Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalizedpseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to berelevant to polynomial angular momentum algebras.

Systematic Study of Stability of Super Heavy Nuclei

A systematic overview on the characteristics of super heavy nuclei from Z = 101 to Z = 130 based on the data by P. Moller et al. is presented. The nuclei which have the biggest mean binding energy in each of their isotope chain show systematic regular behavior, indicating that the mean binding energy is a good criterion to classify super heavy nuclei by their stabilities. Further investigation on the nuclear data at and after Z=127 has been suggested.

Vector Meson Electro-production in Pomeron Exchange Model

Based on Pomeron exchange model, elastic production of vector meson in electro-proton interaction is investigated with both linear and non-linear Pomeron trajectory. A numerical calculation for J/ψ production is performed. The effect of the energy scale so and photon virtuality Q2 on differential cross section are also predicted. Agood agreement with experimental data is obtained. Our conclusions are that the Pomeron exchange model is a successful description of J/ψ electro-production, the dependence of the differential cross sections on Q2 is negligible, the linear trajectory is a good approximation to non-linearity of the Pomeron trajectory, and the value of the energy scale parameter so is dependent on the momentum transfer, namely its effect is moderate at low momentum transfer but it causes no difference at high momentum transfer | t |≥ 1.25 GeV2.

Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

The explicit expressions for indecomposable representations ofnine square-root Lie algebras of vector type,Rレイ (v,ィ = 0,+-1),are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra,the invariant subspaces and the quotient spaces.From Fock representations corresponding to these indecomposablerepresentations,the inhomogeneous boson realizations of are given.The expectation values of R in the angularmomentum coherent states are calculated as well as the corresponding classical limits.

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of α-decay is extended to the regions around doubly magic spherical nucleus 208pb and around deformed shell closure 270Hs, respectively. The effects of spherical shell closures (N = 126 and Z = 82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical α-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus 208 Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of a-decays from the ground state of a parent nucleus to the ground state (0+) of its deformed daughter nucleus and to the first excited state (2+) are .calculated in the framework of the cluster model. The results indicate that a measurement of c spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus 270 Hs.

Collective excitation of spherical sodium cluster within a semiclassical discription

A microscopic semiclassical Vlasov equation approach is used to investigate thedipole giant resonances of spherical cluster Na14. Tile main strength distributions of collectiveresponse function are located around ZeV region, v.dth a fair agreement with the experimentones. The results are quite independent of the choice of parameters of the mean field.

Study of Survival Probability of Super Heavy Nuclei

The survival probability of super heavy nuclei produced in cold fusion reactions is studied by using the standard Fermi gas level density formula and analyzed with fission and neutron evaporation characteristics predicted in different theoretical models. The level density formula used in this letter suppresses the ratio of neutron emission width to fission width, Гn/Гf. The dependence of Гn/Гf on the saddle point level density parameter and excitation energy is also investigated.

Alpha Decay, Shell Structure, and New Elements

We systematically analyze the experimental data of alpha decay in even-even heavy nuclei far from stability and find that the Geiger-Nuttall law brea^s for an isotopic chain when its neutron number is across a marc number or there is a deformed subshell. This break can be used to identify new magic numbers of superheavy nuclei. It is also discovered that there is a new linear relation between the logarithm of half-life and the reciprocal of the square root of decay energy for N = 126 and N = 152 isotones. It could be a new law of alpha decay for nuclei with magic neutron numbers but the physics behind it is to be explored. The significance of these researches for the search of new elements is discussed.

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.

Structure of Hamiltonian Matrix and the Shape of Eigenfunctions：Nuclear Octupole Deformation Model

The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformationmodel, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates ofa quantum integrable system is studied with the help ofgeneralized Brillouin-Wigner pcrturbation theory. The resultsshow that a significant randomness in this distribution can be observed when its classical counterpart is under the strongchaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects ofthe symmetry have been removed.

Statistical Behaviors of Quantum Spectra in Superheavy Nuclei

From the point of view of the interplay between order and chaos, the most regular single-particle motion of neutrons has been found in the superheavy system with Z ＝ 120 and N ＝ 184 based on the Skyrme-Hartree-Fock model and in the system with Z ＝ 120 and N ＝ 172 based on the relativistic mean-field model. It has been shown that the statistical analysis of spectra can give valuable information about the stability of suprheavy systems. In addition it may yield deep insight into the single-particle motion in the mean field formed by the superheavy system.

Dependence of the dilepton production in QGP on the incident energy of colliding nuclei

Initial values of the quark-gluon plasma system form relativistic nucleusnucleus collisions are discussed under thermodynamic equilibrium.From these initial values,the dependence of the dilepton production on the incident energy of colliding nuclei has been studied based on the relativistic hydrodynamic model,and it is found that with increasing incident energy a characterstic plateau indicating the formatioin of the quark-gluon plasma appears in the total yield.

p—A Drell—Yan Process in the Target Rest Frame

At high energies, Drell-Yan process can be viewed in the target rest frame as bremsstrahlung of massive photons, rather than parton annihilation. In this paper, the ratio of the p-A Drell-Yan cross section per nucleon for an 800 GeV proton beam incident on Fe, W, and Be targets are calculated by means of the color dipole approach in the target rest system. It is shown that our calculations can quite well fit the Fermilab E866 experimental data with considering the nuclear shadowing effect in p-A Drell-Yan process and without the energy loss effect in it.

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy.The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite digerent mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections, induced by the halo nuclei due to the very weak binding and the very extended density distribution.

Intermediate mass dilepton production during the chemical equilibration of quark gluon plasma

The production of dileptons from the chemically equilibrating quark gluon plasma in the intermediate mass region has been studied. Comparing with the calculated results based on the thermodynamic equilibrium system of quark gluon plasma, it has been found that the quark phase of the chemically equilibrating system gives rise to an even larger enhancement of the dileptons production. Therefore, such an enhancement of dilepton production may signal the formation of quark gluon plasma.

The Spatiotemporal Evolution of Wave Packets under Chaotic Condition

Using the minimum uncertainty state of quantum integrable system H0 as initial state,the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechanics. Due to the existence of the avoided energy level crossing in the spectrum there exist nonlinear resonances between somepairs of neighboring components of the wave packet,the deterministic dynamical evolution becomes very complicated and appears to be chaotic.It is proposed to use expectation values for the whole set of basic dynamical variables and the corresponding spreading widths to describe the topological features concisely such that the quantum chaotic motion can be studied in contrast with the quantum regular motion and well characterized with the asymptotic behaviors.It has been demonstrated with numerical results that such a wave packet has indeed quantum behaviors of ergodicity asin corresponding classical case.