Some physical and thermodynamic properties of rocket exhaust clouds measured with infrared scanners

Measurements using infrared scanners were made of the radiation from exhaust clouds from liquid- and solid-propellant rocket boosters. Field measurements from four launches were discussed. These measurements were intended to explore the physical and thermodynamic properties of these exhaust clouds during their formation and subsequent dispersion. Information was obtained concerning the initial cloud's buoyancy, the stabilized cloud's shape and trajectory, the cloud volume as a function of time, and it's initial and stabilized temperatures. Differences in radiation intensities at various wavelengths from ambient and stabilized exhaust clouds were investigated as a method of distinguishing between the two types of clouds. The infrared remote sensing method used can be used at night when visible range cameras are inadequate. Infrared scanning techniques developed in this project can be applied directly to natural clouds, clouds containing certain radionuclides, or clouds of industrial pollution

Nonlinear collective nuclear motion

For each real number $\Lambda$ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to $gl(3,{\bf R})$, only the $\Lambda=0$ vector fields correspond to the usual generators of the general linear group. The $\Lambda < 0$ vector fields integrate to a nonstandard action of the general linear group; the $\Lambda >0$ case integrates to a local Lie semigroup. For each $\Lambda$, a family of surfaces is identified that is invariant with respect to the group or semigroup action. For positive $\Lambda$ the surfaces describe fissioning nuclei with a neck, while negative $\Lambda$ surfaces correspond to exotic bubble nuclei. Collective models for neck and bubble nuclei are given by irreducible unitary representations of a fifteen dimensional semidirect sum spectrum generating algebra $gcm(3)$ spanned by its nonlinear $gl(3,{\bf R})$ subalgebra plus an abelian nonlinear inertia tensor subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request

Partial Dynamical Symmetry in the Symplectic Shell Model

We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding new light on this important interaction. Specifically, in the framework of the symplectic shell model of nuclei, we prove the existence of a family of fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction process for the PDS eigenstates with good symmetry and give analytic expressions for the energies of these states and E2 transition strengths between them. Characteristics of both pure and mixed-symmetry PDS eigenstates are discussed and the resulting spectra and transition strengths are compared to those of real nuclei. The PDS concept is shown to be relevant to the description of prolate, oblate, as well as triaxially deformed nuclei. Similarities and differences between the fermion case and the previously established partial SU(3) symmetry in the Interacting Boson Model are considered.Comment: 9 figure

Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page

An exactly solvable model of a superconducting to rotational phase transition

We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of dynamical symmetries. However, the symmetries are basically incompatible with one another; no simple solution exists in intermediate situations. Exact (numerical) solutions are possible and enable one to study the behavior of competing but incompatible symmetries and the phase transitions that result in a semirealistic situation. The results are remarkably simple and shed light on the nature of phase transitions.Comment: 11 pages including 1 figur

Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations

It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio

Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit

We demonstrate a formally exact quantum-classical correspondence between the stationary coherent states associated with the commensurate anisotropic two-dimensional harmonic oscillator and the classical Lissajous orbits. Our derivation draws upon earlier work of Louck et al [1973 \textit {J. Math. Phys.} \textbf {14} 692] wherein they have provided a non-bijective canonical transformation that maps, within a degenerate eigenspace, the commensurate anisotropic oscillator on to the isotropic oscillator. This mapping leads, in a natural manner, to a Schwinger realization of SU(2) in terms of the canonically transformed creation and annihilation operators. Through the corresponding coherent states built over a degenerate eigenspace, we directly effect the classical limit via the expectation values of the underlying generators. Our work completely accounts for the fact that the SU(2) coherent state in general corresponds to an ensemble of Lissajous orbits.Comment: 11 pages, Latex2e, iopart.cls, replaced with published versio

A mixed-mode shell-model theory for nuclear structure studies

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on $^{24}$Mg. The correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space. The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.Comment: 20 pages, 8 figures, revtex 12p

On the equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

The present paper establishes a link between pairing correlations in rotating nuclei and collective vortical modes in the intrinsic frame. We show that the latter can be embodied by a simple S-type coupling a la Chandrasekhar between rotational and intrinsic vortical collective modes. This results from a comparison between the solutions of microscopic calculations within the HFB and the HF Routhian formalisms. The HF Routhian solutions are constrained to have the same Kelvin circulation expectation value as the HFB ones. It is shown in several mass regions, pairing regimes, and for various spin values that this procedure yields moments of inertia, angular velocities, and current distributions which are very similar within both formalisms. We finally present perspectives for further studies.Comment: 8 pages, 4 figures, submitted to Phys. Rev.

Surface reconstruction induced geometries of Si clusters

We discuss a generalization of the surface reconstruction arguments for the structure of intermediate size Si clusters, which leads to model geometries for the sizes 33, 39 (two isomers), 45 (two isomers), 49 (two isomers), 57 and 61 (two isomers). The common feature in all these models is a structure that closely resembles the most stable reconstruction of Si surfaces, surrounding a core of bulk-like tetrahedrally bonded atoms. We investigate the energetics and the electronic structure of these models through first-principles density functional theory calculations. These models may be useful in understanding experimental results on the reactivity of Si clusters and their shape as inferred from mobility measurements.Comment: 9 figures (available from the author upon request) Submitted to Phys. Rev.