Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003     

n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

会聚厄米-双曲余弦高斯光束的光强分布和焦移

 基于厄米-双曲余弦高斯光束通过无光阑限制薄透镜聚焦的解析传输公式，研究了厄米-双曲余弦高斯光束聚焦区域的光强分布，并对光束的焦移进行了分析，讨论了偏心参数对光强主极大位置的影响。结果表明：TEM₁₁模厄米-双曲余弦高斯光束的相对焦移（绝对值）随偏心参数和菲涅尔数的减小而增大，菲涅尔数较大时相对焦移趋于零。TEM₂₂模光束在偏心参数小于0.54时，轴外与轴上光强极大值的比值大于1，此时光强主极大在轴外，偏心参数大于0.54时则相反；在偏心参数等于0.54时比值为1，此时光束有两个主极大，偏心参数愈大光强愈集中于轴上。使用LW法和GH法得到的TEM₂₂模光束的相对焦移（绝对值）随偏心参数和菲涅尔数的变化规律与TEM₁₁模光束一致，但相同参数下使用这两种方法得出的具体结果不同。     

The design of molecules containing planar tetracoordinate carbon

A novel preference for planar tetracoordination was observed over the conventional tetrahedral arrangement in a new series of C₅H₂, C₅H₄, C₅H₄^1+/2+ and related compounds. The stability of these molecules is assessed with the ring-opening barriers, HOMO-LUMO gap, singlet-triplet energy differences and nucleus independent chemical shift values.     

A Possibility for Studying Gravitational Properties of the Neutrino

We consider the effect that the gravitational field of a neutrino pulse radiated in the collapse of presupernova nuclei has on the observable optical radiation spectra of atoms at the supernova surface. We show that at the modern level of development of experimental methods, neutrino monitoring supplemented by optical monitoring of supernova candidates provides a unique possibility to check whether the Einstein equivalence principle is satisfied for neutrinos of each of the three types (electron, muon, and tau-lepton) and their antiparticles, to estimate the change of the gravitational potential at the surface of the star at the instant of the neutrino radiation pulse, and to obtain upper limits on the mass values of these neutrinos in a new way.     

Spectroscopic Studies of 1-Aryl-2,2-Dichlorocyclopropanes

Seventeen 1-aryl-2,2-dichlorocyclopropanes were examined by using IR, ¹³C NMR, and mass spectrometry. The data obtained from IR and ¹³C NMR spectra indicate that the bond strength of carbon-chlorine on the cyclopropane ring and the electron density of that carbon depend on the substituent. The mass fragmentation patterns of compounds in this series resemble those of the dibromo analogues. The fragmentation mechanism is proposed to involve the formation of indenium ion through an electrocyclization.     

二茂铁有机锡衍生物的13C,119Sn NMR研究

本文测定了几种二茂铁有机锡衍生物的¹¹⁹Sn,¹³C NMR谱。对其中几种衍生物的¹³C NMR谱进行了归属,从而进一步验证了这类化合物的结构。着重讨论了结构如化合物中取代基X的改变对¹¹⁹Sn化学位移的影响。并对结构如 类化合物N→Sn异侧配位的问题进行了讨论。     

A facile non-oxidative method for synthesizing 1,3-disubstituted pyrroles from pyrrolidine and aldehydes

Reactions of pyrrolidine with 2 equiv of aldehydes without any catalyst in a pressurized vessel at 140–200 °C yielded 1,3-disubstituted pyrroles. -Branched aldehydes gave fairly good yields of the corresponding products by this method, which provides a facile non-oxidative procedure for synthesizing 1,3-dialkylpyrroles from inexpensive pyrrolidine and aldehydes.     

Newby shift ofK=0 rotational bands in odd-odd rare-earths

A data set of 29 experimentally determined Newby shifts in rare-earth nuclei is examined for the reliability of each values. Using this data set, Newby shifts are obtained which are free from the Coriolis and the particle-particle coupling effects. These new empirical values help resolve the failure of a recently proposed rule for the sign of the Newby shift in the {5/2[413]p − 5/2[642]n} configuration of¹⁶⁰Tb and the {5/2[402]p − 5/2[512]n} configuration of¹⁷⁴Lu. Also the Newby shifts are significantly modified in two other cases namely the {1/2[411]p − 1/2[521]n} configuration in¹⁶⁸Tm and the {1/2[541]p − 1/2[521]n} configuration in¹⁷²Lu. Only marginal changes are seen in the rest of the cases in the rare-earth nuclei.