The Role of One Single Lambda Hyperon on Binding Energy Difference of Hypernuclear Mirror Pair

Investigation on isospin symmetry in light Lambda hypernuclei is one of the most important issues in hypemuclear physics.In order to know the influences introduced by a single Lambda hyperon,we study the binding energy difference of mirror hypemuclear pair with mass A = 16,18,28,40,and 42 using a time-odd triaxial relativistic mean field theory.Effects as the spin-orbit interaction,the time-odd component of vector fields,the core polarization,the proton-neutron mass difference,and the center-of-mass energy correction are self-consistently considered.Compared to the reported results of ordinary nuclei,the binding energy difference of mirror hypernuclei shows trivial change.With core polarization modified by an impurity hyperon,the isospin nonconserving effect between proton and neutron is hardly reduced for nuclei in study.     

不同能量下核束缚能的影响

在不同能量下， 利用核束缚能对虚光子四动量的平方项进行修正， 分别计算了Sn核碰撞中核束缚能对反应截面中湮灭项和康普顿散射项及K因子的影响。 结果表明， 核束缚能在小x区域对反应截面中湮灭项和康普顿散射项及K因子的影响明显， 并且能量越低这种影响越显著， 随着x2增大影响逐渐消失。 We made a revision of square of virtual photon four momentum by means of using nuclear bin ding energy formula in different energy， and we also made an accurate calculation for the effect of nuclear binding energy on K factor and Compton term and annihilate term in the Drell Yan process of the Sn Sn collision. The outcome indicates that the effect of nuclear binding energy on the annihilate term and the Compton term is marked in little x region and the effect will become more obvious with decrease of the energy and come to disappear with increase of the x.     

Some Effects on A Single Particle Energies

With the phenomenological Λ-nucleus potentials of Woods-Saxon shape,the effects of the mass-number dependence of the shrinkage,the effective mass mΛ^* and the charge-symmetry breaking (CSB) on the single particle energies are discussed.It is found that the single particle energies are not sensitive to the effective mass mΛ^*.But the radius parameter depended on the mass number (ro(Ac)=r1 r2Ac^-2/3) can substantially improve the results.We also found that CSB effect is significant for heavy hypernuclei with a large neutron excess.     

Effect of Nuclear Binding Energy to K Factor

We modify the square of virtual photon four-momentum by using nuclear binding energy formula, and calculate the effect of nuclear binding energy to K factor and Compton subprocess and annihilate subprocess in A-A collision Drell-Yan process. The outcome indicates that the effect of nuclear binding energy to K factor is obvious in little x region and it would disappear gradually as x increases.     

利用手征SU(3)夸克模型研究轻双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能

在手征SU(3)夸克集团模型下, 通过共振群方法(RGM)计算了双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能. 结果表明, 假定双Λ超核具有双Λ集团和壳心核集团构成的两集团结构, 得到的^6_ΛΛHe超核的结合能与实验值基本吻合, 表明手征SU(3)夸克集团模型不仅能较好地描述重子谱、N-N和Y-N相互作用及轻Λ超核的结合能, 也能较好地描述Y-Y相互作用及双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能, 指出了它们存在的可能性.     

关于结合能公式的一种改进方法与普适的修正公式

将核子间的相互作用简化为核力键,从而根据核力键假设推导出结合能公式中^[1]的体积能项与表面能项;并利用21H的结合能的实验值给出二者的系数值,从而使得结合能公式的参数个数减少了两个.     

The Formation Mechanism and Binding Energy for the Octahedral Central Structure of the He7+ Cluster

The formation mechanism for the octahedral central structure of the He7 cluster is proposed and its totalenergy curve is calculated by the method of a modified arrangement channel quantum mechanics (MACQM). The energyis a function of separation R between two nuclei at the center and an apex of the octahedral central structure. The resultof the calculation shows that the curve has a minimal energy -19.7296 a.u. At R = 2.40 α0. The binding energy of He7 with respect to He 6He was calculated to be 0.6437 a.u. This means that the cluster of He7 may be formed in thestable octahedral central structure with R = 2.40 α0.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Li3 cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou‘s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 a0. The total energy of Li3 when R approaches ∞ has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Li3. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Li3 is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82a0 stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3+ Cluster

The formation mechanism for the equilateral triangle structure of the He3 cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3 with respect to He He He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3 cluster may be formed in the equilateral triangle structure stably by the interaction of He with two heliumatoms.     

The Formation Mechanism and Binding Energy for the Octahedral Central Structure of the He7^＋ Cluster

The formation mechanism for the octahedral central structure of the He7^ cluster is proposed and its total energy curve is calculated by the method of a modified arrangement channel quantum mechanics (MACQM). The energy is a function of separation R between two nuclei at the center and an apex of the octahedral central structure. The result of the calculation shows that the curve has a minimM energy -19.7296 a.u. at R = 2.40α0. The binding energy of He7^ with respect to He^ 6He was calculated to be 0.6437 a.u. This means that the duster of He7^ may be formed in the stable octahedral central structure with R=2.40 α0.     

Formation Mechanism and Binding Energy for Icosahedral Central Structure of He1+3 Cluster

The formation mechanism for the icosahedral central structure of the He1 13 cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between two nuclei at the center and an apex of the icosahedral central structure. The result of the calculation has shown that the curve has a minimal energy -37.5765 (a.u.) at R = 2.70ao. The binding energy of He 13 with respect to He 12He was calculated to be 1.4046 a.u. This means that the cluster of He 13 may be formed in an icosahedral central structure with strong binding energy.     

Formation Mechanism and Binding Energy for Icosahedral Central Structure of He13^＋ Cluster

The formation mechanism for the icosahedral central structure of the He13^ cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between two nuclei at the center and an apex of the icosahedral central structure. The result of the calculation has shown that the curve has a minimal energy -37.5765 (a.u.) at R=2.70ao. The binding energy of He13^ with respect to He^ 12He was calculated to be 1.4046 a.u. This means that the cluster of He13^ may be formed in an icosahedral central structure with strong binding energy.     

Evaluation of Coulomb Energy Difference for Light Mirror Nuclei Using Slater—Type Orbitals

Behavior of the Coulomb energy difference for light nuclei is explained in terms of the different values of the average Coulomb interaction between two particles.Coulomb energy difference according to shell model of light mirror nuclei in the Coulomb and exchange integrals in the formula can be explained with exponential-type wavefunctions.In this study,using the one-center expansion of exponential-type wavefunctions in terms of Slater-type orbitals with the same center,we derived formula for Coulomb energy difference of light mirror nuclei.     

The Binding Energy, Spin-Excitation Gap, and Charged Gap in the Boson-Fermion Model

In this paper, by applying a simplified version of Lieb ‘s spin-refleetion-positivity method, which was recentlydeveloped by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some generalproperties of the boson-fermion Hamiltonian, which has been widely used as a phenomenological model to describe thereal-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couplingV, which represents the spontaneous decay and recombination process between boson and fermion in the model, thepairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermionHamiltonian is always larger than its charged gap, as predicted by the pre-paired electron theory.     

The Binding Energy, Spin－Excitation Gap, and Charged Gap in the Boson－Fermion Model

In this paper, by applying a simplified version of Lieb‘s spin-reflection-positivity method, which was recently developed by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some general properties of the boeon-fermion Hamiltonlan, which has been widely used as a phenomenological model to describe the real-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couping V, which represents the spontaneous decay and recombination process between boson and fermion in the model, the pairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermion Hamiltonian is always larger than its charged gap, as predicted by the pre-palred electron theory.     

The MACQM Calculation for the BInding Energy of the Equilateral Triangle Structure of H3^— Cluster

Considering that the equilateral triangle structure of H3^- cluster can be formed from the interaction of H^- with two hydrogen atoms,a modified arrangement channel quantum mechanics method has been used to calculate the total energy curve for this structure,The result shows that the cureve has a minimal energy-1.6672 a.u.at an internuclear distance of 1.77a0,so its dissociation energy(binding energy)is D(H^- H H)=0.1395,a.u.This means that the cluster H3^- may be formed in an equilateral triangle structure with a bond length of 1.77α0.     

Formation Mechanism and Binding Energy for Regular Tetrahedral Structure of Li4

The formation mechanism for the regular tetrahedral structure of Li4 cluster is proposed. The curve of the total energy versus the separation R between the two nuclei has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of-29.8279 a.u. at R = 14.50 ao. When R approaches infinity the total energy of four lithium atoms has the value of-29.7121 a.u. So the binding energy of Li4 with respect to four lithium atoms is the difference of 0.1158 a.u.for the above two energy values. Therefore the binding energy per atom for Lh is 0.020 a.u., or 0.7878 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, the binding energy per atom of 0.494 eV for Lia and the binding energy per atom of 0.632 eV for Li5 calculated previously by us. This means that the Li4 cluster may be formed stably in a regular tetrahedral structure of side length R = 14.50 ao with a greater binding energy.     

Formation Mechanism and Binding Energy for Regular Tetrahedral Structure of Li4

The formation mechanism for the regular tetrahedral structure of Li4 cluster is proposed. The curve of the total energy versus the separation R between the two nuclei has been calculated by using the method of Gou‘s modified arrangement channel quantum mechanics (MACQM). The result shows that the curve has a minimal energy of-29.8279 a.u. at R=14.50 a0. When R approaches infinity the total energy of four lithium atoms has the value of-29.7121 a.u. So the binding energy of Li4 with respect to four lithium atoms is the difference of 0.1158 a.u.for the above two energy values. Therefore the binding energy per atom for Li4 is 0.029 a.u., or 0.7878 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, the binding energy pcr atom of 0.494 eV for Li3 and the binding energy per atom of 0.632 eV for Li5 calculated previously by us. This means that the Li4 cluster may be formed stably in a regular tetrahedral structure of side length R=14.50 a0 with a greater binding energy.     

Binding energy and fine structure of the He- ion

The variational method using a multiconfiguration wavefunction is carried out on the core-excited state 1s2s2p 4P0 for helium negative ion,including mass polarization and relativistic corrections.Binding energy and fine structure are reported.The results are compared with other theoretical and experimental date in the literature.