The rotating two-center shell model

The rotating two-center shell model with five deformation parameters has been studied. Spectra showing the dependence of the shell structure on nuclear elongation, necking, mass asymmetry, and angular velocity are exhibited and inferences concerning the stability of rotating nuclei and the changes in deformation with spin are drawn. Finally we examine the limits for stability of a composite system in heavy-ion reactions.     

Quantum chaos in the two-center shell model

Within an axially symmetric two-center shell model single-particle levels with Ω=1/2 are analyzed with respect to their level-spacing distributions and avoided level crossings as functions of the shape parameters. Only for shapes sufficiently far from any additional symmetry, ideal Wigner distributions are found as signature for quantum chaos.     

Potential energy surfaces in the two-center shell model

The two-center shell model of two equal overlapping spheroids is combined with Lawrence's liquid-drop shapes. Within this framework, potential energy surfaces for nuclei from different mass regions are calculated. In particular, the transition of the ground state deformation from spherical to deformed is investigated for a sequence of ruthenium isotopes.     

Quadrupole excitations in the two-center shell model (II)

The distribution of the isoscalar, T = 0, and isovector T = 1, strength of quadrupole modes in the deformed nucleus ²⁴Mg is investigated. A finite-range residual interaction is used in the particle-hole basis of a rotating two-center shell-model potential of two ¹²C nuclei. The model calculation describes semi-quantitatively the main features of the available experimental data for the T = 0, E2 excitations and predicts the location and structure of the isovector, T = 1, E2 strength for which no data has been published to date.     

A two-center model of the concerted molecular decomposition of unsaturated compounds

A semiempirical model of the concerted decomposition of unsaturated compounds (olefins, alcohols, acids, and ethers) and aliphatic esters into two molecules is suggested. The model considers the decomposition reaction as a single-step transfer of the hydrogen atom in one reaction center and the dissociation of a C-C or C-O bond in the other accompanied by a shift of π electrons in the cyclic six-membered transition state. Each elementary event in such a concerted reaction is characterized by its own activation energy, E _abs for the transfer of H, E _>d for bond dissociation, and E _π for the shift of π bonds. The E _abs and E _d activation energies were calculated by the method of intersecting parabolas. The spectrum of activation energies (sets of the E _abs, E _d , and E _π values) for each of 45 decomposition reactions was calculated with the use of experimental data. The contribution of enthalpy to the activation energy of each event was estimated.     

The oscillator shell model with the state dependent frequencies

The frequencies of the oscillator potential are suggested to bs dependent on the state quantum numbers. They may play a role of variational parameters. This procedure is applied in the shell model calculation for light nuclei.On leave fromFaculty of Physics, Hanoi University, Vietnam.The author would like to thank Prof. I. Úlehla for his encouraging interest in this work.     

The shell model and collective structures in54,55,56Fe

Extensive shell-model calculations have been performed on^54,55,56Fe. The results obtained in a model space with two and with up to threef _7/2 holes in the,⁵⁶Ni core are compared with experiment. The Surface Delta Interaction (SDI) and the Kuo Brown interaction (KB) have been used to calculate energy levels, spectroscopic factors and electromagnetic properties resulting especially for⁵⁶Fe in a remarkably good agreement with experiment. Admixtures of three-hole components in the wave functions are significant and increase with mass number. Properties of high-spin states withJ≦15 are discussed. Pronounced collective features derived microscopically are expected in⁵⁶Fe. Finally some suggestions for interesting experiments are given.     

The love-hate relationship between the shell model and cluster models

We adopt a personal approach here reviewing several calculations over the years in which we have experienced confrontations between cluster models and the shell model. In previous cluster conferences, we have noted that cluster models go hand in hand with Skyrme-Hartree-Fock calculations in describing states which cannot easily, if at all, be handled by the shell model. These are the highly deformed (many particle-many hole) intruder states, linear chain states, etc. In the present work, we will consider several topics: the quadrupole moment of ⁶Li; the nonexistence of low-lying intruders in ⁸Be; and then jumping to the f _7/2 shell, we discuss the two-faceted nature of the nuclei, which sometimes display shell-model properties and other times cluster properties.     

The thermal expansion of rubidium chloride by the shell model

The equation of state and the thermal expansion of rubidium chloride have been studied by making use of shell model with both the ions polarisable. The lattice constants at different temperatures have been obtained from the isotherms, drawn between the temperature range 0° and 1000°K; and show good agreement with the experimental results.     

Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

Semiclassical quantization of the shell model

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.