Numerical Solution of the Spin-1 Heisenberg Antiferromagnetic Chains by Using a Projector Method

An eficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-1 Heisenberg antiferromagnetic chains with linear sizes up to N = 40. We have computed them on chains up to N = 40. We have found that the size-dependence of the ground state energy per site has the form[e₀(N)-e₀]～1/N^5/2, which implies that there is a gap between the ground state and the first excited state. The value of the ground state energy per site as N→ ∞ is e₀ = -1.3996. The direct extrapolation of ΔE(N) also shows that a gap of ΔE = 0.36 exists as N→ ∞.     

Numerical Solution of the spin-3/2 Heisenberg Antiferromagnetic Chains Using a Projector Method

An efficient projector method is used to calculate the energies of the ground state and the first excited state, and hence the energy gap between them, of the spin-3/2 Heisenberg antiferromagnetic chains with linear sizes up to N = 32. For the chains up to N = 8 the exact results are obtained, and for longer chains up to N = 32 they are estimated by imposing on Monte Carlo technique. It is found that the size dependence of the ground state energy per site has the form of [eo(N) - eo] ～ 1/N², and the value of the ground state energy per site as N→∞ is eo = -2.8248. Our results show that the energy gap trends to zero as N→∞, which is consistent with the rigorous proof.     

原子核第一激发能的统计规律

原子核的第一激发态能级是所有激发态能级中最重要的一条能级,在一定程度上可直接反映该核素的稳定性。通过对2 125个核素的第一激发态能级纲图进行统计分析,发现传统幻数位置的第一激发能明显高于邻近核素的第一激发能,亦对应于同位素链、同中子素链上原子核第一激发能最大的核素。对于第一激发能较大且明显偏离传统幻数位置的少量核素,发现都具有同质异位素相似态或为裂变核的混合能级,这些给出的值是否是第一激发态,在理论和实验上仍存在一定的不确定性;而对于原子核第一激发能最大的核素,其自旋宇称为2+的最多（高达42%）。对于中重核区内的偶偶核,其第一激发能与价核子N_pN_n关系明显趋于指数的衰减形式。     

Droplet States in the XXZ Heisenberg Chain

We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions. The ground state of this model, restricted to a sector with a fixed number of down spins, describes a droplet of down spins in an environment of up spins. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We prove that there is a gap in the spectrum above the droplet states. As the XXZ Hamiltonian has a gap above the fully magnetized ground states as well, this means that the droplet states (for sufficiently large droplets) form an isolated band. The width of this band tends to zero in the limit of infinitely large droplets. We also prove the analogous results for finite chains with periodic boundary conditions and for the infinite chain. Received: 5 September 2000 / Accepted: 8 December 2000     

Decay of 1+ states as a new probe of the structure of 0+ shape isomers

The nuclides 98Mo and 100Mo have been studied in photon-scattering experiments by using bremsstrahlung produced from electron beams with kinetic energies from 3.2 to 3.8 MeV. Six electromagnetic dipole transitions in 98Mo and 19 in 100Mo were observed for the first time in the energy range from 2 to 4 MeV. A specific feature in the two nuclides is the de-excitation of one state with spin J = 1 to the 0+ ground state as well as to the first excited 0+ state, which cannot be explained in standard models. We present a model that allows us to deduce the mixing coefficients for the two 0+ shape-isomeric states from the experimental ratio of the transition strengths from the J = 1 state to the 0+ ground state and to the 0+ excited state.     

Spectroscopy of 36Mg: interplay of normal and intruder configurations at the neutron-rich boundary of the "island of inversion"

We report on the first spectroscopy study of the very neutron-rich nucleus (36)(12)Mg24 using the direct two-proton knockout reaction 9Be(38Si,36Mg+gamma)X at 83 MeV/nucleon. The energy of the first excited 2+ state of 36Mg, E(2+(1)=660(6) keV, was measured. The magnitude of the partial cross sections to the ground state and the 2+(1) state is indicative of strong intruder admixtures in the lowest-lying states as suggested by Monte Carlo shell-model calculations.     

LiAl分子基态、激发态势能曲线和振动能级

利用单双激发多参考组态相互作用方法获得了LiAl分子基态X¹∑⁺及七个激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的势能曲线, 通过势能曲线得到各态的平衡核间距R_e, 进而求得绝热激发能和垂直激发能.计算结果表明:c³∑⁺ 电子态是一个不稳定的排斥态, A¹∏态是一个较弱的束缚态, 其余6个电子态均为束缚态; b³∑⁺与 c³∑⁺态之间存在预解离现象; 8个电子态分别解离到两个通道, 即Li(²S)+Al(²P⁰)与Li(²P⁰)+Al(²P⁰). 接着将势能曲线拟合到Murrel-Sorbie解析势能函数形式, 据此获得各态的光谱数据:基态X¹∑⁺的平衡键长为0.2863 nm, 谐振频率为316 cm^-1, 解离能D_e为1.03 eV, 激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的垂直激发能依次为0.27, 0.83, 1.18, 1.14, 1.62, 1.81, 2.00 eV; 解离能依次为1.03, 0.82, 0.26, 排斥态, 1.54, 1.10, 0.93 eV, 相应谐振频率 ω_e为339, 237, 394, 排斥态, 429, 192, 178 cm^-1. 通过求解核运动的薛定谔方程找到了J=0时 LiAl分子7个束缚电子态的振动能级和转动惯量. 关键词： LiAl 光谱常数 势能曲线 振动能级     

超短脉冲激光场中间二氯苯的激发态动力学

利用飞秒时间分辨的飞行时间质谱技术研究了间二氯苯的激发态动力学.间二氯苯分子吸收一个200 nm或者267 nm的光子被抽运到激发态,随后再吸收多个800 nm的光子被电离.实验获得了电离产生的离子质谱信号及其随抽运探测激光延迟时间的变化曲线.在200 nm时,分子被抽运到激发态(π,π*),可观察到三个相互竞争的解离通道的寿命:内转换到排斥态(n,σ*)或者(π,σ*)并发生快速解离,其寿命约(0.15±0.01)ps;内转换到基态的高振动态,能量在基态"热"振动态间弛豫的寿命约为(4.94±0.08)ps;系间窜越到相邻的三重态从而发生预解离过程,其寿命约为(110.09±4.33)ps.在267 nm时,分子被抽运到第一激发态的低振动态,可观察到一个长寿命(约(1.06±0.05)ns)的系间窜越过程.除此之外,在碎片离子信号中还观察到了激发态与基态的高振动态之间的内转换过程.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain

In order to confirm the picture of domain-wall excitations in the hidden antiferromagnetic order of the Haldane phase, the structure of the low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain is studied by a quantum Monte Carlo method. It is confirmed that there exists a finite energy gap between the first- and the second-excited states at k = π as well as between the ground state and the first-excited state at k = π. In the thermodynamic limit, the second-excited state at k = π is separated from the ground state by the gap which is three times as large as the Haldane gap. From the size dependences of the low-lying-excitation energies, the interactions between the elementary excitations in the excited states are concluded to be repulsive.     

The nature of 0 excitations in Er

Lifetimes of excited 0⁺ states in ¹⁶⁶Er have been measured with the (n,n′γ) reaction. The first and second excited 0⁺ states have no significant collective enhancements of their decays, and their properties are suggestive of pair-type excitations rather than those of a β vibration or phonon excitation built on the γ vibration. The third excited 0⁺ state at 1934 keV has an enhanced decay to the ground state band with B(E2; 0₄⁺ → 2_gsb⁺) = 8.8 ± 0.9 W.u., consistent with that expected for a β vibration.     

二氢化钚分子激发态结构的外场效应

采用密度泛函(DFT)方法B3LYP/Gen，在Pu为SDD基组、H为6-311++G^**基组水平上优化得到了分子轴方向不同电偶极场(-0.005—0.005a.u.)作用下，二氢化钚的基态电子状态、几何结构、电偶极矩和分子总能量.在优化构型下用同样的基组采用含时密度泛函(TDDFT)方法(TD-B3LYP)研究了同样外电场条件下对二氢化钚的激发能和振子强度的影响.计算结果表明，分子几何构型与电场大小和方向呈现较强的依赖，电场强度增加基态偶极矩随电场强度线性增加，H-Pu-H的角度线性减小，分子总能量线性减小；激发能随电场强度增加而减小，且对电场方向的依赖呈现近似对称性，满足Grozema关系.电场对振子强度的影响比较复杂，但仍满足跃迁选择定则. 关键词： 二氢化钚 激发态 电偶极场 TD-DFT     

Bound magnetopolaron in delta GaAs quantum dot under Rashba effect

This paper presents the influence of Rashba effect on bound magnetopolaron in delta quantum dot. The unitary transformation method and the variational method of Pekar type have been used to derive the ground and first excited state energy. Due to Rashba effect, the ground and first excited states each split into two energies (spin up and down). Results show that the split up(down) energy of ground and first excited states are increasing (decreasing) function of wave vector; the spin splitting of the ground and first excited states are decreasing function of the delta parameter and the increasing function of Rashba parameter. It has also be seen that the splitting of energies levels occur around the value $q=0$. The density of probability has its minimum value at the center of the dot while it is maximal at the boundary of the dot. The decoherence has been studied through the Shannon entropy and the results show increase of entropy with time, delta parameter K, and cyclotron frequency ω_c. It also suggests a way to encrypt information and to control decoherence.     

Non-yrast states of 132Ce polutated in β-decay

Non-yrast low spin states of the nucleus ¹³²Ce were studied by means of γ-spectroscopy following the β-decay of the ground and medium spin isomeric states of ¹³²Pr. The activity was produced with the reaction ¹¹⁷Sn(¹⁹F,4n) ¹³²Pr at the Cologne FN TANDEM accelerator. The γγ coincidences and singles spectra were measured with the OSIRIS cube spectrometer. The β-decay of ¹³²Pr populates states with spins up to 6ħ and excitation energies up to 4.4 MeV in ¹³²Ce. Besides ground and quasi-gamma bands, an excited band based on the 0₂⁺ state and many other low-lying states were observed. The γγ angular correlations were analyzed to assign spins and parities to the excited states, and to determine the multipolarities of the γ-transitions. We found dominant E2 transitions in the quasi-gamma band and from the quasi-gamma band to the ground band. The experimental data are compared with calculations using the Interacting Boson Model (IBM). Good agreement is reached in the vicinity of the O(6) limit.     

Atomic-scale contrast mechanism in atomic force microscopy

We present numerical results for the ground state and low-lying excited states of theS=1 antiferromagnetic Heisenberg chain with exchange and single-ion anisotropy for free boundary conditions and up to 16 spins. The excitation spectrum in the Néel and Haldane phases is interpreted successfully in terms of domain walls (i.e. solitons) only. We present evidence that the transition between these two phases is characterized by the condensation of the lowest soliton modes. The difference between periodic and open boundary conditions, in particular the relevance of open boundary conditions for numerical calculations on finite chains, is discussed.     

链间耦合对聚乙炔多链体系中电子极化子再激发态的影响

从拓展紧束缚模型出发,研究了链间耦合对反式聚乙炔多链体系中电子极化子再激发态的晶格位形、净电荷密度、局域能级波函数和态密度的影响。结果发现：对于两条链体系,当链间耦合很小（eV）时,注入到系统中的电子只会在第一条链上诱发产生一个晶格缺陷,形成电子极化子再激发态,这和单链体系是一致,而第二条链仍是二聚化基态。随着链间耦合的增大,第一条链上缺陷的局域度减少而第二条链上的缺陷局域度相应增加,直至两条链上的位形相同。对于多条链（5条链和6条链）体系,当耦合很小（0.05eV）时,电子极化子再激发态也只会存在于一条链上,当链间耦合较强时,极化子再激发态会在链间层次性地扩展开来,并不会出现多条链位形相同。从两条链的能级图上可以看到随着链间耦合的增大,体系的带隙不断的增大和电子态密度显示的是完全吻合的,体系的导电性减弱。通过分析两条链体系在eV和eV的能级态密度,发现链间耦合越强,则中间局域能级的态密度越小,最后没有中间局域态。     

纤锌矿GaN/AlxGa1-xN量子阱中极化子能量

采用LLP变分方法研究了纤锌矿GaN/Al_xGa_1-xN量子阱材料中极化子的能级,给出极化子基态能量、第一激发态能量和第一激发态到基态的跃迁能量与量子阱宽度和量子阱深度变化的函数关系。研究结果表明,极化子基态能量、第一激发态能量和跃迁能量随着阱宽L的增大而开始急剧减小,然后缓慢下降,最后接近于体材料GaN中的相应值。基态能量和第一激发态到基态的跃迁能量随着量子阱深度的增加而逐渐增加,窄阱时这一趋势更明显。纤锌矿氮化物量子阱中电子-声子相互作用对能量的贡献比较大,这一值(约40meV)远远大于闪锌矿(GaAs/Al_xGa_1-xAs)量子阱中相应的值(约3meV)。因此讨论GaN/Al_xGa_1-xN量子阱中电子态问题时应考虑电子-声子相互作用。     

Quantum entanglement in a soluble two-electron model atom

We investigate the entanglement properties of bound states in an exactly soluble two-electron model, the Moshinsky atom. We present exact entanglement calculations for the ground, first and second excited states of the system. We find that these states become more entangled when the relative inter-particle interaction becomes stronger. As a general trend, we also observe that the entanglement of the eigenstates tends to increase with the states’ energy. There are, however, “entanglement level-crossings” where the entanglement of a state becomes larger than the entanglement of other states with higher energy. In the limit of weak interaction, we also compute (exactly) the entanglement of higher excited states. Excited states with anti-parallel spins are found to involve a considerable amount of entanglement even for an arbitrarily weak (but non zero) interaction. This minimum amount of entanglement increases monotonically with the state’s energy. Finally, the connection between entanglement and the Hartree-Fock approximation in the Moshinsky model is addressed. The quality of the ground-state Hartree-Fock approximation is shown to deteriorate, and the corresponding correlation energy to grow, as the entanglement of the (exact) ground state increases. The present work goes beyond previous related studies because we fully take into account the identical character of the two constituting particles in the entanglement calculations, and provide analytical, exact results both for the ground and the first few excited states.     

Isomerism in Ag and non-yrast levels in Pd and Rh, studied in β decay

The β decay of ⁹⁶Ag (Z=47,N=49) was investigated by measuring positrons, X rays as well as β-delayed protons and γ rays. The γ radiation was studied by means of germanium detectors and a NaI total-absorption spectrometer. Two β-decaying isomers in ⁹⁶Ag were established with half-lives of 4.40(6) and 6.9(6) s and tentative spin–parity assignments of (8⁺) and (2⁺), respectively. For both isomers, the intensities of β transitions to low-lying levels of ⁹⁶Pd (Z=46,N=50) and β-delayed proton decays to levels in ⁹⁵Rh (Z=45,N=50) were measured. Several new ⁹⁶Pd levels were firmly established. The level energies, their γ decays and the Gamow–Teller decay of ⁹⁶Ag are compared to shell-model predictions. A new low-lying level in ⁹⁵Rh was found at 680 keV excitation energy. Through a comparison with low-lying states of N=50 isotones, this level is interpreted as the first excited 7/2⁺ state built on the proton 9/2⁺ ground state. The assignments of further excited states in ⁹⁵Rh are discussed.     

Fourier Transform Spectrum and Term Values for the CO-Stretching Mode of CD3OH Methanol

The Fourier transform infrared (FTIR) spectrum of the CO-stretching fundamental band of CD₃OH has been recorded at a resolution of 0.002 cm^-1. Assignments are reported for 35 subbands in the n = 0 ground torsional state, covering K = 0 to 9 for all torsional symmetries plus K = 10 A, and 12 assorted A and E subbands in the n = 1 first excited torsional state ranging from K = 0 up to K = 5. The subband wavenumbers have been fitted to J(J + 1) power-series energy expansions to obtain subband origins and a compact representation of the spectral observations. With the use of known ground-state energies, CO-stretch energy term values have been determined and tabulated. Least-squares fitting of the subband origins to a fourth-order Hamiltonian model for the CO-stretch mode is discussed.