In recent several years,the tensor force,one of the most important components of the nucleon-nucleon force,has been implemented in time-dependent density functional theories and it has been found to influence many asp...In recent several years,the tensor force,one of the most important components of the nucleon-nucleon force,has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions,such as dissipation dynamics,sub-barrier fusions,and low-lying vibration states of colliding partners.Especially,the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically.In this work,we present a mini review on the recent progress on this topic.Considering the recent progress of low-energy reaction theories,we will also mention more possible effects of the tensor force on reaction dynamics.展开更多
The structure of Ne isotopes has been investigated by using deformed Skyrme-Hartree-Fock （SHF） method and BCS approximation. Especially the effect of tensor force on the halo structure of 29Ne and 31Ne is discussed....The structure of Ne isotopes has been investigated by using deformed Skyrme-Hartree-Fock （SHF） method and BCS approximation. Especially the effect of tensor force on the halo structure of 29Ne and 31Ne is discussed. To this end, the tensor contributions are considered to the energy density function and the single particle potential in SHF theory. For comparison, four Skyrme interactions are used： SLy5 and SGII without tensor force, and SLy5＋T and SGII＋ T with tensor force. The results indicate that the inclusion of tensor force shows a more pronounced halo structure for 31Ne.展开更多
The effects of the tensor force on the and decay nuclear matrix elements(NMEs)of,,,and are studied using the Hartree-Fock-Bogoliubov(HFB)plus proton-neutron quasi-particle random phase approximation(pnQRPA)model based...The effects of the tensor force on the and decay nuclear matrix elements(NMEs)of,,,and are studied using the Hartree-Fock-Bogoliubov(HFB)plus proton-neutron quasi-particle random phase approximation(pnQRPA)model based on the Skyrme energy density functional.We include the full spectra of intermediate states with up to the energy cutoff E=60 MeV,which is sufficient for convergence of NME calculations.The isovector(IV)pairing and tensor interactions are considered in both HFB and QRPA calculations,while the isoscalar(IS)pairing interaction is included only in QRPA calculations.We found that the tensor force shifts Gamow-Teller(GT)transition strengths substantially to low-energy regions and enhances the decay NME.The inclusion of tensor force enhances the NME by approximately 13%for and and 30%for and,for a fixed IS pairing strength.We found that the intermediate 2-state makes an important contribution to the NME,which is slightly enhanced by the inclusion of the tensor force.We also found that the contribution of the state makes important differences through the inclusion of the tensor force,which enhances the contribution largely.However when the IS pairing strength is increased,the contributions from 1+states are rapidly reduced to be very small,resulting in even negative contributions.Thus,tensor and IS pairing effects cancel each other,making the net effect on the NME relatively small.Due to this cancellation,if the IS pairing strength is optimized separately for cases with and without the tensor interaction to reproduce the experimental NME,the consequent NME with the tensor interaction is close to that without the tensor interaction within a 10%difference.展开更多
The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole e...The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole effects originating from the tensor force on both the collectivity and the matrix element for the neutrinoless double-β(0νββ)decay,using the generatorcoordinate method with an effective interaction.To analyze the effect of the tensor force,we employed an effective Hamiltonian associated with the monopole-based universal interaction that explicitly consists of the central,tensor,and spin-orbit coupling terms.The interferences among the shell structure,quadrupole collectivity,nucleon occupancy,and 0νββmatrix elements were analyzed in detail.A better understanding of the tensor force would be of great importance in reducing the theoretical uncertainty in 0νββnuclear matrix element calculations.展开更多
In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigat...In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated.It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter βT associated with the intensity of the tensor force.To understand this phenomenon,we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail.In addition,it is found that some TI J interactions could cause the 2s1/21d3/2 energy level inversion in 48Ca.展开更多
The role of tensor force on the collision dynamics of16O+16O is investigated in the framework of a fully three-dimensional timedependent Hartree-Fock theory.The calculations are performed with modern Skyrme energy fun...The role of tensor force on the collision dynamics of16O+16O is investigated in the framework of a fully three-dimensional timedependent Hartree-Fock theory.The calculations are performed with modern Skyrme energy functional plus tensor terms.Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions.The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom.We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets.The fusion cross section without tensor force overestimates the experimental value by about 25%,while the calculation with tensor force T11 has good agreement with experimental cross section.展开更多
The tensor force and pairing correlation effects on the two-proton radioactivity of^(18)Mg and^(20)Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory....The tensor force and pairing correlation effects on the two-proton radioactivity of^(18)Mg and^(20)Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory.It is shown that the halo sizes are enhanced with the increase in the strength of the tensor force and pairing correlation.Furthermore,the increasing halo sizes lead to the enhancement of diproton emission.Then,the tensor force is found to have a small influence on the two-proton decay energies,and the two-proton decay energies calculated with strong surface pairing are smaller than those with weak mixed pairing.Because the two-proton decay energies are relat-ively large,the predicted order of magnitude of half-lives within the effective liquid drop model is not sensitive to the decay energy variation caused by the tensor force and pairing correlation,which has a value of approximately 10^(-18)s.展开更多
In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+...In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+Te3 and many sets of the TIJ interactions.All of the interactions are the Skyrme interactions and contain a tensor component(tensor force).It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameterβTwhich is associated with the tensor force strength of the Skyrme interactions.To understand this phenomenon,we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameterβTin terms of the spin-orbit potential and the corresponding wave function.We find that the Skyrme interactions can be classified into two groups:(a)T21,T32,T43,T54,SLy5+T,SLy5+Tw,SGII+Te1 and SGII+Te2,which can roughly reproduce the experimental shell gaps of the oxygen isotopes;(b)T1J and SGII+Te3,which can not reproduce the experimental shell gaps.展开更多
The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock （BHF） approach. It is shown that the tensor force manifests it...The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock （BHF） approach. It is shown that the tensor force manifests its effect via the tensor 3SD1 channel. The density dependence of symmetry energy Esym turns out to be determined essentially by the tensor force from the π meson and p meson exchanges via the 3SD1 coupled channel. Increasing the strength of the tensor component due to the p-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to the reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.展开更多
The tensor-force effects on the evolution of spin-orbit spittings in neutron drops are investigated within the framework of the relativistic Hartree-Fock theory.For a fair comparison on the pure mean-field level,the r...The tensor-force effects on the evolution of spin-orbit spittings in neutron drops are investigated within the framework of the relativistic Hartree-Fock theory.For a fair comparison on the pure mean-field level,the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data.Through a quantitative analysis,we certify that theπ-pscudovector(π-PV)coupling affects the evolutionary trend through the embedded tensor force.The strength of the tensor force is explored by enlarging the strength fr of theπ-PV coupling.It is found that weakening the density dependence of fn is slightly better than enlarging it with a factor.We thus provide a semiquantitative support for the renormalization persistency of the tensor force within the frame-work of density functional theory.This will serve as important guidance for further development of relativistic effective interactions with particular focus on the tensor force.展开更多
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invar...The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the a-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudospin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components,revealing clearly the nature of the tensor force.展开更多
The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting ...The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting between proton h11=2 and g7=2 single-particle orbits along the Z=50 isotopes.With the optimized tensor interactions,the binding energies of spherical or weakly deformed nuclei with A=54-228 are studied systematically.The present results show that the global effect of tensor interaction is attractive and systematically increases the binding energies of all these nuclei and makes the nuclei more bound.The root mean squared deviation of the calculated binding energies from the experimental values is significantly improved by the optimized tensor interactions,and the contribution of the tensor interaction to the binding energy is estimated.展开更多
Regarding the stage progress on the relativistic Hartree-Fock(RHF)model achieved recently,we review the extensive developments of the model itself,including the descriptions of axially deformed unstable nuclei and nuc...Regarding the stage progress on the relativistic Hartree-Fock(RHF)model achieved recently,we review the extensive developments of the model itself,including the descriptions of axially deformed unstable nuclei and nuclear spin-isospin excitations,which shows that a complete RHF framework is now available for exploring the tensor force effects in both ground state and excited states of unstable nuclei.Meanwhile,the recent RHF descriptions of the pseudo-spin symmetry restoration and the new magicity are also reviewed.It shows that the Fock terms,particularly theρ-tensor coupling and naturally introduced tensor force components,bring about significant improvements in maintaining the delicate in-medium balance of nuclear attractions and repulsions,and uniformly interpreting the emergence of new magicity inCa.The revealed microscopic mechanisms not only deepen our understanding on the properties of nuclear structure,but also help to guide the further development of the effective nuclear force.展开更多
It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on ...It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading con- ditions.展开更多
An axially quadruple-octupole deformed relativistic Hartree-Fock(O-RHF)model with density-dependent meson-nucleon couplings is developed in this study.In this model,the reflection symmetry is not preserved,and the int...An axially quadruple-octupole deformed relativistic Hartree-Fock(O-RHF)model with density-dependent meson-nucleon couplings is developed in this study.In this model,the reflection symmetry is not preserved,and the integro-differential Dirac equations are solved by expanding the Dirac spinor on the spherical Dirac Woods-Saxon basis.The reliability of the newly developed O-RHF model is demonstrated by taking the octupole nucleus^(144)Ba as an example,and the octupole deformation effects in^(144)Ba are analyzed using the RHF Lagrangians PKOi and RMF Lagrangian DD-ME2.We find that the O-RHF models reproduce the octupole deformation of within the uncertainty of experimental results.Moreover,the presence of the Fock terms can enhance the intrusion of the neutron and proton waves,which leads to enhanced effects of octupole deformation for.In particular,owing to the repulsive tensor coupling between the intruding waves and the core of^(144)Ba,the tensor force component carried by theπ-PV coupling,which contributes only via the Fock terms,likely plays an unfavorable role in the occurrence of the octupole deformation of^(144)Ba.展开更多
It is well known that noncentral nuclear forces, such as the spin-orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical ...It is well known that noncentral nuclear forces, such as the spin-orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known because only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may convey useful information about the in-medium properties of noncentral nuclear interactions, besides earlier studies using the time-dependent Hartree-Fock approach to understand the effects of spin-orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore the dynamical effects of noncentral nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focus of these studies has been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies but so far there are still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.展开更多
This paper is a short revisit to Kuo-Brown effective interaction derived from the Hamada-Johnston nucleon-nucleon potential, done by Gerry Brown and Tom Kuo. This effective interaction, derived in year 1966, is the fi...This paper is a short revisit to Kuo-Brown effective interaction derived from the Hamada-Johnston nucleon-nucleon potential, done by Gerry Brown and Tom Kuo. This effective interaction, derived in year 1966, is the first attempt to describe nuclear structure properties from the free nucleon-nucleon potential. Nowadays much progress has been achieved for the effective interactions in shell model. We would compare the effective interactions obtained in the 1966 paper with up-to-date shell-model interactions in sd-shell and pf-shell model space. Recent knowledge of effective interactions on nuclear structure, can also be traced in the KuoBrown effective interaction, i.e., the universal roles of central and tensor forces, which reminds us that such discovery should be noticed much earlier.展开更多
We investigate many-body correlations caused by two- and three-body （2-, 3bd） forces. Shell-model effective interactions derived from ab initio methods （coupled-cluster method, no-core shell model） are adopted. Vl...We investigate many-body correlations caused by two- and three-body （2-, 3bd） forces. Shell-model effective interactions derived from ab initio methods （coupled-cluster method, no-core shell model） are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.展开更多
基金supported by the National Natural Science Foundation of China(Grants No.11975237,No.11575189,and No.11790325)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB34010000 and No.XDPB15)
文摘In recent several years,the tensor force,one of the most important components of the nucleon-nucleon force,has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions,such as dissipation dynamics,sub-barrier fusions,and low-lying vibration states of colliding partners.Especially,the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically.In this work,we present a mini review on the recent progress on this topic.Considering the recent progress of low-energy reaction theories,we will also mention more possible effects of the tensor force on reaction dynamics.
基金Supported by National Natural Science Foundation of China under Grant Nos.10975116 and 11275160
文摘The structure of Ne isotopes has been investigated by using deformed Skyrme-Hartree-Fock （SHF） method and BCS approximation. Especially the effect of tensor force on the halo structure of 29Ne and 31Ne is discussed. To this end, the tensor contributions are considered to the energy density function and the single particle potential in SHF theory. For comparison, four Skyrme interactions are used： SLy5 and SGII without tensor force, and SLy5＋T and SGII＋ T with tensor force. The results indicate that the inclusion of tensor force shows a more pronounced halo structure for 31Ne.
基金Supported by the National Natural Science Foundation of China(11575120,11822504,12075104)National Key Research and Development(R&D)programe of China(2021YFA1601500)+2 种基金Science Specialty Program of Sichuan University(2020SCUNL210)the support from Chinese Academy of Sciences for the project of Young Scientists in Basic Research(YSBR-099)"From 0 to 1 innovative"program.This work was partially supported by JSPS KAKENHI(JP19K03858)。
文摘The effects of the tensor force on the and decay nuclear matrix elements(NMEs)of,,,and are studied using the Hartree-Fock-Bogoliubov(HFB)plus proton-neutron quasi-particle random phase approximation(pnQRPA)model based on the Skyrme energy density functional.We include the full spectra of intermediate states with up to the energy cutoff E=60 MeV,which is sufficient for convergence of NME calculations.The isovector(IV)pairing and tensor interactions are considered in both HFB and QRPA calculations,while the isoscalar(IS)pairing interaction is included only in QRPA calculations.We found that the tensor force shifts Gamow-Teller(GT)transition strengths substantially to low-energy regions and enhances the decay NME.The inclusion of tensor force enhances the NME by approximately 13%for and and 30%for and,for a fixed IS pairing strength.We found that the intermediate 2-state makes an important contribution to the NME,which is slightly enhanced by the inclusion of the tensor force.We also found that the contribution of the state makes important differences through the inclusion of the tensor force,which enhances the contribution largely.However when the IS pairing strength is increased,the contributions from 1+states are rapidly reduced to be very small,resulting in even negative contributions.Thus,tensor and IS pairing effects cancel each other,making the net effect on the NME relatively small.Due to this cancellation,if the IS pairing strength is optimized separately for cases with and without the tensor interaction to reproduce the experimental NME,the consequent NME with the tensor interaction is close to that without the tensor interaction within a 10%difference.
基金supported by the National Natural Science Foundation of China(No.12275369)the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(No.22qntd3101)the Guangdong Major Project of Basic and Applied Basic Research(2021B0301030006)。
文摘The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole effects originating from the tensor force on both the collectivity and the matrix element for the neutrinoless double-β(0νββ)decay,using the generatorcoordinate method with an effective interaction.To analyze the effect of the tensor force,we employed an effective Hamiltonian associated with the monopole-based universal interaction that explicitly consists of the central,tensor,and spin-orbit coupling terms.The interferences among the shell structure,quadrupole collectivity,nucleon occupancy,and 0νββmatrix elements were analyzed in detail.A better understanding of the tensor force would be of great importance in reducing the theoretical uncertainty in 0νββnuclear matrix element calculations.
基金supported by the National Natural Science Foundation of China (Grant Nos.10975190,11275271 and 11075213)the Funds for Creative Research Groups of China (Grant No.11021504)+2 种基金the Doctoral Funds of Guizhou Normal College (Grant No.12BS020)the Natural Science Foundation of Guizhou Province of China (Grant No.2013GZ62432)the Natural Science Foundation of Hebei Province of China (Grant No.2012210043)
文摘In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated.It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter βT associated with the intensity of the tensor force.To understand this phenomenon,we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail.In addition,it is found that some TI J interactions could cause the 2s1/21d3/2 energy level inversion in 48Ca.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175252,11121403,11120101005,11211120152 and11275248)the National Key Basic Research Program of China(Grant No.2013CB834400)+2 种基金the Knowledge Innovation Project of the Chinese Academy of Sciences(Grant No.KJCX2-EW-N01)the President Fund of UCASthe Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China,the Open Project Program of State Key Laboratory of Theoretical Physics and the Institute of Theoretical Physics,Chinese Academy of Sciences,China(Grant No.Y4KF041CJ1)
文摘The role of tensor force on the collision dynamics of16O+16O is investigated in the framework of a fully three-dimensional timedependent Hartree-Fock theory.The calculations are performed with modern Skyrme energy functional plus tensor terms.Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions.The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom.We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets.The fusion cross section without tensor force overestimates the experimental value by about 25%,while the calculation with tensor force T11 has good agreement with experimental cross section.
基金Supported by the National Natural Science Foundation of China(U1832120,11675265)the Natural Science Foundation for Outstanding Young Scholars of Hebei Province,China(A2020210012)+4 种基金the Natural Science Foundation of Hebei Province,China(A2021210010)the Key Laboratory of High Precision Nuclear Spectroscopy,Institute of Modern Physics,Chinese Academy of Sciences(IMPKFKT2021002)the Graduate Student Innovative Research Project of Shijiazhuang Tiedao University(YC2022062)the Continuous Basic Scientific Research Project(WDJC-2019-13)the Leading Innovation Project(LC 192209000701).
文摘The tensor force and pairing correlation effects on the two-proton radioactivity of^(18)Mg and^(20)Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory.It is shown that the halo sizes are enhanced with the increase in the strength of the tensor force and pairing correlation.Furthermore,the increasing halo sizes lead to the enhancement of diproton emission.Then,the tensor force is found to have a small influence on the two-proton decay energies,and the two-proton decay energies calculated with strong surface pairing are smaller than those with weak mixed pairing.Because the two-proton decay energies are relat-ively large,the predicted order of magnitude of half-lives within the effective liquid drop model is not sensitive to the decay energy variation caused by the tensor force and pairing correlation,which has a value of approximately 10^(-18)s.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.13QN59)the National Natural Science Foundation of China(Grant Nos.11275271 and 11305109)+1 种基金the Funds for Creative Research Groups of China(Grant No.11021504)the Natural Science Foundation of Guizhou Province of China(Grant No.2013GZ62432)
文摘In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+Te3 and many sets of the TIJ interactions.All of the interactions are the Skyrme interactions and contain a tensor component(tensor force).It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameterβTwhich is associated with the tensor force strength of the Skyrme interactions.To understand this phenomenon,we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameterβTin terms of the spin-orbit potential and the corresponding wave function.We find that the Skyrme interactions can be classified into two groups:(a)T21,T32,T43,T54,SLy5+T,SLy5+Tw,SGII+Te1 and SGII+Te2,which can roughly reproduce the experimental shell gaps of the oxygen isotopes;(b)T1J and SGII+Te3,which can not reproduce the experimental shell gaps.
基金Supported by 973 Program of China(2007CB815004)National Natural Science Foundation of China(11175219,11435014)Knowledge Innovation Project(KJCX2-EW-N01) of Chinese Academy of Sciences
文摘The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock （BHF） approach. It is shown that the tensor force manifests its effect via the tensor 3SD1 channel. The density dependence of symmetry energy Esym turns out to be determined essentially by the tensor force from the π meson and p meson exchanges via the 3SD1 coupled channel. Increasing the strength of the tensor component due to the p-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to the reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.
基金Supported by National Natural Science Foundation of China(11905088,11675065,12075104)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB34000000)+2 种基金JSPS Grant-in-Aid for Early-Career Scientists(18K13549)JSPS Grant-in-Aid for JSPS Fellows(19J20543)JSPS Grant-in-Aid for Scientific Research(S)(20H05648)。
文摘The tensor-force effects on the evolution of spin-orbit spittings in neutron drops are investigated within the framework of the relativistic Hartree-Fock theory.For a fair comparison on the pure mean-field level,the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data.Through a quantitative analysis,we certify that theπ-pscudovector(π-PV)coupling affects the evolutionary trend through the embedded tensor force.The strength of the tensor force is explored by enlarging the strength fr of theπ-PV coupling.It is found that weakening the density dependence of fn is slightly better than enlarging it with a factor.We thus provide a semiquantitative support for the renormalization persistency of the tensor force within the frame-work of density functional theory.This will serve as important guidance for further development of relativistic effective interactions with particular focus on the tensor force.
基金Supported by National Natural Science Foundation of China(11375076,11675065)the Fundamental Research Funds for the Central Universities(lzujbky-2016-30)
文摘The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the a-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudospin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components,revealing clearly the nature of the tensor force.
基金supported by the National Natural Science Foundation of China(Nos.11575120 and 11822504)JSPS KAKENHI(No.JP19K03858)
文摘The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting between proton h11=2 and g7=2 single-particle orbits along the Z=50 isotopes.With the optimized tensor interactions,the binding energies of spherical or weakly deformed nuclei with A=54-228 are studied systematically.The present results show that the global effect of tensor interaction is attractive and systematically increases the binding energies of all these nuclei and makes the nuclei more bound.The root mean squared deviation of the calculated binding energies from the experimental values is significantly improved by the optimized tensor interactions,and the contribution of the tensor interaction to the binding energy is estimated.
基金Supported by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB34000000)the Fundamental Research Funds for the Central Universities(lzujbky-2021-sp41 and lzujbky-2021-sp36)
文摘Regarding the stage progress on the relativistic Hartree-Fock(RHF)model achieved recently,we review the extensive developments of the model itself,including the descriptions of axially deformed unstable nuclei and nuclear spin-isospin excitations,which shows that a complete RHF framework is now available for exploring the tensor force effects in both ground state and excited states of unstable nuclei.Meanwhile,the recent RHF descriptions of the pseudo-spin symmetry restoration and the new magicity are also reviewed.It shows that the Fock terms,particularly theρ-tensor coupling and naturally introduced tensor force components,bring about significant improvements in maintaining the delicate in-medium balance of nuclear attractions and repulsions,and uniformly interpreting the emergence of new magicity inCa.The revealed microscopic mechanisms not only deepen our understanding on the properties of nuclear structure,but also help to guide the further development of the effective nuclear force.
基金the financial support of the National Natural Science Foundation of China(51178044)Program for New Century Excellent Talents in University (NCET-11-0579)
文摘It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading con- ditions.
基金Partly supported by the National Natural Science Foundation of China(12275111)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB34000000)+1 种基金the Fundamental Research Funds for the Central Universities lzujbky-2023-stlt01the Supercomputing Center of Lanzhou University。
文摘An axially quadruple-octupole deformed relativistic Hartree-Fock(O-RHF)model with density-dependent meson-nucleon couplings is developed in this study.In this model,the reflection symmetry is not preserved,and the integro-differential Dirac equations are solved by expanding the Dirac spinor on the spherical Dirac Woods-Saxon basis.The reliability of the newly developed O-RHF model is demonstrated by taking the octupole nucleus^(144)Ba as an example,and the octupole deformation effects in^(144)Ba are analyzed using the RHF Lagrangians PKOi and RMF Lagrangian DD-ME2.We find that the O-RHF models reproduce the octupole deformation of within the uncertainty of experimental results.Moreover,the presence of the Fock terms can enhance the intrusion of the neutron and proton waves,which leads to enhanced effects of octupole deformation for.In particular,owing to the repulsive tensor coupling between the intruding waves and the core of^(144)Ba,the tensor force component carried by theπ-PV coupling,which contributes only via the Fock terms,likely plays an unfavorable role in the occurrence of the octupole deformation of^(144)Ba.
基金Acknowledgements This work was supported by the Major State Basic Research Development Program （973 Program） of China under Contract Nos. 2015CB856904 and 2014CB845401, the National Natural Science Foundation of China under Grant Nos. 11320101004, 11475243, and 11421505, the ＂100-Talent Plan＂ of Shanghai Institute of Applied Physics under Grant Nos. Y290061011 and Y526011011 from the Chinese Academy of Sciences, the ＂Shanghai Pujiang Program＂ under Grant No. 13PJ1410600, the U.S. National Science Foundation under Grant No. PHY-1068022, the U.S. Department of Energy Office of Science under Award No. DE-SC0013702, and the CUSTIPEN （China- U.S. Theory Institute for Physics with Exotic Nuclei） under the U.S. Department of Energy Grant No. DE-FG02-13ER42025.
文摘It is well known that noncentral nuclear forces, such as the spin-orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known because only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may convey useful information about the in-medium properties of noncentral nuclear interactions, besides earlier studies using the time-dependent Hartree-Fock approach to understand the effects of spin-orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore the dynamical effects of noncentral nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focus of these studies has been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies but so far there are still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.
基金supported by the National Natural Science Foundation of China(Grant Nos.11275067 and 11447109)the support from the Helmholtz Association(HGF)through the Nuclear Astrophysics Virtual Institute(VH-VI-417)
文摘This paper is a short revisit to Kuo-Brown effective interaction derived from the Hamada-Johnston nucleon-nucleon potential, done by Gerry Brown and Tom Kuo. This effective interaction, derived in year 1966, is the first attempt to describe nuclear structure properties from the free nucleon-nucleon potential. Nowadays much progress has been achieved for the effective interactions in shell model. We would compare the effective interactions obtained in the 1966 paper with up-to-date shell-model interactions in sd-shell and pf-shell model space. Recent knowledge of effective interactions on nuclear structure, can also be traced in the KuoBrown effective interaction, i.e., the universal roles of central and tensor forces, which reminds us that such discovery should be noticed much earlier.
基金Supported by National Natural Science Foundation of China(11505056,U1732138,11605054,11790325,11305108,11575290,11675148,11747312,11775316)the Outstanding Young Talent Research Fund of Zhengzhou University(1521317002)
文摘We investigate many-body correlations caused by two- and three-body （2-, 3bd） forces. Shell-model effective interactions derived from ab initio methods （coupled-cluster method, no-core shell model） are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.
