单粒子薛定谔液体和形变核的转动惯量

将单粒子薛定谔液体理论应用于轴对称形变核的集体运动.也给出了一个相反的例子,即在各向异性谐振子势中处于稳定形变的任意数目的独立核子.而且,通过填充与主量子数n_x,n_y和n_z的可能值相应的单粒子态来构成s-d壳偶偶核:²⁰Ne,²⁴Mg,²⁸Si,³²S和³⁶Ar的基态,并计算了作为谐振子参数hω_x,hω_y和hω_z的函数的这些核的推转模型、刚体模型和稳态模型转动惯量.这些谐振子参数用与质量数A、中子数N、质子数Z和形变参数β有关的非形变参数hω00来描述.这些核的推转模型转动惯量的理论计算结果与实验数据符合甚好.而且,所考虑的轴对称形变核可能是扁椭球形的,也可能不是扁椭球形的,其中²⁴Mg是惟一高度形变的.²⁰Ne和²⁴Mg这两个核的刚体模型和稳态模型转动惯量也与实验数据符合甚好.     

Deformed Schrödinger symmetry on noncommutative space

We construct the deformed generators of Schrödinger symmetry consistent with noncommutative space. The examples of the free particle and the harmonic oscillator, both of which admit Schrödinger symmetry, are discussed in detail. We construct a generalised Galilean algebra where the second central extension exists in all dimensions. This algebra also follows from the Inonu–Wigner contraction of a generalised Poincaré algebra in noncommuting space.     

Independent particle Schrödinger fluid: Moments of inertia

The philosophy of the single particle Schrödinger fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large-A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment has the rigid value. Counter examples are utilized to reject some conditions, and the conjecture is argued that unconstrained shape equilibrium might be the necessary and sufficient condition. The spheroidal square-well problem is identified as a promising test case.     

锕系变形核转动惯量及奇偶差随角频率变化的微观机制

用处理对力的粒子数守恒方法分析了锕系变形核转动惯量及其奇偶差随角频率ω变化的微观机制.建立在高j闯入轨道上的奇A核转动带,如²³⁵U(ν[743]7/2)带的转动惯量,比相邻偶偶核基态带大得多,而且,随ω变化的规律也呈现明显的奇偶差.这些规律在粒子数守恒计算中得到很好地重现.计算中无自由参数,单极和四极有效对力强度由结合能和带首转动惯量奇偶差实验值确定.     

Deformed oscillators algebra formulation of the nonlinear Schrödinger hierarchy and of its symmetry

We present a self-contained formulation of the Nonlinear Schrödinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl _N) and finite W(gl _pN, N.gl _p) algebras is also illustrated in this framework.     

用BCS理论计算稀土核转动惯量的奇偶差

用BCS理论计算了稀土区偶偶核和奇A核的转动惯量.计算结果表明,尽管转动惯量的计算值系统地小于实验值,但实验上观测到的转动惯量奇偶差的大幅度变化能够用BCS理论定性地描述. 这个结论与人们普遍认为的BCS理论给出的奇A核转动惯量应比相邻的偶偶核基态转动惯量大15%的看法相悖,但却证实了20多年以前Gregory和Volkov等人得出的结论,有助于人们在BCS平均场理论框架下理解正常形变核中出现全同带的现象.     

Fluid dynamical form of the linear and nonlinear Schrödinger equations

The Hamiltonian theory of perfect fluids admits the generalization to cases where the internal energy density depends on the gradient of mass density. Though the fluid dynamical equations are not greatly modified, when they are transformed into wave equations, special cases of the generalized fluid are seen to correspond to familiar Schrödinger equations. The irrotational nonrelativistic case is presented here and some of the advantages of the fluid point of view are mentioned.     

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Moments of Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments of inertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNC calculations show that the large odd-even difference in moments of inertia mainly comes from the interference contributions j(μν) from particles in high j intruder orbitals μ and ν quite near the Fermi surface, which have no counterpart in the BCS formalism. The effective monopole and quadrupole pairing interaction strengths are determined to fit the experimental odd-even differences in binding energies and bandhead moments of inertia. The experimental results for the variation of moments of inertia with rotational frequency ω are reproduced well by the PNC calculation. The nearly identical experimental moments of inertia between ²³⁶U(gsb) and ²³⁸U(gsb) at low frequencies ħω≤0.20 MeV are also reproduced quite well.     

Coulomb Potentials between Spherical and Deformed Nuclei

Coulomb potentials for spherical-deformed reaction as well as the conventional formulas. Our results approaches have quite different behaviours in the partners are calculated in terms of the double folding model show that the Coulomb potentials calculated with different internal region of the potential. Because fusion process is sensitive to the barrier height and the internal part of the potential, the fusion excitation function, especially the fusion barrier distribution, should provide a strict test of the interaction potentials. Therefore, we calculate the fusion excitation function and barrier distribution for the ^16O ＋^154Sm system with different versions of the Coulomb potentials, in comparison with the experimental results. It is found that the fusion excitation function and barrier distribution of ^16O＋^154Sm are obviously different for the different versions of the Coulomb potentials. By means of this comparison, we may conclude that the double folding model with the accurate approximate form can provide rather reasonable Coulomb potentials.     

Electric Quadrupole and Magnetic Dipole Moments of Mirror Nuclei and Self-Conjugate Nuclei

A transformation, which brings about the unification of the nuclear collective and single particle models, yields sumrules for the magnetic dipole moments and for the electric quadrupole moments of mirror nuclei. These sumrules are applied to cases, for which the numerical values of these moments are known.     

超重核的球形和变形壳结构

应用宏观 微观模型系统研究了超重核的形状和结构性质.其中,宏观能是由基于核子密度泛函的连续介质模型计算得到.计算结果很好地再现了超重核的结合能、α衰变能和寿命的实验数据.对单粒子能级的计算和分析表明超重核的壳结构是形变和同位旋相关的.位能曲面的计算结果显示,与其它区域的核相比,超重核的形状不易变化. The structure of superheavy nuclei has been studied by using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a functional of nucleon densities. The deformations and structures of superheavy nuclei were investigated systematically. Calculations reproduce well the available data of experimental α decay energies and half-lifes. The investigation of single-particle levels shows that the shell structure is deformed a...     

Non-linear wave and Schrödinger equations

We investigate stability of periodic and quasiperiodic solutions of linear wave and Schrödinger equations under non-linear perturbations. We show in the case of the wave equations that such solutions are unstable for generic perturbations. For the Schrödinger equations periodic solutions are stable while the quasiperiodic ones are not. We extend these results to periodic solutions of non-linear equations.Partially supported by NSERC under Grant NA7901     

Linear and nonlinear Schrödinger equations

The Schrödinger equation for a point particle in a quartic potential and a nonlinear Schrödinger equation are solved by the decomposition method yielding convergent series for the solutions which converge quite rapidly in physical problems involving bounded inputs and analytic functions. Several examples are given to demonstrate use of the method.     

Calculation of Interaction Potentials between Spherical and Deformed Nuclei

The interaction potential for spherical-deformed reaction partners is calculated. The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system ^32S＋^154Sm are investigated within the double-folding model of the deformed nuclei. The effective nucleon-nucleon interaction is taken to be the M3Y-Reid potential. The density is considered for three terms of the expansion using the truncated multipole expansion method, which is a deformed Fermi shape With quadrupole and hexadecapole for the density distribution of ^154Sm. It is found for the interaction potential that the height and the position of barrier strongly depend on the deformations, the orientation angle of the deformed nucleus, and hence produce great effects on fusion cross section. The integrated fusion cross section is in good agreement with the experimental data.     

Nonlinear Schrödinger equation and superfluid hydrodynamics

We show that it is possible to generalize the Gross-Pitaevskii equation describing superfluidity in order to recover the two-fluid model, in the hydrodynamic limit, when the deviations from the equilibrium state are of long wavelength. When short distances are relevant, it is possible to keep trace of the purely quantum, non-hydrodynamic term of the Gross-Pitaevskii equation, so that the Hills-Roberts model, which describes the healing phenomenon, is finally obtained. Received: 19 August 1997 / Revised: 16 October 1997 / Accepted: 6 November 1997     

Schrödinger and Dirac quantum random walks

Quantum random walks, whose amplitude evolutions are given by generalizations of discrete versions of Schrödinger and Dirac equations, are constructed. The results are given in three dimensions and it is shown that they cannot be reduced to stochastically independent one-dimensional motions. Properties of these quantum random walks are analyzed and expressions for their characteristic functions and free propagators are derived.