量子 deformed W_N代数及其屏蔽流代数

构造了 ｄｅｆｏｒｍｅｄ Ｗ Ｎ 代数的量子理论和与之相对应的量子ｄｅｆｏｒｍ ｅｄ Ｍｉｕｒａ 变换．还研究了 ｄｅｆｏｒｍｅｄ Ｗ Ｎ 代数的屏蔽流代数．     

经典-deformed WN代数

构造了经典-deformed W_N代数,得到了与之相对应的-deformed Miura变换.当畸变参数→0时,该代数将退化为通常的经典W_N代数.关键词：     

Properties of deformed Λ hypernuclei

The properties of Be and B isotopes and the corresponding Λ hypernuclei are studied by using a deformed Skyrme Hartree-Fock approach with realistic nucleonic Skyrme forces, pairing correlations, and a microscopically determined lambda-nucleon interaction based on Brueckner-Hartree-Fock calculations of hypernuclear matter. The results suggest that the core nuclei and the corresponding hypernuclei have similar deformations with the same sign.     

Properties of deformed Λ hypernuclei

The properties of Be and B isotopes and the corresponding Λ hypernuclei are studied by using a deformed Skyrme Hartree-Fock approach with realistic nucleonic Skyrme forces, pairing correlations, and a microscopically determined lambda-nucleon interaction based on Brueckner-Hartree-Fock calculations of     

“Shells” in deformed nuclei

New calculation results based on the shell correction method are described. The results are presented in such a way as to illustrate more clearly many effects of nucleon shells in deformed and spherical nuclei. Some complementary theoretical arguments related to the shell correction method and details of the calculation are given.     

经典李代数Dr上推广的Toda力学系统

根据经典李代数D_r根系的特点构造Laxpair,得到李代数D_r上推广的Toda链(这些链用一组有序整数(m,n)表示,m、n分别表示正、负根的级数),并给出m,n≤3时系统的运动方程、哈密顿量以及泊松括号的具体形式.     

Proton radioactivity — spherical and deformed

The proton drip line defines one of the fundamental limits to nuclear stability. Nuclei lying beyond this line are energetically unbound to the emission of a constituent proton from their ground states. For near-spherical nuclei in the region of the drip line between Z=69 (Tm) and Z=81 (T1), proton decay transition rates have been shown to be well reproduced by WKB calculations using spectroscopic factors derived from a low-seniority shell model calculation [2]. Another approach using spectroscopic factors obtained from the independent quasiparticle approximation has also proved successful in this region [3]. These interpretations have allowed the extraction of nuclear structure information from nuclei well beyond the proton drip line.     

Anharmonicities of γ-vibrations in deformed nuclei

The anharmonicities of γ-vibrations are studied within the multiphonon method in different even-even deformed nuclei where the first K^π = 2⁺ vibrational state appears well below the energy gap: ¹³⁰Ce, ^162–164Dy, ^164–168Er, ¹⁸⁶Os. The anharmonicities previously obtained in ¹⁶⁸Er appear to be a general property of these nuclei.     

Non-singular Brans–Dicke collapse in deformed phase space

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.     

Convergent perturbation theory for a q–deformed anharmonic oscillator

A q–deformed anharmonic oscillator is defined within the framework of q–deformed quantum mechanics. It is shown that the Rayleigh–Schr?dinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit. Received: 6 August 1998 / Published online: 16 September 1998     

Are deformed modes still Raman active for single-wall carbon nanotubes?

Using group theory calculations combined with the force-constant model and molecular-dynamics simulations, whether the deformed modes are Raman active or not for (10,10) and (10,0) single-wall carbon nanotubes under hydrostatic pressure is discussed. With increasing pressure, the tube symmetry lowers from D_20h to D_2h then to C_2h point group. For D_20h, A_1g is changed to A_g, while E_1g and E_2g are split: E_1g→B_2g+B_3g→2B_g and E_2g→A_g+B_1g→2A_g. On the basis of the correlation between D_20h, D_2h, and C_2h point groups, the deformed modes should be still Raman active. The result can help us clarify the essence of the experimental observations.     

Absolute γ-ray transition probabilities in doubly odd deformed nuclei

A compilation is presented which contains data about the available absolute electromagnetic transition probabilities between two-quasiparticle states in doubly odd deformed nuclei of medium-mass number. Comparisons of dipole transitions between the same Nilsson states in doubly odd and odd-mass nuclei are performed on the basis of Weisskopf and Nilsson hindrance factors. Some level assignments are critically considered. Octupole transitions are also systematized.     

黑克、布劳、及伯曼-温采尔代数的诱导及分导系数和量子经典李代数的耦合与重新耦合系数

本文总结了计算黑克、布劳、及伯曼 温采尔代数在各种工数链下诱导及分导系数的线性方程方法(LEM)。特别强调了关于A,B,C,D型李代数及其量子情形与其中心代数之间的舒尔 魏尔 布劳双关性关系。这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。讨论了从该方法得到B,C,D型李代数不可约表示克罗内克积分解的应用。基于LEM还得到了处理对应于置换群CG系列问题的黑克代数张量积的方法。     

多项式角动量代数的代数表示及实现

本文利用三参数李群求代数表示的方法求出多项式角动量代数的代数表示及其酉表示,找到一个能同时承载李代数及相对应的多项式角动量代数的基底,并在该基底下求出两种代数之间的联系,利用该联系则也可求出多项式角动量代数的代数表示.最后求出多项式角动量代数的单玻色实现及其在有限维多项式函数空间的微分实现.关键词：多项式角动量代数Higgs代数su(2)代数     

Construction of AFLT States for W_NH Symmetry,Analytic Continuation and Integrability on AGT Relation

We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c ∞. We analyze the triangular structure hidden in the AGT relation with WNsymmetry in detail and the triangular structure implies the integrability.