Low-lying states of heavy nuclei within the nucleon pair approximation

In this article we perform systematic calculations on low-lying states of 33 nuclei with A=202-212, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one J=4 valence neutron pair, and one J=4,6,8 valence proton pair, in addition to the usual S and D pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and E2 transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained.

A novel approach to isoscaling: The role of the order parameter m = N-f-Z(f)/A(f)

Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m(6)) theory. In this model m = N-f-Z(f)/A(f) is the order parameter, a consequence of (one of) the symmetries of the nuclear Hamiltonian. Within this framework we show that isoscaling depends mainly on this order parameter through the 'external (conjugate) field' H. The external field is just given by the difference in chemical potentials of the neutrons and protons of the two sources. To distinguish from previously employed isoscaling relationships, this approach is dubbed: m-scaling. We discuss the relationship between this framework and the standard isoscaling formalism and point out some substantial differences in interpretation of experimental results which might result. These should be investigated further both theoretically and experimentally. (C) 2010 Elsevier B.V. All rights reserved.

二维无关联振子系统的量子化及能谱中长程关联的理论分析

量子经典对应是人们一直关心的基本问题．早期的WKB量子论及其推广EBK理论分别给出了一维及多维可积系统周期轨道的作用量量子化条件，但是，这些理论都没有明确的给出周期轨道与量子能级之间的对应关系．另一方面，近年来，人们在数值计算中发现量子能谱中存在着与周期轨道有紧密联系的长程关联，但是目前对长程关联的研究大多局限于数值计算，其背后的动力学原因有待进一步的探讨。应用二维无关联振子系统具有的标度不变性，对量子态密度进行Fourier变换，得到二维无关联振子系统的回归函数．另一方面，在有理环面上积分Hamiltonian运动方程，数值计算给出二维无关联四次振子系统的半经典回归谱。对二维无关联四次振子系统的量子回归谱和经典回归谱进行比较，量子和经典回归谱中的峰(显示了能级之间存在着长程关联)的位置大致一定验证了Berry-Tabor求迹公式的有效性。从可积系统的Be：rry-Tabor公式出发，导出了二维可积系统周期轨道作用量量子化条件，考虑有理环面上周期轨道必须满足的周期性条件，找到了量子能级与经典周期轨道之间的对应关系．这一对应关系表明，二维无关联振子系统的一组能级与一组周期轨道之间存在着一一对应关系。这组能级对应的周期轨道具有相同的拓扑，但每条周期轨道对应的系统能量等于它所对应的量子能级。进一步的，我们用二维无关联振子系统的量子经典对应关系去分析量子能谱中的长程关联。分析表明，当二维无关联振子系统回归函数中的作用量取某一系统能量下某一周期轨道的作用量的值时，那些与这一周期轨道拓扑相同的周期轨道对应的量子能级对回归函数的贡献相干。这些具有相同拓扑的周期轨道对应的量子能级间存在着长程关联。

应用IBM-2对混合对称态的一些探讨

本文应用相互作用玻色子模型（IBM-2）的理论对混合对称态作了一些讨论。首先给出IBM-2普遍的和一种简化的Hamiltonian的Casimir算子展开式，通过对几种简化Hamiltonian动力学对称性和F-旋对称性的分析，并且考虑最主要的核子相互作用，选择了一种较理想的简化Hamiltonian。其次，用最小二乘法提取了部分U（5）类核和O（6）类核的玻色子等效电荷，并用此计算了它们的混合对称态的电磁跃迁几率。最后，用数值方法系统地计算和分析了~(150,152,154)Gd核混合对称态的能级和电磁跃迁几率，得到~(150)G和~(152,154)Gd核最低能量的混合对称态分别为2_M~+和I_M~+。另外，还详细讨论了Majorana相互作用参数对能级和电磁跃迁几率的影响

Syntheses, structures, and magnetic properties of two novel three-dimensional frameworks built from M4O4 cubanes and dicyanamide bridges

Two novel coordination polymers Ni-4(CH3O)(4)(CH3OH)(4)(dca)(4) (1) and Co-4(CH3O)(4)(CH3OH)(4)(dca)(4) (2) have been synthesized by solvethermal reaction. X-ray single-crystal analysis reveals that the two complexes are isostrutural and possess 3D frameworks that are built from the M4O4(M= Ni (1) and Co (2)) cubanelike building blocks linked by dicyanamide (dca) bridges. The temperature dependence of the magnetic susceptibility was measured and the DC experiment data were fitted using the Heisenberg spin Hamiltonian.

Synthesis, crystal structure, and magnetic properties of {[Cu(oxbe)]Mn(H2O)[Cu(oxbe)(DMF)]}(n)center dot nDMF center dot nH(2)O: From dissymmetrical mononuclear entities to a 3D heterometallic supramolecular coordination polymer

Self-assembly of the building block [Cu(oxbe)](-) with Mn(II) led to a novel coordination polymer {[Cu(oxbe)]Mn(H2O)(Cu(oxbe)(DMF)]}(n).nDMF.nH(2)O, where H(3)oxbe is a new dissymmetrical ligand N-benzoato-N'-(2-aminoethyl)-oxamido and DMF = dimethylformamide. The crystal forms in the triclinic system, space group P(1)over-bar, with a = 9.260(4) angstorm, b = 12.833(5) angstrom, c = 15.274(6) angstrom , alpha = 76.18(3)degrees, beta = 82.7(3)degrees, gamma = 82.31(3)degrees, and Z = 2. The crystal structure of the title complex reveals that the two-dimensional bimetallic layers are constructed of (CuMnII)-Mn-II-Cu-II chains linked together by carboxylate bridge and hydrogen bonds help to produce a novel three-dimensional channel-like structure. The magnetic susceptibility measurements (5-300 K) were analyzed by means of the Hamiltonian (H)over-cap = -2J(S)over-cap (Mn)((S)over-cap(Cu1) + (S)over-cap(Cu2)), leading to J = -17.4 cm(-1).

Vibrational spectra and structure of zinc phthalocyanine

Semi-empirical molecular orbital calculations using PM3 Hamiltonian were employed to determine qualitative assignments of the vibrational spectrum of zinc phthalocyanine (ZnPc). The assignments are from the potential energy distribution calculations in the normal coordinate analysis and optimized geometry in the PM3 calculations. The structure of the ZnPc molecule is also deduced. (C) 1999 Elsevier Science B.V. All rights reserved.

地震波场模拟及叠前深度偏移的李群方法

The processes of seismic wave propagation in phase space and one way wave extrapolation in frequency-space domain, if without dissipation, are essentially transformation under the action of one parameter Lie groups. Consequently, the numerical calculation methods of the propagation ought to be Lie group transformation too, which is known as Lie group method. After a fruitful study on the fast methods in matrix inversion, some of the Lie group methods in seismic numerical modeling and depth migration are presented here. Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method. Under the frame of Hamiltonian, the propagation of seismic wave is a symplectic group transformation with one parameter and consequently, the numerical calculation methods of the propagation ought to be symplectic method. After discrete the wave field in time and phase space, many explicit, implicit and leap-frog symplectic schemes are deduced for numerical modeling. Compared to symplectic schemes, Finite difference (FD) method is an approximate of symplectic method. Consequently, explicit, implicit and leap-frog symplectic schemes and FD method are applied in the same conditions to get a wave field in constant velocity model, a synthetic model and Marmousi model. The result illustrates the potential power of the symplectic methods. As an application, symplectic method is employed to give synthetic seismic record of Qinghai foothills model. Another application is the development of Ray+symplectic reverse-time migration method. To make a reasonable balance between the computational efficiency and accuracy, we combine the multi-valued wave field & Green function algorithm with symplectic reverse time migration and thus develop a new ray+wave equation prestack depth migration method. Marmousi model data and Qinghai foothills model data are processed here. The result shows that our method is a better alternative to ray migration for complex structure imaging. Similarly, the extrapolation of one way wave in frequency-space domain is a Lie group transformation with one parameter Z and consequently, the numerical calculation methods of the extrapolation ought to be Lie group methods. After discrete the wave field in depth and space, the Lie group transformation has the form of matrix exponential and each approximation of it gives a Lie group algorithm. Though Pade symmetrical series approximation of matrix exponential gives a extrapolation method which is traditionally regarded as implicit FD migration, it benefits the theoretic and applying study of seismic imaging for it represent the depth extrapolation and migration method in a entirely different way. While, the technique of coordinates of second kind for the approximation of the matrix exponential begins a new way to develop migration operator. The inversion of matrix plays a vital role in the numerical migration method given by Pade symmetrical series approximation. The matrix has a Toepelitz structure with a helical boundary condition and is easy to inverse with LU decomposition. A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix. The major merit of LU decomposition with spectral factorization (SF Decomposition) is its efficiency in dealing with a large number of matrixes. After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table. However, the relationship among arrays is ignored in this method, which brings errors in decomposition method. Especially for numerical calculation in complex model, the errors is fatal. Direct elimination method can give the exact LU decomposition But even it is simplified in our case, the large number of decomposition cost unendurable computer time. A hybrid method is proposed here, which combines spectral factorization with direct elimination. Its decomposition errors is 10 times little than that of spectral factorization, and its decomposition speed is quite faster than that of direct elimination, especially in dealing with a large number of matrix. With the hybrid method, the 3D implicit migration can be expected to apply on real seismic data. Finally, the impulse response of 3D implicit migration operator is presented.