Structure of 6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, <'6>He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.     

一级近似下的单模激光增益模型随机共振

把周期信号输入单模激光,对激光增益模型中的乘法噪声项取一级近似通过计算相关函数得到功率谱,发现输出信号是洛伦兹型的.信噪比随抽运噪声强度和量子噪声强度的变化均出现随机共振,但共振峰对应的噪声强度比零级近似下的小.     

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.     

Manifestations of a dineutron cluster in elastic α 6He scattering

A consistent theoretical analysis of elastic α ⁶He scattering is performed with allowance for the correction associated with the exchange of a dineutron cluster. It is shown that the inclusion of the exchange mechanism, along with that of potential scattering, makes it possible to reproduce the measured cross section over the entire range of the ⁶He scattering angle. Concurrently, one can also obtain information about the spatial distribution of the dineutron cluster and the α particle in the ground state of the ⁶He nucleus.     

ΛΛ 6 hypernucleus in α + 2Λ cluster model

The binding energy of the double hypernucleus _ΛΛ ⁶ is calculated in α + 2Λ cluster model using the method of translation invariant basis TIMO. As regards the required interaction potentials we use a density dependent effective ΛN force and a gaussian form for ΛΛ potential. With these interactions a very reasonable value ofB _ΛΛ is obtained if the oscillator states up to the excitation quantum numberN=12 are taken into account in the expansion of wavefunction of the hypernucleus. This value ofN is much smaller than that obtained in an earlier study. This lowering inN value is attributed to a much better choice of ΛN potential used in the present study.     

关联对的结构

利用了类似于H–F的方法来自洽地确定S对(和D对)的结构,此外,为了避免因辛弱数混合而产生的伪态困难,改进了S对的定义并用不成对粒子算符来构造D对,以使它们相互独立.     

6Li formfactors in the refined cluster model

A soft core central potential is used to calculate independently⁶Li ground state and excited state wave functions in the refined cluster model. Charge density, elastic formfactor and transition formfactor to the 3⁺ state are derived and agree reasonably well with experiment.     

Electronic Structure of Helium Atom in a Quantum Dot

Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method.To be specific,precise energy eigenvalues of bound 1sns(~1S~e)(n=1-6)states and the resonance parameters i.e.positions and widths of~lS~e states due to 2sns(n=2-5)and 2pnp(n=2-5)configurations of confined helium below N=2 ionization threshold of He~+have been estimated.The two-parameter(Depth and Width)finite oscillator potential is used to represent the confining potential due to the quantum dot.It has been explicitly demonstrated that the electronic structural properties become sensitive functions of the dot size.It is observed from the calculations of ionization potential that the stability of an impurity ion within a quantum dot may be manipulated by varying the confinement parameters.A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.     

6He中t+t结构的实验研究

在25MeV/u ⁶He轰击⁹Be靶的反应中,用探测器望远镜测得氚碎片,得到了5个角度的能谱,经过仔细的分析取得了高能直接破碎成分的角分布.利用Serber模型进行了破碎反应的理论计算,证实了实验中高能成分的t来自于⁶He的直接破碎反应.利用Fermi破碎模型计算了⁶He中各破碎反应道基于相空间的百分比产额,进而估算出⁶He初态中t+t结构的概率约占1/3, 而⁴He核心加价中子的组态约占2/3.     

Structure of the <Superscript>6</Superscript>He nucleus in the three-particle model

The properties of the ⁶He nucleus were investigated in a three-particle approximation (a alpha-particle cluster plus two neutrons) on the basis of the variational approach by using a Gaussian basis. For nn and nα interactions, potentials that make it possible to describe S-wave phase shifts for elastic scattering and, simultaneously, to reproduce faithfully the energy and the size of the ⁶He nucleus were proposed. Characteristic structural features of this nucleus that are manifested in the density distributions, elastic form factor, pair correlation functions, and momentum distributions of particles constituting the ⁶He nucleus in the three-particle model were revealed.     

Effective diffusion in a stochastic velocity field

Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative space-time correlated noise.     

Tiling problems and undecidability in the cluster variation method

In cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small, finite subsystem (cluster), approximations being made for the influence of the surrounding system. In this context we study, for translation-invariant classical lattice systems, the conditions under which a state for a cluster admits an extension to a global translation-invariant state. This extension problem is related to undecidable tiling problems. The implication is that restrictions of global translation-invariant states cannot be characterized purely locally in general. This means that there is an unavoidable element of uncertainty in the application of a cluster approximation.     

Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems

We have examined the validity of the time-dependent variational approximation (TDVA) to the Gaussian wavepacket method (GWM) for quantum double-well (DW) systems, by using the quasi-exact spectral method (SM). Comparisons between results of wavefunctions, averages of position and momentum, the auto-correlation function, and an uncertainty product calculated by SM and TDVA have been made. It has been shown that a given initial Gaussian wavepacket in SM is quickly deformed at t>0$t>0$ where a wavepacket cannot be expressed by a single Gaussian, and that assumptions on averages of higher-order fluctuations in TDVA are not justified. These results cast some doubt on an application of TDVA to DW systems. Gaussian wavepacket dynamics in anharmonic potential systems is studied also.     

Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz

We report a benchmark calculation for the Lipkin model in nuclear physics with a variational quantum eigensolver in quantum computing. Special attention is paid to the unitary coupled cluster (UCC) ansatz and structure learning (SL) ansatz for the trial wave function. Calculations with both the UCC and SL ansatz can reproduce the ground-state energy well; however, it is found that the calculation with the SL ansatz performs better than that with the UCC ansatz, and the SL ansatz has even fewer quantum gates than the UCC ansatz.     

基于变分方法的有限区域风场分解与重构I: 理论框架和仿真实验

众所周知, 风场分解与重构最有效的方法就是引入速度势和流函数, 其一般通过求解两个Poisson 方程得到. 由于速度势和流函数在边界上的耦合性质,有限区域风场分解是不唯一的, 这对风场分解带来了很大困难. 本文采用变分伴随结合正则化方法来克服风场分解的不唯一性, 其核心是把速度势和流函数的边值作为控制变量来反演. 目标泛函由两部分组成, 一是衡量重构风场误差大小的观测项; 二是保证风场分解问题适定的正则化项, 其目的在于寻求具有气象意义的稳定正则化解. 数值试验结果表明, 在正确选取正则化参数后, 利用变分伴随结合正则化方法进行有限区域风场分解与重构是有效可行的.     

单模非线性光学系统的弛豫速率与随机共振

应用变分法研究了一个单模非线性光学系统的弛豫速率对噪声强度的依赖性，并由线性响应理论考察了该系统的随机共振行为.研究结果表明当系统没有偏置时，单稳与多稳情形下的松弛速率对噪声强度的依赖性表现出很大的不同.揭示了对称的一维单稳系统中的随机共振现象，并针对一维单稳系统中随机共振存在的一般条件进行了分析. 关键词： 弛豫速率 随机共振 变分法 线性响应理论     

Consistent relations in the method of reducibility in the cluster variation method

A redundancy is noted in the set of Lagrange multipliers—effective fields and effective interactions—used in the expressions of the reduced density matrices given by Morita⁽⁴⁾ in some problems with less symmetry⁽⁶⁾. The expressions of the reduced density matrices without this redundancy are given. An argument showing that a certain expression of the free energy in terms of the Lagrange multipliers is stationary with respect to the variations of these is presented.