We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam e...According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.展开更多
The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing correlations.The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weigh...The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing correlations.The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weight functions.The particle–hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional,while pairing is treated dynamically in the standard BCS approximation with time-dependent pairing tensor and single-particle occupation probabilities.With the inclusion of pairing correlations,various time-dependent phenomena in open-shell nuclei can be described more realistically.The model is applied to the description of saddle-to-scission dynamics of induced fission.The generalized TD-GCM charge yields and total kinetic energy distribution for the fission of 240Pu,are compared to those obtained using the standard time-dependent density functional theory(TD-DFT)approach,and with available data.展开更多
Based on the beyond-mean-field Skyrme-Hartree-Fock model,impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and^(29)ΛSi are investigated,respectively.Four cases,in which theΛhyperon occupies the s...Based on the beyond-mean-field Skyrme-Hartree-Fock model,impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and^(29)ΛSi are investigated,respectively.Four cases,in which theΛhyperon occupies the single-particle orbitals L[000]1+/2,L[110]1-/2,L[101]3-/2 and L[101]1-/2,are focused.In each case,the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of theΛhyperon on the nuclear core.Beside the shrinkage effect that is induced by theΛhyperon occupying the sΛorbital,it is found that theΛhyperon on the pΛorbital,L[110]1-/2,drives the nuclear core toward a prolate shape,while the ones on the other two pΛorbitals,L[101]3-/2 and L[101]1-/2,drive the nuclear core toward an oblate shape.The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.展开更多
The intrinsic vibrational motion and the rotational behavior of the scissors mode in well deformed nuclei are investigated with an angular-momentum-projected approach,which is interpreted as a generator-coordinatemeth...The intrinsic vibrational motion and the rotational behavior of the scissors mode in well deformed nuclei are investigated with an angular-momentum-projected approach,which is interpreted as a generator-coordinatemethod with the generator coordinates corresponding to the degrees of freedom of interest.The picture of the intrinsic and rotational motion of the scissors mode is illustrated from the collective wave function within the framework of the generator-coordinate-method.The harmonicity of the scissors vibration is found to arise naturally from the present model but can be disturbed by the Coriolis effect as spin increases.The odd and even spin members of the rotational band based on the scissors mode rotate about different axes perpendicular to each other,leading to the flipping moment of inertia and the consequent splitting behavior that has been suggested previously.展开更多
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
基金Specialized Research Fund for the Doctoral Program of Higher Education (No.20070247002)
文摘According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.
基金This work was supported in part by the Highend Foreign Experts Plan of China,the National Key R&D Program of China(Contract No.2018YFA0404400)the National Natural Science Foundation of China(Grant Nos.12070131001,11875075,11935003,11975031,and 12141501)+1 种基金the High-performance Computing Platform of Peking University,the QuantiXLie Centre of Excellence,a project co-financed by the Croatian Government and European Union through the European Regional Development Fund-the Competitiveness and Cohesion Operational Programme(KK.01.1.1.01.0004)the Croatian Science Foundation under the project Uncertainty quantification within the nuclear energy density framework(IP-2018-01-5987).
文摘The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing correlations.The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weight functions.The particle–hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional,while pairing is treated dynamically in the standard BCS approximation with time-dependent pairing tensor and single-particle occupation probabilities.With the inclusion of pairing correlations,various time-dependent phenomena in open-shell nuclei can be described more realistically.The model is applied to the description of saddle-to-scission dynamics of induced fission.The generalized TD-GCM charge yields and total kinetic energy distribution for the fission of 240Pu,are compared to those obtained using the standard time-dependent density functional theory(TD-DFT)approach,and with available data.
基金supported by the National Natural Science Foundation of China(Nos.11905165,11775081 and 11547044)the Fundamental Research Funds for the Central Universities(Nos.JB160510 and XJS18020).
文摘Based on the beyond-mean-field Skyrme-Hartree-Fock model,impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and^(29)ΛSi are investigated,respectively.Four cases,in which theΛhyperon occupies the single-particle orbitals L[000]1+/2,L[110]1-/2,L[101]3-/2 and L[101]1-/2,are focused.In each case,the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of theΛhyperon on the nuclear core.Beside the shrinkage effect that is induced by theΛhyperon occupying the sΛorbital,it is found that theΛhyperon on the pΛorbital,L[110]1-/2,drives the nuclear core toward a prolate shape,while the ones on the other two pΛorbitals,L[101]3-/2 and L[101]1-/2,drive the nuclear core toward an oblate shape.The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.
基金partly supported by the Fundamental Research Funds for the Central Universities,Lanzhou University(lzujbky-2023-04)the Natural Science Foundation of Gansu Province,China(24JRRA400)the National Natural Science Foundation for Young Scientists of China(11905172)。
文摘The intrinsic vibrational motion and the rotational behavior of the scissors mode in well deformed nuclei are investigated with an angular-momentum-projected approach,which is interpreted as a generator-coordinatemethod with the generator coordinates corresponding to the degrees of freedom of interest.The picture of the intrinsic and rotational motion of the scissors mode is illustrated from the collective wave function within the framework of the generator-coordinate-method.The harmonicity of the scissors vibration is found to arise naturally from the present model but can be disturbed by the Coriolis effect as spin increases.The odd and even spin members of the rotational band based on the scissors mode rotate about different axes perpendicular to each other,leading to the flipping moment of inertia and the consequent splitting behavior that has been suggested previously.
