9 Be Low-Lying Spectrum Within a Three-Cluster Model

The energy spectrum of ⁹Be is studied within the cluster model ???+ ???+?n. Configuration space Faddeev equations are applied to calculate energies of the bound state and resonances. LS coupling is used for partial wave analysis. The ⁹Be low-lying levels are classified as members of spin-flip doublets, in compliance with the total orbital momentum of the ???+????+?n system. The ⁹Be spectral data are well reproduced by the proposed model.     

Borromean Bound States

The Hall-Post inequalities relating N-body to (N − 1)-body energies of quantum bound states are applied to delimit, in the space of coupling constants, the domain of Borromean binding where a composite system is bound while the smaller subsystems are unbound.     

超变形核的转动模型

为处理超变形核的转动谱,提出了一个简单的转动模型,即:冻结振动自由度,把超变形核看成是一个刚性转子．将转动哈密顿量在轴对称陀螺波函数所张开的空间中对角化时,进一步考虑了Ｓｉｇｎａｔｕｒｅ为好量子数,重新计算了Ａ～１９０区偶偶核的超变形带,自旋指定与ａｂ公式自旋指定仍然一致．并计算了Ａ～１５０区１５２Ｄｙ的超变形带,结果也与实验值拟合得很好,但自旋指定与ａｂ公式差异较大.To deal with the SD bands, a single rotational model is proposed, i . e. freeze the degree of vibrational freedom, and regard the SD nuclei as a rigid rotor. Also, the Signature is considered to be a good quantum number . 10 SD bands were calculated, all of the assigned nuclear spins are equal to those determined by ab formula. 190 Hg and 152 Dy were also calculated, but the results of assigned nuclear spins are different to the ones of ab formula.     

Relativistic Borromean states

In this work,the existence of Borromean states is discussed for bosonic and fermionic cases in both therelativistic and non-relativistic limits from the 3-momentum shell renormalization.With the linear bosonic model,we check the existence of Efimov-like states in the bosonic system.In both limits a geometric series of singularities is found in the 3-boson interaction vertex,while the energy ratio is reduced by around 70%in the relativistic limit because of the anti-particle contribution.Motivated by the quark-diquark model in heavy baryon studies,we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale.This may indicate a special baryonic state of light quarks in high energy quark matter.In other cases,trivialresults are obtained as expected.In the relativistic limit,for both bosonic and fermionic cases,potential Borromean states are independent of the mass,which means the results would also be valid even in the zero-mass limit.     

Borromean rings and linkings

For links of 3 components, such as Borromean rings, which escape the detection of Gauss linking, we define and compute combinatorically and explicitly the higher linking. And as in perturbative quantum field theory, this higher linking is presented as a sum of Chern–Simons–Witten configuration space integrals.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

Tensor-Optimized Few-Body Model for s-Shell Nuclei

We propose a tensor-optimized few-body model (TOFM) in the few-body framework with bare nucleon–nucleon interaction. The physical concept of TOFM comes from the tensor-optimized shell-model (TOSM), which is applicable for the study of medium and heavy nuclei. The TOSM wave function describes the deuteron-like tensor correlation and provides a good reproduction of the binding energy with the bare nucleon–nucleon interaction. Using the spirit of the TOSM approximation, we show the performance of TOFM for s-shell nuclei. It is found that the TOFM can account for the contribution of the tensor interaction very well and almost reproduces the total energy and various energy components as compared with rigorous few-body calculations. The relative correlation function is also provided to improve the performance of TOSM for the study of heavy nuclei.     

轻丰中子核的壳模型计算

对9≤A≤14,3≤Z≤5的核进行了壳模型计算.以⁸He作为core,选用修正的表面δ相互作用(MSDI)作为残余相互作用,挑选了24个实验能谱数据,定出了MSDI的参数和单粒子能量,并计算了结合能、低激发谱、电磁性质等,得到与实验较符合的结果.并着重讨论了¹¹Be的宇称反转和halo结构的物理机理.计算程序为OXBASH.     

Solving Three-Cluster OCM Equations in the Faddeev Formalism

Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three--particle model interacting via the deep potential by Buck, Friedrich, and Wheatley is investigated.     

Occurrence conditions for two-dimensional Borromean systems

Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, biphoton ququarts can display different features in dependence on whether experiments involve purely polarization or (alternatively) polarization-frequency measurements. If in experiments one uses only polarization measurements, the originally pure states of ququarts can be seen as mixed biphoton polarization states. Features of such states are described and discussed in details. Schemes of coincidence measurements for reconstruction of the ququart’s parameters are suggested and described.     

Tensor Optimized Few-body Model for Light Nuclei

The tensor interaction plays an important role to determine the nuclear structure. In this study, we propose a tensor-optimized few-body model (TOFM) in the few body framework with bare nucleon-nucleon interaction. In TOFM, the configurations caused by the one-operation of the tensor operator to the S-wave ground state are introduced in the total wave function. It is shown that TOFM reproduces more than 90 % of the total binding energy and the tensor correlation of the few-body results for s-shell nuclei. We further apply TOFM to the p-shell, as ⁵He. We work out the variational calculation for ⁵He and discuss the structure difference between two resonance states 3/2^? and 1/2^?. In particular, we shed light on the roles of the tensor interaction in two states, such as the LS splitting energy.     

Borromean Triads of Phonons in a Magnet

Doklady Physics - The results of experimental observation of coupled excitations of three pairwise noninteracting phonons, two of which belong to continuous and the third to discrete acoustic...     

The Quadrupole Response of Borromean Bosonic Trimers

The inelastic response of a Borromean trimer composed of three identical bosons is explored. To this end we use the quadrupole approximation as the excitation mechanism of the bosonic system from its ground state. We utilize the hyperspherical-harmonics expansion to solve the Schroedinger equation and the Lorentz integral transform method to calculate the reaction. It is found that the magnitude of the response function and corresponding sum rules increase as a power law when approaching the three-body threshold. It is also found that this increase is governed by unnatural exponents.     

Nonexistence of Large Nuclei in the Liquid Drop Model

We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.     

Ground State Properties of Superheavy Nuclei in Macroscopic-Microscopic Model

The ground state properties of superheavy nuclei are systematically calculated by the macroscopic- microscopic （MM） model with the Nilsson potential. The calculations well produced the ground state binding energies, α-decay energies, and half lives of superheavy nuclei. The calculated results are systematically compared with available experimental data. The calculated results are also compared with theoretical results from other MM models and from relativistic mean-field model. The calculations and comparisons show that the MM model is reliable in superheavy region and that the MM model results are not very sensitive to the choice of microscopic single-particle potential.