In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)...In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).展开更多
The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory ...The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory with covariant chiral interactions is a promising ab initio approach to describe both nuclear matter and finite nuclei.In the description of finite nuclei with the current RBHF theory,the covariant chiral interactions have to be localized to make calculations feasible.In order to examine the reliability and validity,in this letter,the RBHF theory with local and nonlocal covariant chiral interactions at leading order is applied to nuclear matter.The low-energy constants in the covariant chiral interactions determined with the local regularization are close to those with the nonlocal regularization.Moreover,the RBHF theory using covariant chiral interactions with local and nonlocal regulators provides an equally good description of the saturation properties of nuclear matter.The present work paves the way for the implementation of covariant chiral interactions in RBHF theory for finite nuclei.展开更多
Based on spin-unrestricted hartree fock theory, we present the spin unrestricted multi- configuration time dependent hartree lock theory （UMCTDHF） to describe the electron correlation dynamics of systems interacting...Based on spin-unrestricted hartree fock theory, we present the spin unrestricted multi- configuration time dependent hartree lock theory （UMCTDHF） to describe the electron correlation dynamics of systems interacting with laser field. The positive spin orbitals and the negative spin orbitals are propagated in their own subspace respectively. The spin orbital in the spin-down subspace acts with that in the spin-up subspace by the reduced density matrix and mean field operator. The ground energy is acquired by propagating the trial wave function in the imaginary time by using spin-restricted MCTDHF （RMCTDHF） and UMCTDHF respectively. Then the ionization probabilities and the electrons energies are calculated by using RMCTDHF and UMCTDHF when the laser field is present. The ionization probability calculated with UMCTDHF agrees with the previous theoretical reports very well. The UMCTDHF method is accurate and applicable for open shell system beyond the capability of the RMCTDHF method.展开更多
In order to describe the exotic nuclear structure in unstable odd-A or odd-odd nuclei,the deformed relativistic Hartree Bogoliubov theory in continuum is extended to incorporate the blocking effect due to the odd nucl...In order to describe the exotic nuclear structure in unstable odd-A or odd-odd nuclei,the deformed relativistic Hartree Bogoliubov theory in continuum is extended to incorporate the blocking effect due to the odd nucleon.For a microscopic and self-consistent description of pairing correlations,continuum,deformation,blocking effects,and the extended spatial density distribution in exotic nuclei,the deformed relativistic Hartree Bogoliubov equations are solved in a Woods Saxon basis in which the radial wave functions have a proper asymptotic behavior at large r.The formalism and numerical details are provided.The code is checked by comparing the results with those of spherical relativistic continuum Hartree Bogoliubov theory in the nucleus 19O.The prolate deformed nucleus 15 C is studied by examining the neutron levels and density distributions.展开更多
The deformed relativistic Hartree theory(DRH)is solved both in coordinate space(DRH-c)and in harmonic oscillator basis(DRH-o).Results obtained from these two methods are compared in details.The DRH-c and DRH-o calcula...The deformed relativistic Hartree theory(DRH)is solved both in coordinate space(DRH-c)and in harmonic oscillator basis(DRH-o).Results obtained from these two methods are compared in details.The DRH-c and DRH-o calculations give similar total binding energies,deformation,level structures and radii for nitrogen iso topes,while their descriptions on the density distributions for drip-line nuclei are very different.The large spatiai istributions of nucleon densities,which is crucial to understand a weakly bound system,can only be obtained by DRH-c calculations.This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.展开更多
In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
文摘In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12435006,12435007,12475117,12141501,and 123B2080)the National Key R&D Program of China(Grant No.2024YFE0109803)the National Key Laboratory of Neutron Science and Technology(Grant No.NST202401016)。
文摘The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory with covariant chiral interactions is a promising ab initio approach to describe both nuclear matter and finite nuclei.In the description of finite nuclei with the current RBHF theory,the covariant chiral interactions have to be localized to make calculations feasible.In order to examine the reliability and validity,in this letter,the RBHF theory with local and nonlocal covariant chiral interactions at leading order is applied to nuclear matter.The low-energy constants in the covariant chiral interactions determined with the local regularization are close to those with the nonlocal regularization.Moreover,the RBHF theory using covariant chiral interactions with local and nonlocal regulators provides an equally good description of the saturation properties of nuclear matter.The present work paves the way for the implementation of covariant chiral interactions in RBHF theory for finite nuclei.
文摘Based on spin-unrestricted hartree fock theory, we present the spin unrestricted multi- configuration time dependent hartree lock theory （UMCTDHF） to describe the electron correlation dynamics of systems interacting with laser field. The positive spin orbitals and the negative spin orbitals are propagated in their own subspace respectively. The spin orbital in the spin-down subspace acts with that in the spin-up subspace by the reduced density matrix and mean field operator. The ground energy is acquired by propagating the trial wave function in the imaginary time by using spin-restricted MCTDHF （RMCTDHF） and UMCTDHF respectively. Then the ionization probabilities and the electrons energies are calculated by using RMCTDHF and UMCTDHF when the laser field is present. The ionization probability calculated with UMCTDHF agrees with the previous theoretical reports very well. The UMCTDHF method is accurate and applicable for open shell system beyond the capability of the RMCTDHF method.
基金Supported by the National Science Foundation of China(10771151,10901115, 11126335)the Scientific Research Found of Sichuan Provincial Education Department(10ZB003)the Scientific Research Found of Sichuan Provincial Science and Technology Department(2010JY0057)
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 10875157,10975100,10979066,11105005,11175002,and 11175252,the National Basic Research Program of China(2007CB815000)the Knowledge Innovation Project of Chinese Academy of Sciences(KJCX2-EW-N01 and KJCX2-YW-N32),the Oversea Distinguished Professor Project from Ministry of Education(MS2010BJDX001)the DFG Cluster of Excellence“Origin and Structure of the Universe”(www.universe-cluster.de),and the Supercomputing Center,CNIC of CAS.
文摘In order to describe the exotic nuclear structure in unstable odd-A or odd-odd nuclei,the deformed relativistic Hartree Bogoliubov theory in continuum is extended to incorporate the blocking effect due to the odd nucleon.For a microscopic and self-consistent description of pairing correlations,continuum,deformation,blocking effects,and the extended spatial density distribution in exotic nuclei,the deformed relativistic Hartree Bogoliubov equations are solved in a Woods Saxon basis in which the radial wave functions have a proper asymptotic behavior at large r.The formalism and numerical details are provided.The code is checked by comparing the results with those of spherical relativistic continuum Hartree Bogoliubov theory in the nucleus 19O.The prolate deformed nucleus 15 C is studied by examining the neutron levels and density distributions.
基金Supported in part by the Major State Basic Research Development Program Under Contract No.G2000077407National Natural Science Foundation of China under Grant Nos.19847002 and 19935030.
文摘The deformed relativistic Hartree theory(DRH)is solved both in coordinate space(DRH-c)and in harmonic oscillator basis(DRH-o).Results obtained from these two methods are compared in details.The DRH-c and DRH-o calculations give similar total binding energies,deformation,level structures and radii for nitrogen iso topes,while their descriptions on the density distributions for drip-line nuclei are very different.The large spatiai istributions of nucleon densities,which is crucial to understand a weakly bound system,can only be obtained by DRH-c calculations.This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
基金supported by NSFC(11761082)Yunnan Province,Young Academic and Technical Leaders Program(2015HB028)
文摘In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
