The O(6) description of the nuclear rotation

A recently developed algebraic version of the collective model has shown that a full range of Bohr model calculations can be executed in bases that range continuously from those of a spherical vibrator to a beta-vibrational Wilets-Jean limit. Thus, the establishment of close relationships between the algebraic structure of this model and the IBM is of special importance because one can learn from the complementary perspectives they afford. In this paper, we show by calculations that the familiar rotor-gamma vibrational spectra of the Bohr model can be obtained in the IBM by the addition of a scalar cubic in the quadrupole moment operators, of the type considered recently by Van Isacker, to an O(6) Hamiltonian. Simple fits of the low-lying spectra, electromagnetic transition rates and moments of inertia of the ground and gamma bands of¹⁶²Dy and¹⁶⁸Er are presented.     

Uniform Supersonic Expansion for FTIR Absorption Spectroscopy: The nu(5) Band of (NO)(2) at 26 K

A high-resolution Fourier transform interferometer (Bruker IFS 120 HR) was combined with a uniform supersonic expansion produced by means of axisymmetric Laval nozzles. The geometry profile of the nozzle enabled us to work under precise thermodynamic and kinetic conditions. The effect of the cooling rate of different nozzles on cluster nucleation is illustrated. The experimental sensitivity was tested by recording the nu(5) band of (NO)(2) at 26 K. Copyright 2000 Academic Press.     

Constrained quantum mechanics and a coordinate independent theory of the collective path

The settings for two formulations of quantum mechanics are, respectively, Hilbert spaces and symplectic manifolds. The former leads naturally to matrix mechanics and, for example, the shell model while the latter leads to hamiltonian mechanics, of which the time-dependent Hartree-Fock theory is a standard example. In order to obtain practical approximate theories one needs to restrict the dynamics in both cases to suitable finite-dimensional subspaces. This paper addresses the problem of constructing subspaces of the projective Hilbert space, the fundamental symplectic manifold of quantum mechanics. The collective paths of Villars, Goeke and Reinhard, the valley path and the collective path and submanifold of Rowe and Basserman are examined and phrased in a coordinate independent manner. In this way we expose the dynamical foundations and the essential geometrical structures upon which they are based.     

Comparison of silicon LIII,II electron loss spectra and optical absorption

Threshold structure due to L_III,II excitation in the electron loss spectra of silicon at 100.2 ± 0.3 eV is in good agreement with optical absorption measurements of 100.1 ± 0.1 eV.     

A study of collective paths in the time-dependent hartree-fock approach to large amplitude collective nuclear motion

In a simple two-dimensional landscape model the collective paths of Rowe-Bassermann and Marumori, of Villars, of Goeke-Reinhard, and of Baranger-Veneroni are determined and compared. The uniqueness of the solutions and the practicability of the methods regarding numerical applications are discussed.     

On pionic degrees of freedom in atomic nuclei

The possibility of explicit pionic degrees of freedom in atomic nuclei and their association with pionic reactions involving fragment emission is discussed. Although no present direct evidence for such degrees of freedom is available they could be searched for in doorway states — other than the anticipated N¹ doorway — in the excitation function in the pion-induced partial reaction cross sections. Such a search is underway. A framework is discussed in terms of which such new pion doorways might be described.     

Adiabatic and non-adiabattc cranking models for the solution of the large amplitude time-dependent Hartree-Fock equations and the calculation of nuclear energy surfaces

An analysis is made of the device of forced vibrations to reduce the difficult large amplitude TDHF (time-dependent Hartree-Fock) problem to a simpler static problem. It is shown that cranking is a perfectly valid technique if the cranking field is defined by the criterion that the constrained static wave function be identical at a given instant of time to the freely oscillating TDHF wave function. On the basis of this criterion an exact general expression is derived for the cranking field and adiabatic and non-adiabatic cranking models are proposed as practical means of solving the large amplitude TDHF equations and calculating energy surfaces for fission and heavy ion reactions. The non-adiabatic model, which is favoured, corresponds to cranking the nucleus to move always in the direction of a local decoupled “normal mode” calculated from its unconstrained time-dependent equations of motion. The familiar Belyaev cranking model and the Baranger-Kumar model are discussed in the context of the new formalism.     

Convergence criteria for the Hartree iterative solution of the general self-consistent field equations

The traditional Hartree method of solving the Hartree-Fock equations, by repeated diagonalization and recalculation of the single-particle Hamiltonian, is expressed in terms of repeated unitary transformations and shown to be applicable to the general SCF (self-consistent field) equations. The necessary and sufficient conditions for convergence to a unique local SCF solution are derived and it is shown that only a small class of solutions are obtainable by this method.