant states.Neutron occupation patterns near the Fermi surface,particularly in orbitals 1/2^(−)_(3) and 3/2^(−)_(2),were determined to be crucial in halo formation.The study provided detailed insights into the density distributions,shape evolution,and structure of neutron-rich sodium isotopes,contributing valuably to the field of nuclear physics.
基金This project is granted financial support from NSFC (11071079)NSFC (10901056)+2 种基金Shanghai Science and Technology Commission Venus (11QA1402200)Ningbo Natural Science Foundation (2010A610097)the Fundamental Research Funds for the Central Universities and Zhejiang Natural Science Foundation (Y6110043)
文摘In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method.
基金Supported by the National Natural Science Foundation of China(11875070)the Natural Science Foundation of Anhui Province(1908085MA16)。
文摘To explore the properties of neutron-rich nuclei with approximately 40 protons,the density-dependent point coupling(DD-PC1)effective interaction parameter is adopted in the relativistic mean-field theory with the complex momentum representation(RMF-CMR).The calculated two-neutron separation energy(S_(2n))and root-mean-square(rms)radii support the halo structure that appear in Mo and Ru isotopic chains.Besides,the neutron skin structures appear in Kr and Sr isotopes.The conclusions drawn are also supported by the single-particle energy levels and their occupancy probability and density distribution.Particularly,the energy levels,which reduce to bound states or are approximately 0 MeV with a small orbital angular momentum,are suggested to provide the primary contribution to increasing the neutron radius.Moreover,the single-particle energy levels significantly reflect the shell structure.In addition,the neutron drip line nuclei for Kr,Sr,Mo,and Ru elements are proposed via the changes in S_(2n).
基金Supported by National Natural Science Foundation of China(11575002,11175001,11205004,11305002)Program for New Century Excellent Talents at the University of China(NCET-05-0558)+2 种基金Natural Science Foundation of Anhui Province(1408085QA21)Key Research Foundation of Education Ministry of Anhui Province of China(KJ2016A026)211 Project of Anhui University
文摘Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane.We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature,and the dependence on the contour of momentum integration.Satisfactory results are obtained.^17O is chosen as an example,and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.
基金Supported by the National Natural Science Foundation of China(12205001,11935001)the Scientific Research Program of Anhui University of Finance and Economics(ACKYC22080,ACKYC220801)。
文摘The recently developed relativistic-mean-field in complex momentum representation with the functional NL3^(*)was used to explore the exotic properties of neutron-rich Pd,Cd,Te,and Xe isotopes.The results were compared with those obtained using the relativistic Hartree-Bogoliubov(RHB)calculations and available experimental data.The single-particle levels were obtained for the bound and resonant states.The two neutron separation energies and root mean square(rms)radii agree with the experimental data.It is shown that there is a halo structure in extremely neutron-rich^(164-180)Te and^(164-182))Xe,,as well as a thick neutron skin in extremely neutron-rich Pd and Cd isotopes.From the numbers of neutrons(N_(λ))Te and(N_(0)),occupying the levels above the Fermi surface and zero-potential energy level,it was found that pairing correlations play an important role in the formation of halo phenomena.These findings are further supported by investigating S_(2n),rms radii,occupation probabilities,contributions of single-particle levels to the neutron rms radii,and density distributions.The neutron rms radii increased sharply,evidently deviating from the traditional rule r■N^(1/3),and the density distributions were very diffuse.Finally,the contributions of different single-particle levels to the total neutron density and wavefunction are discussed.It was found that the sudden increase in the neutron rms radii and diffuse density distributions mainly arise from the resonant levels with a lower orbital angular momentum near the continuum threshold.
